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https://vi.stackexchange.com/questions/15370/unmap-all-combinations-starting-with-certain-key
|
# Unmap all combinations starting with certain key
I am experimenting with default key mappings and am considering remapping the g key entirely. But first I would like to turn off all the existing mappings that g has. For now I am using this kind of hack:
" disable all g maps
let g:netrw_nogx = 1 " allows disabling gx
let s:chars1 = map(range(char2nr('a'), char2nr('x')), 'nr2char(v:val)')
let s:chars2 = map(range(char2nr('A'), char2nr('Z')), 'nr2char(v:val)')
let s:chars = s:chars1 + s:chars2
let s:chars = s:chars+['0','1','2','3','4','5','6','7','8','9','+','-','=','_']
let s:chars = s:chars+['~','','!','@','#','\$','%','^','&','*','(',')','/','?']
let s:chars = s:chars+['[',']','{','}','\','\|',':',';','"',"'",'<',">",'.',',']
for char in s:chars
execute 'noremap g' . char . ' <nop>'
endfor
But this is very messy and g<ctrl-_> maps are still left in.
Is there some cleaner way to accomplish this?
• I think there is no better way other than to iterate over all combinations. – Christian Brabandt Feb 27 '18 at 7:55
• Just out of curiosity: why do you need to remap all of these combinations to <nop>? Also, I agree with Christian that is probably the best way to do it. – statox Feb 27 '18 at 12:09
• Agree with @statox why not use unmap? – D. Ben Knoble Feb 27 '18 at 12:25
• @DavidBenKnoble I think what Karolis wants to do is to disable the built-in normal mode commands like gq, gU, etc while unmap would be useful to delete mappings created by the user. What I was wondering is, why does one need to disable all of these built-in commands? – statox Feb 27 '18 at 12:32
• @statox I am just experimenting with making (neo)vim maps more intuitive. For example my current experiment is to only use g prefix for "goto" commands. I.E. gg goes to top G goes to bottom, gf goes to file, gb and gB would traverse buffers, etc. No big reason to disable all g prefix maps, but it would help in a sense that I would be sure pressing g will put me into a goto context and would not do something else by accident. – Karolis Koncevičius Feb 27 '18 at 15:27
### Suppressing the built-in g
Here's a mapping that will suppress all g-prefixed bindings, and only allow custom mappings that begin with g.
function! SuppressG()
let c = nr2char(getchar())
if maparg('g'.c, 'n') != ''
return 'g'.c
else
return '\<Nop>'
endif
endfunction
nnoremap <expr> g SuppressG()
The idea is to make a top-level mapping for g itself that then reads a single character from the keyboard. If a Normal mode mapping to g followed by the input character exists, return that. Otherwise, return <Nop>. It works with chords, too.
The effect is that when you haven't defined any other mappings beginning with g, all of Vim's built-in bindings beginning with g will do nothing. For example, ge, which normally moves backwards to the end of a word, would now be a no-op.
### Creating a custom mapping
If you also defined a custom mapping to ge, then your mapping would take effect. Example:
nnoremap ge G
Now ge moves to the last line of the buffer, but all other g bindings still do nothing.
### Restoring built-ins
You can also restore the g mappings you want to keep. For example:
nnoremap gg gg
This makes gg once again move to the first line of the buffer.
• This works really well for "g" and "z" but for some reason I cannot figure out how to make it work for "ctrl". Maybe you have any tips? – Karolis Koncevičius Aug 12 '18 at 18:53
• Ctrl itself isn't mappable, it's just part of a chord. Vim sees things like Ctrl+x as a single character. – tommcdo Sep 25 '18 at 18:44
• Does it gets called immediately? Not waiting for any longer combination that could surpass it? – eyal karni Oct 23 '19 at 21:21
If your version of vim is recent enough, you could obtain all the mappings starting with g thanks to getcompletion('g', 'mapping').
However, you won't know the mode associated, you'd need to filter the list with mapcheck().
Of course, you won't obtain the default keybindings this way.
• Presumably you'd need to do this in a VimEnter autocommand (to unmap mappings added by plugins)? – Rich Mar 8 '18 at 15:02
A small generalization to tommcdo's excellent suggestion:
function! SuppressAllStartingWith(c1)
let c2 = nr2char(getchar())
if maparg(a:c1.c2, 'n') != ''
return a:c1.c2
else
return '\<Nop>'
endif
endfunction
Then you can use it like so:
nnoremap <expr> q SuppressAllStartingWith('q')
nnoremap <expr> z SuppressAllStartingWith('z')
As for motivation, in command mode I'm always fat-fingering 'z' when I'm heading for 'x', or 'q' when I'm heading for 'a', and I'm tired of that.
• Welcome to Vi and Vim! Does this prevent you from recording macros q{letter} or using the fold and other z commands (zt, etc.)? – D. Ben Knoble Feb 12 at 15:18
• Yes, it does. For certain of my editing jobs, I don't want any accidental keystrokes moving the cursor far away, or changing modes, or turning on anything. I just want local motions and text insert/delete, basically. This gets me partially there. If there's a WYSIWYG mode to vim, or a better way to achieve this, I'd love to hear about it. – Charles Feb 13 at 16:26
• Vim is WYSIWYG if what you get is plain-text, so I don't follow that. But you could look at :help -y`. – D. Ben Knoble Feb 13 at 19:37
• I was using WYSIWG in the sense of what the nano editor gives you, i.e., exactly what -y gives you in vim, thanks for that tip. But what I'd like to achieve in vim is allowing editing commands that operate on the current line, or a few lines around it, and suppressing commands that take me to other parts of the file when I mistype them. So for example I never use z because I have no use for what it does, and when I accidentally hit it, I don't want what it does. – Charles Feb 15 at 15:12
|
2021-04-21 23:46:21
|
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|
https://physics.stackexchange.com/questions/335761/what-conditions-must-eigenvalues-satisfy-for-degenerate-states
|
# What conditions must eigenvalues satisfy for degenerate states?
Due to comments below this answer I note the term "degenerate states" was subjective so firstly I'll give a formal definition:
Degenerate states results when two (or more) different eigenstates to an eigenvalue equation correspond to the same eigenvalue.
I'm tasked with the following question on a problem sheet set by my lecturer:
Do degenerate states always have the same energy?
False (they have the same eigenvalue of any operator, not necessarily energy)
My interpretation of the quotation above is as follows: The eigenvalues of any operator can be the same but the energy can be different. At the moment it is my understanding that Eigenvalues=Energy Eigenvalues=Energies. Is there a distinction between these terms when considering the Hamiltonian? If my interpretation of the answer is wrong could someone please explain what the correct interpretation is? If you are able to do this there is no need to read any more of the content below until you reach the line, where below is my main question.
I do not understand how this answer can be false, so I will use the eigenvalues to the two dimensional Simple Harmonic Oscillator as an example that I believe contradicts the answer statement:
The TISE eigenvalue equation for the SHO is $$\hat Hu(x,y)=\left[-\frac{\hbar^2}{2m}\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)+\frac{m\,{\omega_{x}}^2x^2}{2}+\frac{m\,{\omega_{y}}^2y^2}{2}\right]u(x,y)=E\,u(x,y)\tag{1}$$
Using separation of variables $u(x,y)=X(x)Y(y)$ such that $(1)$ becomes
$$-\frac{\hbar^2}{2m}\left(Y\frac{\partial^2X}{\partial x^2}+X\frac{\partial^2Y}{\partial y^2}\right)+\frac{m\,{\omega_{x}}^2x^2}{2}XY+\frac{m\,{\omega_{y}}^2y^2}{2}XY=EXY$$
and dividing throughout by $XY$ gives
$$\left(-\frac{\hbar^2}{2m}\frac{1}{X}\frac{\partial^2X}{\partial x^2}+\frac{m\,{\omega_{x}}^2x^2}{2}\right)+\left(-\frac{\hbar^2}{2m}\frac{1}{Y}\frac{\partial^2Y}{\partial y^2}+\frac{m\,{\omega_{y}}^2y^2}{2}\right)=E$$
Where $E=E_x+E_y$, I can now write equations involving $x$ and $y$:
$$-\frac{\hbar^2}{2m}\frac{\partial^2X}{\partial x^2}+\frac{m\,{\omega_{x}}^2x^2}{2}X=E_xX\tag{a}$$
$$-\frac{\hbar^2}{2m}\frac{\partial^2Y}{\partial y^2}+\frac{m\,{\omega_{y}}^2y^2}{2}Y=E_yY\tag{b}$$
Since $(\mathrm{a})$ and $(\mathrm{b})$ are one dimensional SHO eigenstate equations in $x$ and $y$ respectively; then we immediately know the eigenvalues:
$$E_x=\left(n_x + \frac12\right)\hbar\,\omega_x\quad\text{&}\quad E_y=\left(n_y + \frac12\right)\hbar\,\omega_y$$
Hence, the total energy $E$ is
$$E=E_x+E_y=\left(n_x + \frac12\right)\hbar\,\omega_x+\left(n_y + \frac12\right)\hbar\,\omega_y\tag{2}$$
So we now need two quantum numbers $n_x$ and $n_y$ to label eigenstates $$u_{{n_{x}}{n_{y}}}\equiv u_{n_{x}}(x)\,u_{n_{y}}(y)\tag{c}$$
Now suppose we are given a Central Potential such that $\omega_{x}=\omega_{y}=\omega_0$
Then $$V(x,y)=\frac{m\,{\omega_{x}}^2x^2}{2}+\frac{m\,{\omega_{y}}^2y^2}{2}=\frac{m\,{\omega_0}^2(x^2+y^2)}{2}=\frac{m\,{\omega_0}^2r^2}{2}=V(r)\tag{3}$$
As a result of $(2)$ and $(3)$ the energies are now given by
$$E=E_x+E_y=(n_x+n_y+1)\hbar\,\omega_0$$
The ground state clearly has $n_x=n_y=0$, for which $E_0=\hbar\,\omega_0$. However, there are now two first excited states, given by $n_x=1,n_y=0$ and $n_x=0,n_y=1$, both of which have $\fbox{$\color{blue}{E_1=2\hbar\,\omega_0}$}$. So from the definiton $(\mathrm{c})$ I have two degenerate states: $u_{10}$ and $u_{01}$ with eigenvalue equations $$\hat H u_{10}=E_1 u_{10}$$ and $$\hat H u_{01}=E_1 u_{01}$$
So I have found a case where same eigenvalues $E_1$ are the same energy.
Is this just a one-off coincidence, or can anyone provide me with an example where the energies are different but the Eigenvalues are the Same?
More importantly suppose we have a free particle with $$E=\frac{{\hbar}^2 k^2}{2m}$$
and a wavefunction $\psi$ satisfying $$\frac{d^2 \psi}{dx^2}+k^2\psi=0\tag{4}$$
$(4)$ has two possible solutions: $$\psi_1(x)=Ae^{ikx}\quad\text{and}\quad\psi_2(x)=Ae^{-ikx}$$
Applying the momentum operator $$\hat p=-i\hbar\frac{d}{dx}$$ to the two wavefunctions that solve $(4)$ gives for $\psi_1(x)$ $$\hat p\psi_1(x)=-i\hbar\frac{d}{dx}\left(Ae^{ikx}\right)=-i\hbar(ik)Ae^{ikx}=(\hbar k)Ae^{ikx}=\color{red}{(\hbar k)}\psi_1(x)$$ Similarly for $\psi_2(x)$ $$\hat p\psi_2(x)=\color{red}{-(\hbar k)}\psi_2(x)$$
So I have two degenerate states: $\psi_1(x)$ and $\psi_2(x)$ that apparently share eigenvalues.
But $$\color{red}{\hbar k} \ne \color{red}{-\hbar k}$$ If the eigenvalues are different how can the states be degenerate?
Or put in another way; since $\psi_1(x)$ and $\psi_2(x)$ no longer have the same eigenvalue this violates the definition of degenerate states in the first quotation at the beginning of this post.
## EDIT:
It was my understanding that the minus sign belongs to the eigenvalue.
Do we simply consider the absolute value of the eigenvalue so that $\color{red}{\hbar k}$ will be the same for $\psi_1(x)$ and $\psi_2(x)$?
• What does the book mean by degenerate states? May 27, 2017 at 16:32
• As @ValterMoretti implies I'd say that it depends on your definition. Usually, you state that some solutions are degenerate if they have the same eigenvalue for the Hamiltonian (i.e. they have the same energy). But it would seem that your lecturer uses degeneracy in a more general context so that degenerate solutions may have the same eigenvalues for whatever operator. Note that this would require the lecturer to state: these solutions are degenerate with respect to operator $\hat{X}$. May 27, 2017 at 17:07
• In your example the modes would be degenerate with respect to $\hat{H}$ but not with respect to $\hat{H_x}$ May 27, 2017 at 17:08
• Actually I cannot understand well the question in any sense. In general one speaks about degenerate levels rather than degenerate states, meaning eigenvalues (energies) of the Hamiltonian operator whose eigenspaces have dimension greater than $1$. May 27, 2017 at 18:29
• So, in general I may agree with your initial answer...however the point is that "degenerate states" is not standard terminology so, without a precise definition, it is not possible to answer. May 27, 2017 at 18:32
Question: do degenerate states always have the same energy?
The answer depends on what one means by degenerate. This word typically means two or more states with the same energy, in which case the answer is trivially yes.
On the other hand, it seems that according to your professor, degenerate means two or more states that share the eigenvalue with respect to some operator. This definition is not particularly useful, because all states are eigenvectors of the identity, with eigenvalue one, which means that all states are degenerate. And even if we restrict ourselves to operators other than the identity, the notion of degenerate is still trivial, because one may consider arbitrary projectors of the form $$P=|\varphi_1\rangle\langle\varphi_1|+|\varphi_2\rangle\langle\varphi_2|$$ which would make $\varphi_1,\varphi_2$ degenerate, for any pair of states $\varphi_1,\varphi_2$. In this sense, this definition of degenerate is vacuous.
Finally, if by degenerate we mean eigenvectors that share the eigenvalue with respect to a particular operator $A$ (fixed, i.e., not arbitrary), then the question becomes more interesting: given a pair of states $a_1,a_2$, such that \begin{aligned} A|a_1\rangle&=a|a_1\rangle\\ A|a_2\rangle&=a|a_2\rangle \end{aligned} then do we necessarily have \begin{aligned} H|a_1\rangle&=E|a_1\rangle\\ H|a_2\rangle&=E|a_2\rangle \end{aligned} for some energy $E$?
The answer is not necessarily, as can be seen by constructing simple counter-examples.
• Hi, thanks for your answer, please see my edited version as there is another question at the bottom of the post that has two eigenvalues that are supposedly equal even though they differ by a minus sign. Any ideas on that one? Regards.
– user138066
May 29, 2017 at 23:05
• @user395550 I'm not sure I understand your edit. You found two states with the same energy but different momentum. What's bugging you about that? May 31, 2017 at 21:48
• What's bugging me is that this violates the defintion of degeneracy (in the quote at the beginning of the post) as the two states $\psi_1(x)$ and $\psi_2(x)$ are not both equal to $\color{red}{\hbar k}$. They no longer share eigenvalues.
– user138066
Jun 3, 2017 at 4:55
• @user395550 please note that "degenerate" does not mean that the eigenvalues are the same for all operators. It just means that they are the same for at least one operator. In this case, the energy eigenvalue is the same, even though the momentum eigenvalue is not. In other words, $E_1=E_2$ and $p_1\neq p_2$. As the energies are the same, the states are degenerate. Jun 3, 2017 at 14:29
• @user395550 because $E=\frac{{\hbar}^2 k^2}{2m}$, as you wrote in the OP. In this case, $k_1=-k_2$, and therefore $k_1^2=k_2^2$ and therefore $E_1=E_2$. Jun 3, 2017 at 18:04
The most common reference to the word 'degenerate' is when we refer to the energy eigenstates. If the eigenvalue of the energy operator is same for more than one state of the system, such states are called degenerate. \begin{aligned} H|a_1\rangle&=E|a_1\rangle\\ H|a_2\rangle&=E|a_2\rangle \end{aligned}
There is also a different definition of degenerate, in a general sense. If two or more eigenstates for some fixed("given") operator say A have the same eigenvalue, then those states are called as degenerate. The interesting observation about eigenstates is that if you have two eigenstates say, \begin{aligned} |a_1\rangle, |a_2\rangle \end{aligned} for some observable A, then any linear combination of them is also an eigenstate and hence, we have a 2 dimensional eigenspace, and we have a degree of freedom in the choice of the two eigenvectors from the eigenspace. Similarly, the more the degeneracy, the higher the dimension of the eigenspace.
Okay, now let's suppose you want to uniquely specify a quantum state. What do you do? This is how we can do it :-
1) You find the eigenvalues corresponding to some observable,(say X) but it turned out to show degenerate values for some of it's eigenstates. Hence, just labeling the states using only X is not enough to distinguish the states uniquely.
2)You find another observable which commutes with X,(say Y) so that it has the same set of eigenvectors as X. The eigenvalues of this operator provided unique values for some of the eigenvectors and hence, a greater number of states can now be uniquely specified but suppose there are still eigenvectors which are degenerate that is have the same eigenvalue for both X and Y. What do we do? We execute step 3.
3)Find another such commuting observable and keep on doing so till every eigenstate can be labeled uniquely. This is why we say that in QM, the state of any system is specified by the Complete set of Commuting Observable's.
The above mentioned thought process was carried out to show the role of degeneracy and what it exactly is, in a general sense. There is much more to degenracy than just this. For example, Symmetry of a system with respect to some observable results in degenrate states of that observable.
As I am a 2nd year undergrad. Hence, some of the things mentioned might be wrong. If anyone wants to correct or add something, feel free to do so. I love critics. They help us be better versions of ourselves!!
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2022-05-17 14:51:22
|
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|
https://byjus.com/question-answer/curved-surface-area-of-a-cone-is-308-cm-2-its-slant-height-is-14/
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Question
# Curved surface area of a cone. is $$308\ cm^{2}$$ its slant height is $$14\ cm$$. Find(i) radius of the base and(ii) total surface area of the cone.
Solution
## Given : Curved surface area of the cone $$= 308 cm^2$$ and Slant height or $$l = 14$$ cm.Curved surface area of the cone $$= πrl$$$$308 = \dfrac{22}{7} \times r\times14$$$$r= \dfrac{(308\times7)}{(22\times14)}$$$$r = 7 cm$$Total surface area of the cone $$= πr(r+l)$$$$= (\dfrac{22}{7}\times7)(7+14)$$$$= 22\times21$$Total surface area of the cone $$= 462 cm^2$$So, the radius of the base of the cone is $$7$$ cm and the total surface area of the cone is $$462 cm^2$$.Mathematics
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2022-01-19 08:21:20
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https://cgns.github.io/cgns-modern.github.io/standard/SIDS/block.html
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# 4. Building Block Structure Definition¶
This section defines and describes low-level structures types that are used in the definition of more complex structures within the hierarchy.
## 4.1. Definition DataClass_t¶
DataClass_t is an enumeration type that identifies the class of a given piece of data.
DataClass_t := Enumeration(
DataClassNull,
DataClassUserDefined,
Dimensional,
NormalizedByDimensional,
NormalizedByUnknownDimensional,
NondimensionalParameter,
DimensionlessConstant ) ;
These classes divide data into different categories depending on dimensional units or normalization associated with the data. Dimensional specifies dimensional data. NormalizedByDimensional specifies nondimensional data that is normalized by dimensional reference quantities. In contrast, NormalizedByUnknownDimensional specifies nondimensional data typically found in completely nondimensional databases, where all field and reference data is nondimensional. NondimensionalParameter specifies nondimensional parameters such as Mach number and lift coefficient. Constants such as $$π$$ are designated by DimensionlessConstant. The distinction between these different classes is further discussed in Data-Array Structure Definition.
## 4.2. Definition Descriptor_t¶
Descriptor_t is a documentation or annotation structure that contains a character string. Characters allowed within the string include newlines, tabs and other special characters; this potentially allows for unlimited documentation inclusion within the database. For example, a single Descriptor_t structure could be used to “swallow” an entire ASCII file. In the hierarchical structures defined in the next sections, each allows for the inclusion of multiple Descriptor_t substructures. Conventions could be made for names of often-used Descriptor_t structure entities, such as ReadMe or YouReallyWantToReadMeFirst.
Descriptor_t :=
{
Data(char, 1, string_length) ; (r)
} ;
where string_length is the length of the character string.
## 4.3. Definition DimensionalUnits_t¶
DimensionalUnits_t describes the system of units used to measure dimensional data. It is composed of a set of enumeration types that define the units for mass, length, time, temperature, angle, electric current, substance amount, and luminous intensity.
MassUnits_t := Enumeration( MassUnitsNull, MassUnitsUserDefined,
Kilogram, Gram, Slug, PoundMass ) ;
LengthUnits_t := Enumeration( LengthUnitsNull, LengthUnitsUserDefined,
Meter, Centimeter, Millimeter, Foot,
Inch ) ;
TimeUnits_t := Enumeration( TimeUnitsNull, TimeUnitsUserDefined,
Second ) ;
TemperatureUnits_t := Enumeration( TemperatureUnitsNull,
TemperatureUnitsUserDefined, Kelvin,
Celsius, Rankine, Fahrenheit ) ;
AngleUnits_t := Enumeration( AngleUnitsNull, AngleUnitsUserDefined,
ElectricCurrentUnits_t := Enumeration( ElectricCurrentUnitsNull,
ElectricCurrentUnitsUserDefined, Ampere,
Abampere, Statampere, Edison, auCurrent ) ;
SubstanceAmountUnits_t := Enumeration( SubstanceAmountUnitsNull,
SubstanceAmountUnitsUserDefined, Mole,
Entities, StandardCubicFoot,
StandardCubicMeter ) ;
LuminousIntensityUnits_t := Enumeration( LuminousIntensityUnitsNull,
LuminousIntensityUnitsUserDefined,
Candela, Candle, Carcel, Hefner, Violle ) ;
DimensionalUnits_t :=
{
MassUnits_t MassUnits ; (r)
LengthUnits_t LengthUnits ; (r)
TimeUnits_t TimeUnits ; (r)
TemperatureUnits_t TemperatureUnits ; (r)
AngleUnits_t AngleUnits ; (r)
{
ElectricCurrentUnits_t ElectricCurrentUnits ; (r)
SubstanceAmountUnits_t SubstanceAmountUnits ; (r)
LuminousIntensityUnits_t LuminousIntensityUnits ; (r)
}
} ;
The International System (SI) uses the following units.
Physical Quantity
Unit
Mass
Kilogram
Length
Meter
Time
Second
Temperature
Kelvin
Angle
Electric Current
Ampere
Substance Amount
Mole
Luminous Intensity
Candela
For an entity of type DimensionalUnits_t, if all the elements of that entity have the value Null (i.e., MassUnits = MassUnitsNull, etc.), this is equivalent to stating that the data described by the entity is nondimensionsal.
## 4.4. Definition DimensionalExponents_t¶
DimensionalExponents_t describes the dimensionality of data by defining the exponents associated with each of the fundamental units.
DimensionalExponents_t :=
{
real MassExponent ; (r)
real LengthExponent ; (r)
real TimeExponent ; (r)
real TemperatureExponent ; (r)
real AngleExponent ; (r)
{
real ElectricCurrentExponent ; (r)
real SubstanceAmountExponent ; (r)
real LuminousIntensityExponent ; (r)
}
} ;
For example, an instance of DimensionalExponents_t that describes velocity is,
DimensionalExponents_t =
{{
MassExponent = 0 ;
LengthExponent = +1 ;
TimeExponent = -1 ;
TemperatureExponent = 0 ;
AngleExponent = 0 ;
}} ;
## 4.5. Definition GridLocation_t¶
GridLocation_t identifies locations with respect to the grid; it is an enumeration type.
GridLocation_t := Enumeration(
GridLocationNull,
GridLocationUserDefined,
Vertex,
CellCenter,
FaceCenter,
IFaceCenter,
JFaceCenter,
KFaceCenter,
EdgeCenter ) ;
Vertex is coincident with the grid vertices. CellCenter is the center of a cell; this is also appropriate for entities associated with cells but not necessarily with a given location in a cell. For structured zones, IFaceCenter is the center of a face in 3-D whose computational normal points in the i direction. JFaceCenter and KFaceCenter are similarly defined, again only for structured zones. FaceCenter is the center of a generic face that can point in any coordinate direction. These are also appropriate for entities associated with a face, but not located at a specific place on the face. EdgeCenter is the center of an edge. See Structured Grid Notation and Indexing Conventions for descriptions of cells, faces and edges.
All of the entities of type GridLocation_t defined in this document use a default value of Vertex.
## 4.6. Definition IndexArray_t¶
IndexArray_t specifies an array of indices. An argument is included that allows for specifying the data type of each index; typically the data type will be integer (int). IndexArray_t defines an array of indices of size ArraySize, where the dimension of each index is IndexDimension.
IndexArray_t< int IndexDimension, int ArraySize, DataType > :=
{
Data( DataType, 2, [IndexDimension,ArraySize] ) ; (r)
} ;
## 4.7. Definition IndexRange_t¶
IndexRange_t specifies the beginning and ending indices of a subrange. The subrange may describe a portion of a grid line, grid plane, or grid volume.
IndexRange_t< int IndexDimension > :=
{
int[IndexDimension] Begin ; (r)
int[IndexDimension] End ; (r)
} ;
where Begin and End are the indices of the opposing corners of the subrange.
## 4.8. Definition Rind_t¶
Rind_t describes the number of rind planes (for structured grids) or rind points and elements (for unstructured grids) associated with a data array containing grid coordinates, flow-solution data or any other grid-related discrete data.
Rind_t< int IndexDimension > :=
{
int[2*IndexDimension] RindPlanes ; (r)
} ;
For structured grids, RindPlanes contains the number of rind planes attached to the minimum and maximum faces of a zone. The face corresponding to each index n of RindPlanes in 3-D is:
n = 1 –> i-min n = 2 –> i-max n = 3 –> j-min n = 4 –> j-max n = 5 –> k-min n = 6 –> k-max
For a 3-D grid whose “core” size is II×JJ×KK, a value of RindPlanes = [a,b,c,d,e,f] indicates that the range of indices for the grid with rind is:
i: (1 - a, II + b) j: (1 - c, JJ + d) k: (1 - e, KK + f)
For unstructured grids, RindPlanes does not actually contain planes, but rather contains the number of rind points or elements. The points are defined by the grid coordinates rind node, and the elements by the element set rind node. Note that to maintain consistency with the structured usage of Rind_t, RindPlanes is still dimensioned 2*IndexDimension for unstructured grids (and, for unstructured grids, IndexDimension = 1). The first RindPlanes value is the number of rind nodes/elements stored before the core data, and the second is the number stored after. Thus RindPlanes[2] = {1 2} would mean there is one rind value before the core data, and two after the core data. However, it is preferable to write all the rind points or elements at the end of the array; in other words, for unstructured grids RindPlanes[2] should be set to {0 nrind}, where nrind is the number of rind points or elements.
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2022-05-19 16:18:05
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https://physics.stackexchange.com/questions/444062/what-kind-of-ideal-gas-process-a-positively-sloped-line-in-a-pv-diagram-repres
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# What kind of ideal gas process a positively sloped line in a $pV$-diagram represents?
I've come across an ideal gas process which can be represented by a positively sloped line in the $$pV$$ diagram. I found something about this on KhanAcademy, but it's simply a worked example on how to compute the work done by such a process. My question is what kind of a physical process does this represent? It's clearly not isochoric, isobaric, isothermal or adiabatic and it doesn't seem to appear in any basic heat engines.
Here's an image of the process (from KhanAcademy):
• This probably isn't very common, but you could get this behavior if you heated the gas while the piston was pushed down by a spring. As the volume goes up, so does the spring force and hence the pressure. – knzhou Nov 29 '18 at 16:08
It does not have a name, and I am not sure how practical is to do it, it is just an expansion in which the pressure increases linearly with the volume. In order to do that you need to put the gas in contact with a variable thermal source whose temperature will augment quadratically with the volume: $$T=(a+bV)V/nR$$
• "In order to do that you need to put the gas in contact with a variable thermal source whose temperature will augment quadratically with the volume: $T=(a+bV)V/nR$" Why? This is not obvious to me. – Drew Nov 29 '18 at 15:55
• @Drew All he is saying is that the temperature is rising in a specific way along the process path. From the ideal gas law, T=PV/nR, so for any combination of P and V along the process path, you can calculate a corresponding temperature. – Chet Miller Nov 29 '18 at 16:11
• @Drew yes, just as Chester Miller said – Wolphram jonny Nov 29 '18 at 16:13
• @Drew The equation of the straight line in this case is $P = bV + a$, compare with the general equation of a straight line $y=mx+c$, and the equation of state is $PV=nRT$ – Farcher Nov 29 '18 at 17:38
Any path on the $$PV$$ graph (or on any other thermodynamic plane) represents a quasistatic process that can, in principle, be conducted experimentally. How easily, that's another question. Some paths represent simple processes, for example isothermal, isobaric, isentropic etc. Others require elaborate setups.
For the linear path on the $$PV$$ plane we might construct a temperature controller that adjusts the temperature to make the path a straight line. For an ideal gas, the controller would set the temperature according to the current volume as follows:
$$T = \frac{V \left(P_0 V-P_0 V_1-P_1 V+P_1 V_0\right)}{n R \left(V_0-V_1\right)}$$
If you plug this temperature in the ideal gas law it will produce a linear path between $$(P_0,V_0)$$ and $$(P_1,V_1)$$. That's the same quadratic formula of @Wolphram jonny, evaluated for the specific end points of the path.
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2019-08-19 03:55:45
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https://training.galaxyproject.org/topics/metagenomics/tutorials/metatranscriptomics/tutorial.html?utm_source=schedule&utm_medium=click&utm_campaign=smorgasbord2
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Metatranscriptomics analysis using microbiome RNA-seq data
Overview
Questions:
• How to analyze metatranscriptomics data?
• What information can be extracted of metatranscriptomics data?
• How to assign taxa and function to the identified sequences?
Objectives:
• Choose the best approach to analyze metatranscriptomics data
• Understand the functional microbiome characterization using metatranscriptomic results
• Understand where metatranscriptomics fits in ‘multi-omic’ analysis of microbiomes
• Visualise a community structure
Requirements:
Time estimation: 5 hours
Level: Introductory Introductory
Supporting Materials:
Last modification: May 20, 2021
Overview
In this tutorial we will perform a metatranscriptomics analysis based on the ASAIM workflow (Batut et al. 2018), using data from Kunath et al. 2018.
comment Note: Two versions of this tutorial
Because this tutorial consists of many steps, we have made two versions of it, one long and one short.
This is the extended version. We will run every tool manually and discuss the results in detail. If you would like to run through the tutorial a bit quicker and use workflows to run groups of analysis steps (e.g. data cleaning) at once, please see the shorter version of this tutorial
You can also switch between the long and short version at the start of any section.
Introduction
Microbiomes play a critical role in host health, disease, and the environment. The study of microbiota and microbial communities has been facilitated by the evolution of technologies, specifically the sequencing techniques. We can now study the microbiome dynamics by investigating the DNA content (metagenomics), RNA expression (metatranscriptomics), protein expression (metaproteomics) or small molecules (metabolomics):
New generations of sequencing platforms coupled to numerous bioinformatic tools have led to a spectacular technological progress in metagenomics and metatranscriptomics to investigate complex microorganism communities. These techniques are giving insight into taxonomic profiles and genomic components of microbial communities. Metagenomics is packed with information about the present taxonomies in a microbiome, but do not tell much about important functions. That is where metatranscriptomics and metaproteomics play a big part.
In this tutorial, we will focus on metatranscriptomics.
Metatranscriptomics analysis enables understanding of how the microbiome responds to the environment by studying the functional analysis of genes expressed by the microbiome. It can also estimate the taxonomic composition of the microbial population. It provides scientists with the confirmation of predicted open‐reading frames (ORFs) and potential identification of novel sites of transcription and/or translation from microbial genomes. Metatranscriptomics can enable more complete generation of protein sequences databases for metaproteomics.
To illustrate how to analyze metatranscriptomics data, we will use data from time-series analysis of a microbial community inside a bioreactor (Kunath et al. 2018). They generated metatranscriptomics data for 3 replicates over 7 time points. Before amplification the amount of rRNA was reduced by rRNA depletion. The sequencing libray was prepared with the TruSeq stranded RNA sample preparation, which included the production of a cDNA library.
In this tutorial, we focus on biological replicate A of the 1st time point. In a follow-up tutorial we will illustrate how to compare the results over the different time points and replicates. The input files used here are trimmed version of the original file for the purpose of saving time and resources.
To analyze the data, we will follow the ASaiM workflow and explain it step by step. ASaiM (Batut et al. 2018) is an open-source Galaxy-based workflow that enables microbiome analyses. Its workflow offers a streamlined Galaxy workflow for users to explore metagenomic/metatranscriptomic data in a reproducible and transparent environment. The ASaiM workflow has been updated by the GalaxyP team (University of Minnesota) to perform metatranscriptomics analysis of large microbial datasets.
The workflow described in this tutorial takes in paired-end datasets of raw shotgun sequences (in FastQ format) as an input and proceeds to:
1. Preprocess
2. Extract and analyze the community structure (taxonomic information)
3. Extract and analyze the community functions (functional information)
4. Combine taxonomic and functional information to offer insights into the taxonomic contribution to a function or functions expressed by a particular taxonomy.
A graphical representation of the ASaiM workflow which we will be using today is given below:
commentWorkflow also applicable to metagenomics data
The approach with the tools described here can also apply to metagenomics data. What will change are the quality control profiles and proportion of rRNA sequences.
Agenda
In this tutorial, we will cover:
1. Create a new history for this tutorial and give it a proper name
Tip: Creating a new history
Click the new-history icon at the top of the history panel.
If the new-history is missing:
1. Click on the galaxy-gear icon (History options) on the top of the history panel
2. Select the option Create New from the menu
Tip: Renaming a history
1. Click on Unnamed history (or the current name of the history) (Click to rename history) at the top of your history panel
2. Type the new name
3. Press Enter
2. Import Tool: upload1 T1A_forward and T1A_reverse from Zenodo or from the data library (ask your instructor)
https://zenodo.org/record/4776250/files/T1A_forward.fastqsanger
https://zenodo.org/record/4776250/files/T1A_reverse.fastqsanger
• Open the Galaxy Upload Manager (galaxy-upload on the top-right of the tool panel)
• Select Paste/Fetch Data
• Paste the link into the text field
• Press Start
• Close the window
Tip: Importing data from a data library
As an alternative to uploading the data from a URL or your computer, the files may also have been made available from a shared data library:
• Go into Shared data (top panel) then Data libraries
• Navigate to the correct folder as indicated by your instructor
• Select the desired files
• Click on the To History button near the top and select as Datasets from the dropdown menu
• In the pop-up window, select the history you want to import the files to (or create a new one)
• Click on Import
As default, Galaxy takes the link as name, so rename them.
3. Rename galaxy-pencil the files to T1A_forward and T1A_reverse
Tip: Renaming a dataset
• Click on the galaxy-pencil pencil icon for the dataset to edit its attributes
• In the central panel, change the Name field
• Click the Save button
4. Check that the datatype is fastqsanger (e.g. not fastq). If it is not, please change the datatype to fastqsanger.
Tip: Changing the datatype
• Click on the galaxy-pencil pencil icon for the dataset to edit its attributes
• In the central panel, click on the galaxy-chart-select-data Datatypes tab on the top
• Select fastqsanger
• tip: you can start typing the datatype into the field to filter the dropdown menu
• Click the Save button
Preprocessing
exchange Switch to short tutorial
Quality control
During sequencing, errors are introduced, such as incorrect nucleotides being called. These are due to the technical limitations of each sequencing platform. Sequencing errors might bias the analysis and can lead to a misinterpretation of the data.
Sequence quality control is therefore an essential first step in your analysis. In this tutorial we use similar tools as described in the tutorial “Quality control”:
• FastQC generates a web report that will aid you in assessing the quality of your data
• MultiQC combines multiple FastQC reports into a single overview report
• Cutadapt for trimming and filtering
hands_on Hands-on: Quality control
1. FastQC Tool: toolshed.g2.bx.psu.edu/repos/devteam/fastqc/fastqc/0.72+galaxy1 with the following parameters:
• param-files “Short read data from your current history”: both T1A_forward and T1A_reverse datasets selected with Multiple datasets
Tip: Select multiple datasets
1. Click on param-files Multiple datasets
2. Select several files by keeping the Ctrl (orCOMMAND) key pressed and clicking on the files of interest
2. Inspect the webpage output of FastQC tool for the T1A_forward dataset
solution Solution
The read length is 151 bp.
3. MultiQC Tool: toolshed.g2.bx.psu.edu/repos/iuc/multiqc/multiqc/1.7 with the following parameters to aggregate the FastQC reports:
• In “Results”
• “Which tool was used generate logs?”: FastQC
• In “FastQC output”
• “Type of FastQC output?”: Raw data
• param-files “FastQC output”: both Raw data files (outputs of FastQC tool)
4. Inspect the webpage output from MultiQC for each FASTQ
For more information about how to interpret the plots generated by FastQC and MultiQC, please see this section in our dedicated Quality Control Tutorial.
question Questions
Inspect the webpage output from MultiQC
1. How many sequences does each file has?
2. How is the quality score over the reads? And the mean score?
3. Is there any bias in base content?
4. How is the GC content?
5. Are there any unindentified bases?
6. Are there duplicated sequences?
7. Are there over-represented sequences?
8. Are there still some adapters left?
9. What should we do next?
solution Solution
1. Both files have 260,554 sequences
2. The “Per base sequence quality” is globally good: the quality stays around 40 over the reads, with just a slight decrease at the end (but still higher than 35)
The reverse reads have a slight worst quality than the forward, a usual case in Illumina sequencing.
The distribution of the mean quality score is almost at the maximum for the forward and reverse reads:
3. For both forward and reverse reads, the percentage of A, T, C, G over sequence length is biased. As for any RNA-seq data or more generally libraries produced by priming using random hexamers, the first 10-12 bases have an intrinsic bias.
We could also see that after these first bases the distinction between C-G and A-T groups is not clear as expected. It explains the error raised by FastQC.
4. With sequences from random position of a genome, we expect a normal distribution of the %GC of reads around the mean %GC of the genome. Here, we have RNA reads from various genomes. We do not expect a normal distribution of the %GC. Indeed, for the forward reads, the distribution shows with several peaks: maybe corresponding to mean %GC of different organisms.
5. Almost no N were found in the reads: so almost no unindentified bases
6. The forward reads seem to have more duplicated reads than the reverse reads with a rate of duplication up to 60% and some reads identified over 10 times.
In data from RNA (metatranscriptomics data), duplicated reads are expected. The low rate of duplication in reverse reads could be due to bad quality: some nucleotides may have been wrongly identified, altering the reads and reducing the duplication.
7. The high rate of overrepresented sequences in the forward reads is linked to the high rate of duplication.
8. Illumina universal adapters are still present in the reads, especially at the 3’ end.
9. After checking what is wrong, we should think about the errors reported by FastQC: they may come from the type of sequencing or what we sequenced (check the “Quality control” training: FastQC for more details): some like the duplication rate or the base content biases are due to the RNA sequencing. However, despite these challenges, we can still get slightly better sequences for the downstream analyses.
Even though our data is already of pretty high quality, we can improve it even more by:
1. Trimming reads to remove bases that were sequenced with low certainty (= low-quality bases) at the ends of the reads
3. Removing reads that are too short to be informative in downstream analysis
question Questions
What are the possible tools to perform such functions?
solution Solution
There are many tools such as Cutadapt, Trimmomatic, Trim Galore, Clip, trim putative adapter sequences. etc. We choose here Cutadapt because it is error tolerant, it is fast and the version is pretty stable.
There are several tools out there that can perform these steps, but in this analysis we use Cutadapt (Martin 2011).
Cutadapt also helps find and remove adapter sequences, primers, poly-A tails and/or other unwanted sequences from the input FASTQ files. It trims the input reads by finding the adapter or primer sequences in an error-tolerant way. Additional features include modifying and filtering reads.
hands_on Hands-on: Read trimming and filtering
• “Single-end or Paired-end reads?”: Paired-end
• param-files “FASTQ/A file #1”: T1A_forward
• param-files “FASTQ/A file #2”: T1A_reverse
The order is important here!
• In “Filter Options”
• “Minimum length”: 150
• “Quality cutoff”: 20
• In “Output Options”
• “Report”: Yes
question Questions
Why do we run the trimming tool only once on a paired-end dataset and not twice, once for each dataset?
solution Solution
The tool can remove sequences if they become too short during the trimming process. For paired-end files it removes entire sequence pairs if one (or both) of the two reads became shorter than the set length cutoff. Reads of a read-pair that are longer than a given threshold but for which the partner read has become too short can optionally be written out to single-end files. This ensures that the information of a read pair is not lost entirely if only one read is of good quality.
2. Rename galaxy-pencil
• Read 1 output to QC controlled forward reads
• Read 2 output to QC controlled reverse reads
Cutadapt tool outputs a report file containing some information about the trimming and filtering it performed.
question Questions
Inspect the output report from Cutadapt tool.
1. How many basepairs have been removed from the forwards reads because of bad quality? And from the reverse reads?
2. How many sequence pairs have been removed because at least one read was shorter than the length cutoff?
solution Solution
1. 203,654 bp has been trimmed for the forward read (read 1) and 569,653 bp bp on the reverse (read 2). It is not a surprise: we saw that at the end of the sequences the quality was dropping more for the reverse reads than for the forward reads.
2. 27,677 (10.6%) reads were too short after trimming and then filtered.
Ribosomal RNA fragments filtering
Metatranscriptomics sequencing targets any RNA in a pool of micro-organisms. The highest proportion of the RNA sequences in any organism will be ribosomal RNAs.
These rRNAs are useful for the taxonomic assignment (i.e. which organisms are found) but they do not provide any functional information, (i.e. which genes are expressed). To make the downstream functional annotation faster, we will sort the rRNA sequences using SortMeRNA (Kopylova et al. 2012). It can handle large RNA databases and sort out all fragments matching to the database with high accuracy and specificity:
hands_on Hands-on: Ribosomal RNA fragments filtering
1. Filter with SortMeRNA Tool: toolshed.g2.bx.psu.edu/repos/rnateam/sortmerna/bg_sortmerna/2.1b.6 with the following parameters:
• “Sequencing type”: Reads are paired
• param-file “Forward reads: QC controlled forward reads (output of Cutadapt tool)
• param-file “Reverse reads: QC controlled reverse reads (output of Cutadapt tool)
• “If one of the paired-end reads aligns and the other one does not”: Output both reads to rejected file (--paired_out)
• “Databases to query”: Public pre-indexed ribosomal databases
• “rRNA databases”: param-check Select all
• param-check rfam-5s-database-id98
• param-check silva-arc-23s-id98
• param-check silva-euk-28s-id98
• param-check silva-bac-23s-id98
• param-check silva-euk-18s-id95
• param-check silva-bac-16s-id90
• param-check rfam-5.8s-database-id98
• param-check silva-arc-16s-id95
• “Include aligned reads in FASTA/FASTQ format?”: Yes (--fastx)
• “Include rejected reads file?”: Yes
• “Generate statistics file”: Yes
2. Expand the aligned and unaligned forward reads datasets in the history
question Questions
How many sequences have been identified as rRNA and non rRNA?
solution Solution
Aligned forward read file has 1,947 sequences and the unaligned 2,858 sequences. Then 1,947 reads have been identified as rRNA and 2,858 as non rRNA. The numbers are the same for the reverse reads.
question Questions
Inspect the log output from SortMeRNA tool, and scroll down to the Results section.
1. How many reads have been processed?
2. How many reads have been identified as rRNA given the log file?
3. Which type of rRNA are identified? Which organisms are we then expected to identify?
solution Solution
1. 465,754 reads are processed: 232,877 for forward and 232,877 for reverse (given the Cutadapt report)
2. Out of the 465,754 reads, 119,646 (26%) have passed the e-value threshold and are identified as rRNA.
The proportion of rRNA sequences is then quite high (around 40%), compared to metagenomics data where usually they represent < 1% of the sequences. Indeed there are only few copies of rRNA genes in genomes, but they are expressed a lot for the cells.
Some of the aligned reads are forward (resp. reverse) reads but the corresponding reverse (resp. forward) reads are not aligned. As we choose “If one of the paired-end reads aligns and the other one does not”: Output both reads to rejected file (--paired_out), if one read in a pair does not align, both go to unaligned.
3. The 20.56% rRNA reads are 23S bacterial rRNA, 2.34% 16S bacterial rRNA and 1.74% 18S eukaryotic rRNA. We then expect to identify mostly bacteria but also probably some archae (18S eukaryotic rRNA).
The tool for functional annotations needs a single file as input, even with paired-end data.
We need to join the two separate files (forward and reverse) to create a single interleaced file, using FASTQ interlacer, in which the forward reads have /1 in their id and reverse reads /2. The join is performed using sequence identifiers (headers), allowing the two files to contain differing ordering. If a sequence identifier does not appear in both files, it is output in a separate file named singles.
We use FASTQ interlacer on the unaligned (non-rRNA) reads from SortMeRNA to prepare for the functional analysis.
hands_on Hands-on: Interlace FastQ files
1. FASTQ interlacer Tool: toolshed.g2.bx.psu.edu/repos/devteam/fastq_paired_end_interlacer/fastq_paired_end_interlacer/1.2.0.1+galaxy0 with the following parameters:
• “Type of paired-end datasets”: 2 separate datasets
• param-file “Left-hand mates”: Unaligned forward reads (output of SortMeRNA tool)
• param-file “Right-hand mates”: Unaligned reverse reads (output of SortMeRNA tool)
2. Rename galaxy-pencil the pair output to Interlaced non rRNA reads
Extraction of the community profile
exchange Switch to short tutorial
The first important information to get from microbiome data is the community structure: which organisms are present and in which abundance. This is called taxonomic profiling.
Different approaches can be used:
• Identification and classification of Operational Taxonomic Units OTUs, as used in amplicon data
Such an approach first requires sequence sorting to extract only the 16S and 18S sequences (e.g. using the aligned reads from SortMeRNA), then again using the same tools as for amplicon data (as explained in tutorials like 16S Microbial Analysis with mothur or 16S Microbial analysis with Nanopore data).
However, because rRNA sequences represent less than 50% of the raw sequences, this approach is not the most statistically supported.
• Assignment of taxonomy on the whole sequences using databases with marker genes
In this tutorial, we follow second approach using MetaPhlAn (Truong et al. 2015). This tool uses a database of ~1M unique clade-specific marker genes (not only the rRNA genes) identified from ~17,000 reference (bacterial, archeal, viral and eukaryotic) genomes.
As rRNAs reads are good marker genes, we will use directly the quality controlled files (output of Cutadapt) with all reads (not only the non rRNAs).
hands_on Hands-on: Extract the community structure
1. MetaPhlAn Tool: toolshed.g2.bx.psu.edu/repos/iuc/metaphlan/metaphlan/3.0.8+galaxy0 with the following parameters:
• In “Input(s)”
• “Input(s)”: Fasta/FastQ file(s) with metagenomic reads
• “Fasta/FastQ file(s) with metagenomic reads: Paired-end files
• param-file “Forward paired-end Fasta/FastQ file with metagenomic reads: QC controlled forward reads (output of Cutadapt tool)
• param-file “Reverse paired-end Fasta/FastQ file with metagenomic reads: QC controlled reverse reads (outputs of Cutadapt tool)
• “Database with clade-specific marker genes”: Locally cached
• “Cached database with clade-specific marker genes”: MetaPhlAn clade-specific marker genes (mpa_v30_CHOCOPhlAn_201901)
• In “Analysis”
• “Type of analysis to perform”: rel_ab: Profiling a metagenomes in terms of relative abundances
• “Taxonomic level for the relative abundance output”: All taxonomic levels
• *“Generate a report for each taxonomic level?”: Yes
• “Quantile value for the robust average”: 0.1
• “Organisms to profile”:
• param-check Profile viral organisms (add_viruses)
• In “Output”
• “Output for Krona”: Yes
This step may take a couple of minutes as each sequence is compare to the full database with ~1 million reference sequences.
5 files and a collection are generated by MetaPhlAn tool:
• The main output: A tabular file called Predicted taxon relative abundances with the *community profile
#mpa_v30_CHOCOPhlAn_201901
# ....
#SampleID Metaphlan_Analysis
k__Bacteria 2 99.40284
k__Archaea 2157 0.59716
k__Bacteria|p__Firmicutes 2|1239 94.67418
k__Bacteria|p__Coprothermobacterota 2|2138240 4.72866
k__Archaea|p__Euryarchaeota 2157|28890 0.59716
k__Bacteria|p__Firmicutes|c__Clostridia 2|1239|186801 94.67418
k__Bacteria|p__Coprothermobacterota|c__Coprothermobacteria 2|2138240|2138243 4.72866
k__Archaea|p__Euryarchaeota|c__Methanobacteria
Each line contains 4 columns:
1. the lineage with different taxonomic levels
2. the previous lineage with NCBI taxon id
3. the relative abundance found for our sample for the lineage
The file starts with high level taxa (kingdom: k__) and go to more precise taxa.
question Questions
Inspect the Predicted taxon relative abundances file output by MetaPhlAn tool
1. How many taxons have been identified?
2. What are the different taxonomic levels we have access to with MetaPhlAn?
3. What genus and species are found in our sample?
4. Has only bacteria been identified in our sample?
solution Solution
1. The file has 20 lines, including an header. Therefore, 17 taxons of different levels have been identified
2. We have access: kingdom (k__), phylum (p__), class (c__), order (o__), family (f__), genus (g__), species (s__), strain (t__)
3. In our sample, we identified:
• 3 genera: Coprothermobacter, Methanothermobacter, Hungateiclostridium
• 3 species: Coprothermobacter proteolyticus, Methanothermobacter thermautotrophicus, Hungateiclostridium thermocellum
4. As expected from the rRNA sorting, we have some archaea, Methanobacteria, in our sample.
• A collection with the same information as in the tabular file but splitted into different files, one per taxonomic level
• A tabular file called Predicted taxon relative abundances for Krona with the same information as the previous file but formatted for visualization using Krona. We will use this file later
• A BIOM file with the same information as the previous file but in BIOM format
BIOM format is quite common in microbiomics. This is standard, for example, as the input for tools like mothur or QIIME.
• A SAM file with the results of the sequence mapping on the reference database.
• A tabular file called Bowtie2 output with similar information as the one in the SAM file
comment Note: Analyzing an isolated metatranscriptome
We are analyzing our RNA reads as we would do for DNA reads. This approach has one main caveat. In MetaPhlAn, the species are quantified based on the recruitment of reads to species-specific marker genes. In metagenomic data, each genome copy is assumed to donate ~1 copy of each marker. But the same assumption cannot be made for RNA data: markers may be transcribed more or less within a given species in this sample compared to the average transcription rate. A species will still be detected in the metatranscriptomic data as long as a non-trivial fraction of the species’ markers is expressed.
We should then carefully interpret the species relative abundance. These values reflect species’ relative contributions to the pool of species-specific transcripts and not the overall transcript pool.
Some downstream tools need the MetaPhlAn table with predicted taxon abundance with only 2 columns: the lineage and the abundance.
hands_on Hands-on: Format taxon relative abundances table
1. Cut Tool: Cut1 with the following parameters:
• “Cut columns”: c1,c3
• param-file “From”: Predicted taxon relative abundances (output of MetaPhlAn)
2. Rename Cut predicted taxon relative abundances table
Community structure visualization
Even if the output of MetaPhlAn can be easy to parse, we want to visualize and explore the community structure. 2 tools can be used there:
• Krona for an interactive HTML output
• Graphlan for a publication ready visualization
hands_on Hands-on: Interactive community structure visualization with KRONA
1. Krona pie chart Tool: toolshed.g2.bx.psu.edu/repos/crs4/taxonomy_krona_chart/taxonomy_krona_chart/2.7.1+galaxy0 with
• “What is the type of your input data”: Tabular
• param-file “Input file”: Predicted taxon relative abundances for Krona (output of MetaPhlAn)
Krona Ondov et al. 2011 renders results of a metagenomic profiling as a zoomable pie chart. It allows hierarchical data, here taxonomic levels, to be explored with zooming, multi-layered pie charts
question Questions
Inspect the output from Krona tool. (The interactive plot is also shown below)
1. What are the abundances of 2 kingdoms identified here?
2. When zooming on Bacteria, what are the 2 subclasses identified?
solution Solution
1. Archaea represents 0.6% so bacteria are 99.4% of the organisms identified in our sample
2. 5% of bacteria are Coprothermobacter proteolyticus and the rest Hungateiclostridium thermocellum .
GraPhlAn is another software tool for producing high-quality circular representations of taxonomic and phylogenetic trees.
It takes a taxonomic tree file as the input. We first need to convert the MetaPhlAn output using Export to GraPhlAn. This conversion software tool produces both annotation and tree file for GraPhlAn.
hands_on Hands-on: Publication-ready community structure visualization with GraPhlAn
1. Export to GraPhlAn Tool: toolshed.g2.bx.psu.edu/repos/iuc/export2graphlan/export2graphlan/0.20+galaxy0 with the following parameters:
• param-file “Input file”: Cut predicted taxon relative abundances table
• “List which levels should be annotated in the tree”: 1,2
• “List which levels should use the external legend for the annotation”: 3,4,5
• “List which levels should be highlight with a shaded background”: 1
2. Generation, personalization and annotation of tree Tool: toolshed.g2.bx.psu.edu/repos/iuc/graphlan_annotate/graphlan_annotate/1.0.0.0 with the following parameters:
• param-file “Input tree”: Tree (output of Export to GraPhlAn)
• param-file “Annotation file”: Annotation (output of Export to GraPhlAn)
3. GraPhlAn Tool: toolshed.g2.bx.psu.edu/repos/iuc/graphlan/graphlan/1.0.0.0 with the following parameters:
• param-file “Input tree”: Tree in PhyloXML
• “Output format”: PNG
4. Inspect GraPhlAn output
Extract the functional information
exchange Switch to short tutorial
We would now like to answer the question “What are the micro-organisms doing?” or “Which functions are performed by the micro-organisms in the environment?”.
In the metatranscriptomics data, we have access to the genes that are expressed by the community. We can use that to identify genes, their functions, and build pathways, etc., to investigate their contribution to the community using HUMAnN (Franzosa et al. 2018). HUMAnN is a pipeline developed for efficiently and accurately profiling the presence/absence and abundance of microbial pathways in a community from metagenomic or metatranscriptomic sequencing data.
To identify the functions made by the community, we do not need the rRNA sequences, specially because they had noise and will slow the run. We will then use the output of SortMeRNA, but also the identified community profile from MetaPhlAn. This will help HUMAnN to focus on the known sequences for the identified organisms.
hands_on Hands-on: Extract the functional information
1. HUMAnN Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann/humann/3.0.0+galaxy1 with the following parameters:
• “Input(s)”: Quality-controlled shotgun sequencing reads (metagenome (DNA reads) or metatranscriptome (RNA reads))
• param-file “Quality-controlled shotgun sequencing reads (metagenome (DNA reads) or metatranscriptome (RNA reads))”: Interlaced non rRNA reads
• “Steps”: Bypass the taxonomic profiling step and creates a custom ChocoPhlAn database of the species provided afterwards
• param-file“Taxonomic profile file”: Predicted taxon relative abundances (output of MetaPhlAn tool)
• In “Nucleotide search / Mapping reads to community pangenomes”
• “Nucleotide database”: Locally cached
• “Nucleotide database”: Full ChocoPhlAn for HUMAnN
• In “Translated search / Aligning unmapped reads to a protein database”
• “Protein database”: Locally cached
• “Protein database”: Full UniRef90 for HUMAnN
tip Tip: Running low on time? Import the HUMAnN outputs
1. Import the 2 files:
https://zenodo.org/record/4776250/files/T1A_HUMAnN_Gene_families_and_their_abundance.tabular
https://zenodo.org/record/4776250/files/T1A_HUMAnN_Pathways_and_their_abundance.tabular
HUMAnN tool generates 4 files:
1. A tabular file with the gene families and their abundance:
# Gene Family humann_Abundance-RPKs
UNMAPPED 98294.0000000000
UniRef90_A3DCI4 42213.2661898446
UniRef90_A3DCI4|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 42205.5707425926
UniRef90_A3DCI4|unclassified 7.6954472520
UniRef90_A3DCB9 39273.2031556915
UniRef90_A3DCB9|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 39273.2031556915
This file details the abundance of each gene family in the community. Gene families are groups of evolutionarily-related protein-coding sequences that often perform similar functions. Here we used UniRef90 gene families: sequences in a gene families have at least 50% sequence identity.
Gene family abundance at the community level is stratified to show the contributions from known and unknown species. Individual species’ abundance contributions sum to the community total abundance.
Gene family abundance is reported in RPK (reads per kilobase) units to normalize for gene length. It reflects the relative gene (or transcript) copy number in the community.
The “UNMAPPED” value is the total number of reads which remain unmapped after both alignment steps (nucleotide and translated search). Since other gene features in the table are quantified in RPK units, “UNMAPPED” can be interpreted as a single unknown gene of length 1 kilobase recruiting all reads that failed to map to known sequences.
question Questions
Inspect the Gene families and their abundances file from HUMAnN tool
1. What is the most abundant family?
2. Which species is involved in production of this family?
3. How many gene families have been identified?
solution Solution
1. The most abundant family is the first one in the family: UniRef90_A3DCI4. We can use the tool Rename features of a HUMAnN generated table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_rename_table/humann_rename_table/3.0.0+galaxy1 to add extra information about the gene family.
2. Beta-lactamase TEM seems mostly produced here by Hungateiclostridium thermocellum.
3. There is 6,374 lines in gene family file. But some of the gene families have multiple lines when the involved species are known.
To know the number of gene families, we need to remove all lines with the species information, i.e. lines with | in them using the tool Split a HUMAnN table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_split_stratified_table/humann_split_stratified_table/3.0.0+galaxy1
The tool generates 2 output file:
• a stratified table with all lines with | in them
• a unstratied table with all lines without | in them
In the unstratified table, there are 3,175 lines, so 3,174 gene families.
2. A tabular file with the pathways and their abundance:
# Pathway humann_Abundance
UNMAPPED 21383.0328532606
UNINTEGRATED 123278.2617863865
UNINTEGRATED|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 114029.8324087679
UNINTEGRATED|unclassified 6301.1699240597
UNINTEGRATED|g__Coprothermobacter.s__Coprothermobacter_proteolyticus 5407.2826151090
PWY-1042: glycolysis IV 194.7465938041
This file shows each pathway and their abundance. Here, we used the MetaCyc Metabolic Pathway Database, a curated database of experimentally elucidated metabolic pathways from all domains of life.
The abundance of a pathway in the sample is computed as a function of the abundances of the pathway’s component reactions, with each reaction’s abundance computed as the sum over abundances of genes catalyzing the reaction. The abundance is proportional to the number of complete “copies” of the pathway in the community. Indeed, for a simple linear pathway RXN1 --> RXN2 --> RXN3 --> RXN4, if RXN1 is 10 times as abundant as RXNs 2-4, the pathway abundance will be driven by the abundances of RXNs 2-4.
The pathway abundance is computed once for all species (community level) and again for each species using species gene abundances along the components of the pathway. Unlike gene abundance, a pathway’s abundance at community-level is not necessarily the sum of the abundance values of each species. For example, for the same pathway example as above, if the abundances of RXNs 1-4 are [5, 5, 10, 10] in Species A and [10, 10, 5, 5] in Species B, the pathway abundance would be 5 for Species A and Species B, but 15 at the community level as the reaction totals are [15, 15, 15, 15].
question Questions
View the Pathways and their abundance output from HUMAnN tool
1. What is the most abundant pathway?
2. Which species is involved in production of this pathway?
3. How many gene families have been identified?
4. What is the “UNINTEGRATED” abundance?
solution Solution
1. The most abundant pathway is PWY-6609. It produces the adenine and adenosine salvage III.
2. Like the gene family, this pathway is mostly achieved by Hungateiclostridium thermocellum.
3. There are 118 lines in the pathway file, including the lines with species information. To compute the number of gene families, we need to apply a similar approach as for the gene families by removing the lines with | in them using the tool Split a HUMAnN table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_split_stratified_table/humann_split_stratified_table/3.0.0+galaxy1 . The unstratified output file has 64 lines, including the header, UNMAPPED and UNINTEGRATED. Therefore, 61 MetaCyc pathways have been identified for our sample.
4. The “UNINTEGRATED” abundance corresponds to the total abundance of genes in the different levels that do not contribute to any pathways.
3. A file with the pathways and their coverage:
Pathway coverage provides an alternative description of the presence (1) and absence (0) of pathways in a community, independent of their quantitative abundance.
4. A log file
comment Note: Analyzing an isolated metatranscriptome
As we already mentioned above, we are analyzing our RNA reads as we would do for DNA reads and therefore we should be careful when interpreting the results. We already mentioned the analysis of the species’ relative abundance from MetaPhlAn, but there is another aspect we should be careful about.
From a lone metatranscriptomic dataset, the transcript abundance can be confounded with the underlying gene copy number. For example, transcript X may be more abundant in sample A relative to sample B because the underlying X gene (same number in both samples) is more highly expressed in sample A relative to sample B; or there are more copies of gene X in sample A relative to sample B (all of which are equally expressed). This is a general challenge in analyzing isolated metatranscriptomes.
The best approach would be to combine the metatranscriptomic analysis with a metagenomic analysis. In this case, rather than running MetaPhlAn on the metatranscriptomic data, we run it on the metagenomic data and use the taxonomic profile as input to HUMAnN. RNA reads are then mapped to any species’ pangenomes detected in the metagenome. Then we run HUMAnN on both metagenomics and metatranscriptomic data. We can use both outputs to normalize the RNA-level outputs (e.g. transcript family abundance) by corresponding DNA-level outputs to the quantification of microbial expression independent of gene copy number.
Here we do not have a metagenomic dataset to combine with and need to be careful in our interpretation.
Normalize the abundances
Gene family and pathway abundances are in RPKs (reads per kilobase), accounting for gene length but not sample sequencing depth. While there are some applications, e.g. strain profiling, where RPK units are superior to depth-normalized units, most of the time we need to renormalize our samples prior to downstream analysis.
hands_on Hands-on: Normalize the gene family abundances
1. Renormalize a HUMAnN generated table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_renorm_table/humann_renorm_table/3.0.0+galaxy1 with
• “Gene/pathway table”: Gene families and their abundance (output of HUMAnN)
• “Normalization scheme”: Relative abundance
• “Normalization level”: Normalization of all levels by community total
2. Rename galaxy-pencil the generated file Normalized gene families
question Questions
Inspect galaxy-eye the Normalized gene families file
1. What percentage of sequences has not been assigned to a gene family?
2. What is the relative abundance of the most abundant gene family?
solution Solution
1. 14% (0.14438 x 100) of the sequences have not be assigned to a gene family.
2. The UniRef90_A3DCI4 family represents 6% of the reads.
Let’s do the same for the pathway abundances.
hands_on Hands-on: Normalize the pathway abundances
1. Renormalize a HUMAnN generated table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_renorm_table/humann_renorm_table/3.0.0+galaxy1 with
• “Gene/pathway table”: Pathways and their abundance (output of HUMAnN)
• “Normalization scheme”: Relative abundance
• “Normalization level”: Normalization of all levels by community total
2. Rename galaxy-pencil the generated file Normalized pathways
question Questions
Inspect galaxy-eye the Normalized pathways file.
1. What is the UNMAPPED percentage?
2. What percentage of reads assigned to a gene family has not be assigned to a pathway?
3. What is the relative abundance of the most abundant gene family?
solution Solution
1. UNMAPPED, here 14% of the reads, corresponds to the percentage of reads not assigned to gene families. It is the same value as in the normalized gene family file.
2. 83% (UNINTEGRATED) of reads assigned to a gene family have not be assigned to a pathway
3. The PWY-6609 pathway represents 0.2% of the reads.
Identify the gene families involved in the pathways
We would like to know which gene families are involved in our most abundant pathways and which species. For this, we use the tool Unpack pathway abundances to show genes included tool from HUMAnN tool suites.
hands_on Hands-on: Normalize the gene family abundances
1. Unpack pathway abundances to show genes included Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_unpack_pathways/humann_unpack_pathways/3.0.0+galaxy1 with
• “Gene family or EC abundance file”: Normalized gene families
• “Pathway abundance file”: Normalized pathways
This tool unpacks the pathways to show the genes for each. It adds another level of stratification to the pathway abundance table by including the gene family abundances:
# Pathway humann_Abundance-RELAB
ANAGLYCOLYSIS-PWY: glycolysis III (from glucose) 0.000312308
BRANCHED-CHAIN-AA-SYN-PWY: superpathway of branched chain amino acid biosynthesis 0.00045009
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 0.00045009
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DIY4 9.67756e-06
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DIE1 0.000123259
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DID9 9.73261e-05
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DDR1 7.97357e-05
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DF94 1.4837e-05
BRANCHED-CHAIN-AA-SYN-PWY|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DIY3 0.000117313
question Questions
Inspect galaxy-eye the output from Unpack pathway abundances to show genes included tool
Which gene families are involved in the PWY-6609 pathway (the most abundant one)? And which species?
solution Solution
If we search the generated file for (using CTRF or CMDF):
PWY-6609: adenine and adenosine salvage III 0.00192972
PWY-6609|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 0.000448128
PWY-6609|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DD28 4.47176e-05
PWY-6609|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DHM7 0.000235689
PWY-6609|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum|UniRef90_A3DEQ4 3.68298e-05
The gene families UniRef90_A3DD28, UniRef90_A3DHM7 and UniRef90_A3DEQ4 are identified, for Hungateiclostridium thermocellum.
Group gene families into GO terms
The gene families can be a long list of ids and going through the gene families one by one to identify the interesting ones can be cumbersome. To help construct a big picture, we could identify and use categories of genes using the gene families.
Gene Ontology (GO) analysis is widely used to reduce complexity and highlight biological processes in genome-wide expression studies. There is a dedicated tool which groups and converts UniRef50 gene family abundances generated with HUMAnN into GO terms.
hands_on Hands-on: Group abundances into GO terms
1. Regroup HUMAnN table features Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_regroup_table/humann_regroup_table/3.0.0+galaxy1 with the following parameters:
• param-file “Gene families table”: Gene families and their abundance (output of HUMAnN)
• “How to combine grouped features?”: Sum
• “Grouping”: Grouping with larger mapping
• Mapping to use for the grouping”: Mapping (full) for Gene Ontology (GO) from UniRef90
The output is a table with the GO terms, their abundance and the involved species:
# Gene Family humann_Abundance-RPKs
UNMAPPED 98294.0
UNGROUPED 174431.144
UNGROUPED|g__Coprothermobacter.s__Coprothermobacter_proteolyticus 6941.859
UNGROUPED|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 151964.371
UNGROUPED|unclassified 15524.915
GO:0000015 250.882
GO:0000015|g__Coprothermobacter.s__Coprothermobacter_proteolyticus 11.313
GO:0000015|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 239.568
question Questions
How many GO term have been identified?
solution Solution
Using the tool Split a HUMAnN table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_split_stratified_table/humann_split_stratified_table/3.0.0+galaxy1 , we see that the unstratified table has 1,171 lines (including the UNMAPPED, UNGROUPED and the header). So 1,168 GO terms have been identified.
The GO term with their id are quite cryptic. We can rename them and then split them in 3 groups (molecular functions [MF], biological processes [BP] and cellular components [CC])
hands_on Hands-on: Rename GO terms
1. Rename features of a HUMAnN generated table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_rename_table/humann_rename_table/3.0.0+galaxy0 with the following parameters:
• param-file “Gene families table”: output of Regroup HUMAnN table features
• “Type of feature renaming”: Advanced feature renaming
• “Features to be renamed”: Mapping (full) between Gene Ontology (GO) ids and names
2. Select lines that match an expression Tool: Grep1 with the following parameters:
• param-file “Select lines from”: output of last Rename features of a HUMAnN generated table
• “that”: Matching
• “the pattern”: $CC$
3. Rename galaxy-pencil the generated file [CC] GO terms and their abundance
4. Select lines that match an expression Tool: Grep1 with the following parameters:
• param-file “Select lines from”: output of last Rename features of a HUMAnN generated table
• “that”: Matching
• “the pattern”: $MF$
5. Rename galaxy-pencil the generated file [MF] GO terms and their abundance
6. Select lines that match an expression Tool: Grep1 with the following parameters:
• param-file “Select lines from”: output of last Rename features of a HUMAnN generated table
• “that”: Matching
• “the pattern”: $BP$
7. Rename galaxy-pencil the generated file [BP] GO terms and their abundance
question Questions
Inspect galaxy-eye the 3 outputs of these steps
1. How many GO terms have been identified?
2. Which of the GO terms related to molecular functions is the most abundant?
solution Solution
1. After running Split a HUMAnN table Tool: toolshed.g2.bx.psu.edu/repos/iuc/humann_split_stratified_table/humann_split_stratified_table/3.0.0+galaxy1 on the 3 outputs, we found:
• 414 BP GO terms
• 689 MF GO terms
• 59 CC GO terms
2. The GO terms in the [MF] GO terms and their abundance file are not sorted by abundance:
GO:0000030: [MF] mannosyltransferase activity 16.321
GO:0000030: [MF] mannosyltransferase activity|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 16.321
GO:0000036: [MF] acyl carrier activity 726.249
GO:0000036: [MF] acyl carrier activity|g__Coprothermobacter.s__Coprothermobacter_proteolyticus 10.101
GO:0000036: [MF] acyl carrier activity|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 572.281
GO:0000036: [MF] acyl carrier activity|unclassified 143.868
GO:0000049: [MF] tRNA binding 4818.299
So to identify the most abundant GO terms, we first need to sort the file using the Sort data in ascending or descending order Tool: toolshed.g2.bx.psu.edu/repos/bgruening/text_processing/tp_sort_header_tool/1.1.1 tool (on column 2, in descending order):
GO:0015035: [MF] protein disulfide oxidoreductase activity 42908.123
GO:0003735: [MF] structural constituent of ribosome 42815.337
GO:0015035: [MF] protein disulfide oxidoreductase activity|g__Hungateiclostridium.s__Hungateiclostridium_thermocellum 40533.997
GO:0005524: [MF] ATP binding 37028.271
GO:0046872: [MF] metal ion binding 31068.144
The most abundant GO terms related to molecular functions seem to be linked to protein disulfide oxidoreductase activity, but also to structural constituent of ribosome and ATP and metal ion binding.
Combine taxonomic and functional information
With MetaPhlAn and HUMAnN, we investigated “Which micro-organims are present in my sample?” and “What functions are performed by the micro-organisms in my sample?”. We can go further in these analyses, for example using a combination of functional and taxonomic results. Although we did not detail that in this tutorial you can find more methods of analysis in our tutorials on shotgun metagenomic data analysis.
Although gene families and pathways, and their abundance may be related to a species, in the HUMAnN output, relative abundance of the species is not indicated. Therefore, for each gene family/pathway and the corresponding taxonomic stratification, we will now extract the relative abundance of this gene family/pathway and the relative abundance of the corresponding species and genus.
hands_on Hands-on: Combine taxonomic and functional information
1. Combine MetaPhlAn2 and HUMAnN2 outputs Tool: toolshed.g2.bx.psu.edu/repos/bebatut/combine_metaphlan2_humann2/combine_metaphlan2_humann2/0.1.0 with the following parameters:
• param-file “Input file corresponding to MetaPhlAN output”: Cut predicted taxon relative abundances table
• param-file “Input file corresponding HUMAnN output”: Normalized gene families
• “Type of characteristics in HUMAnN file”: Gene families
2. Inspect the generated file
The generated file is a table with 7 columns:
1. genus
2. abundance of the genus (percentage)
3. species
4. abundance of the species (percentage)
5. gene family id
6. gene family name
7. gene family abundance (percentage)
genus genus_abundance species species_abundance gene_families_id gene_families_name gene_families_abundance
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_A3DCI4 6.199410892039433
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_A3DCB9 5.768680830061254
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_A3DC67 4.872720701140655
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_A3DBR3 3.3930004882222335
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_A3DI60 2.924280420777634
Hungateiclostridium 94.67418 Hungateiclostridium_thermocellum 94.67418 UniRef90_G2JC59 2.639170379752865
question Questions
1. Are there gene families associated with each genus identified with MetaPhlAn?
2. How many gene families are associated to each genus?
3. Are there gene families associated to each species identified with MetaPhlAn?
4. How many gene families are associated to each species?
solution Solution
1. To answer the questions, we need to group the contents of the output of Combine MetaPhlAn2 and HUMAnN2 outputs by 1st column and count the number of occurrences of gene families. We do that using Group data by a column tool:
hands_on Hands-on: Group by genus and count gene families
1. Group data by a column Tool: Grouping1
• “Select data”: output of Combine MetaPhlAn2 and HUMAnN2 outputs
• “Group by column”: Column:1
• “Operation”:
• Click on param-repeat “Insert Operation”
• “Type”: Count
• “On column”: Column:5
With MetaPhlAn, we identified 3 genus (Coprothermobacter, Methanothermobacter, Hungateiclostridium). But in the output of Combine MetaPhlAn2 and HUMAnN2 outputs, we have only gene families for Coprothermobacter and Hungateiclostridium. The abundance of Methanothermobacter is probably too low to correctly identify correctly some gene families.
2. 1,889 gene families are associated to Hungateiclostridium and 528 to Coprothermobacter and 202 to Methanothermobacter.
3. For this question, we should group on the 3rd column:
hands_on Hands-on: Group by species and count gene families
1. Group data by a column Tool: Grouping1
• “Select data”: output of Combine MetaPhlAn2 and HUMAnN2 outputs
• “Group by column”: Column:3
• “Operation”:
• Click on param-repeat “Insert Operation”
• “Type”: Count
• “On column”: Column:5
Only 2 species (Coprothermobacter_proteolyticus and Hungateiclostridium thermocellum) identified by MetaPhlAn are associated to gene families.
4. As the species found derived directly from the genus (not 2 species for the same genus here), the number of gene families identified are the sames: 528 for Coprothermobacter proteolyticus and 1,889 for Hungateiclostridium thermocellum.
We could now apply the same tool to the pathways and run similar analysis.
Conclusion
In this tutorial, we analyzed one metatranscriptomics sample from raw sequences to community structure, functional profiling. To do that, we:
1. preprocessed the raw data: quality control, trimming and filtering, sequence sorting and formatting
2. extracted and analyzed the community structure (taxonomic information)
We identified bacteria to the level of strains, but also some archaea.
3. extracted and analyzed the community functions (functional information)
We extracted gene families, pathways, but also the gene families involved in pathways and aggregated the gene families into GO terms
4. combined taxonomic and functional information to offer insights into taxonomic contribution to a function or functions expressed by a particular taxonomy
The workflow can be represented this way:
The dataset used here was extracted from a time-series analysis of a microbial community inside a bioreactor (Kunath et al. 2018) in which there are 3 replicates over 7 time points. We analyzed here only one single time point for one replicate.
Key points
• Metatranscriptomics data have the same QC profile that RNA-seq data
• A lot of metatranscriptomics sequences are identified as rRNA sequences
• With shotgun data, we can extract information about the studied community structure and also the functions realised by the community
• Metatranscriptomics data analyses are complex and must be careful done, specially when they are done without combination to metagenomics data analyses
Have questions about this tutorial? Check out the tutorial FAQ page or the FAQ page for the Metagenomics topic to see if your question is listed there. If not, please ask your question on the GTN Gitter Channel or the Galaxy Help Forum
Useful literature
Further information, including links to documentation and original publications, regarding the tools, analysis techniques and the interpretation of results described in this tutorial can be found here.
References
2. Ondov, B. D., N. H. Bergman, and A. M. Phillippy, 2011 Interactive metagenomic visualization in a Web browser. BMC bioinformatics 12: 385.
3. Kopylova, E., L. Noé, and H. Touzet, 2012 SortMeRNA: fast and accurate filtering of ribosomal RNAs in metatranscriptomic data. Bioinformatics 28: 3211–3217.
4. Truong, D. T., E. A. Franzosa, T. L. Tickle, M. Scholz, G. Weingart et al., 2015 MetaPhlAn2 for enhanced metagenomic taxonomic profiling. Nature methods 12: 902.
5. Batut, B., K. Gravouil, C. Defois, S. Hiltemann, J.-F. Brugère et al., 2018 ASaiM: a Galaxy-based framework to analyze microbiota data. GigaScience 7: giy057.
6. Franzosa, E. A., L. J. McIver, G. Rahnavard, L. R. Thompson, M. Schirmer et al., 2018 Species-level functional profiling of metagenomes and metatranscriptomes. Nature methods 15: 962.
7. Kunath, B. J., F. Delogu, A. E. Naas, M. Ø. Arntzen, V. G. H. Eijsink et al., 2018 From proteins to polysaccharides: lifestyle and genetic evolution of Coprothermobacter proteolyticus. The ISME journal 1.
Feedback
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Citing this Tutorial
1. Pratik Jagtap, Subina Mehta, Ray Sajulga, Bérénice Batut, Emma Leith, Praveen Kumar, Saskia Hiltemann, 2021 Metatranscriptomics analysis using microbiome RNA-seq data (Galaxy Training Materials). https://training.galaxyproject.org/training-material/topics/metagenomics/tutorials/metatranscriptomics/tutorial.html Online; accessed TODAY
2. Batut et al., 2018 Community-Driven Data Analysis Training for Biology Cell Systems 10.1016/j.cels.2018.05.012
details BibTeX
@misc{metagenomics-metatranscriptomics,
author = "Pratik Jagtap and Subina Mehta and Ray Sajulga and Bérénice Batut and Emma Leith and Praveen Kumar and Saskia Hiltemann",
title = "Metatranscriptomics analysis using microbiome RNA-seq data (Galaxy Training Materials)",
year = "2021",
month = "05",
day = "20"
url = "\url{https://training.galaxyproject.org/training-material/topics/metagenomics/tutorials/metatranscriptomics/tutorial.html}",
note = "[Online; accessed TODAY]"
}
@article{Batut_2018,
doi = {10.1016/j.cels.2018.05.012},
url = {https://doi.org/10.1016%2Fj.cels.2018.05.012},
year = 2018,
month = {jun},
publisher = {Elsevier {BV}},
volume = {6},
number = {6},
pages = {752--758.e1},
author = {B{\'{e}}r{\'{e}}nice Batut and Saskia Hiltemann and Andrea Bagnacani and Dannon Baker and Vivek Bhardwaj and Clemens Blank and Anthony Bretaudeau and Loraine Brillet-Gu{\'{e}}guen and Martin {\v{C}}ech and John Chilton and Dave Clements and Olivia Doppelt-Azeroual and Anika Erxleben and Mallory Ann Freeberg and Simon Gladman and Youri Hoogstrate and Hans-Rudolf Hotz and Torsten Houwaart and Pratik Jagtap and Delphine Larivi{\{e}}re and Gildas Le Corguill{\'{e}} and Thomas Manke and Fabien Mareuil and Fidel Ram{\'{\i}}rez and Devon Ryan and Florian Christoph Sigloch and Nicola Soranzo and Joachim Wolff and Pavankumar Videm and Markus Wolfien and Aisanjiang Wubuli and Dilmurat Yusuf and James Taylor and Rolf Backofen and Anton Nekrutenko and Björn Grüning},
title = {Community-Driven Data Analysis Training for Biology},
journal = {Cell Systems}
}
`
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2022-08-19 08:16:54
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https://zbmath.org/?q=an:0512.76068
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## Stable viscosities and shock profiles for systems of conservation laws.(English)Zbl 0512.76068
Wide classes of high order “viscosity” terms are determined, for which small amplitude shock wave solutions of a nonlinear hyperbolic system of conservation laws $$u_t + f(u)_x = 0$$ are realized as limits of traveling wave solutions of a dissipative system $u_t + f(u)_x = \nu (D_1u_x)_x + \cdots + \nu ^n(D_nu^{(n)})_x.$ The set of such “admissible” viscosities includes those for which the dissipative system satisfies a linearized stability condition previously investigated in the case $$n = 1$$ by A. Majda and this author [J. Differ. Equ. 56, 229–262 (1985; Zbl 0512.76067)]. When $$n = 1$$ we also establish admissibility criteria for singular viscosity matrices $$D_1(u)$$, and apply our results to the compressible Navier-Stokes equations with viscosity and heat conduction, determining minimal conditions on the equation of state which ensure the existence of the “shock layer” for weak shocks.
### MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76L05 Shock waves and blast waves in fluid mechanics 35L65 Hyperbolic conservation laws 35C07 Traveling wave solutions 76E99 Hydrodynamic stability 76D99 Incompressible viscous fluids
Zbl 0512.76067
Full Text:
### References:
[1] Joseph G. Conlon, A theorem in ordinary differential equations with an application to hyperbolic conservation laws, Adv. in Math. 35 (1980), no. 1, 1 – 18. · Zbl 0426.35068 [2] I. M. Gel$$^{\prime}$$fand, Some problems in the theory of quasi-linear equations, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 87 – 158 (Russian). [3] David Gilbarg, The existence and limit behavior of the one-dimensional shock layer, Amer. J. Math. 73 (1951), 256 – 274. · Zbl 0044.21504 [4] Tai Ping Liu, The entropy condition and the admissibility of shocks, J. Math. Anal. Appl. 53 (1976), no. 1, 78 – 88. · Zbl 0332.76051 [5] Andrew Majda and Stanley Osher, A systematic approach for correcting nonlinear instabilities. The Lax-Wendroff scheme for scalar conservation laws, Numer. Math. 30 (1978), no. 4, 429 – 452. · Zbl 0368.65048 [6] Andrew Majda and Robert L. Pego, Stable viscosity matrices for systems of conservation laws, J. Differential Equations 56 (1985), no. 2, 229 – 262. · Zbl 0512.76067 [7] Akitaka Matsumura and Takaaki Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 9, 337 – 342. · Zbl 0447.76053 [8] Robert L. Pego, Nonexistence of a shock layer in gas dynamics with a nonconvex equation of state, Arch. Rational Mech. Anal. 94 (1986), no. 2, 165 – 178. · Zbl 0652.76047 [9] R. Shapiro, Shock waves as limits of progressive wave solutions of higher order equations, Ph. D. thesis, Univ. of Mchigan, 1973. [10] J. A. Smoller and R. Shapiro, Dispersion and shock-wave structure, J. Differential Equations 44 (1982), no. 2, 281 – 305. Special issue dedicated to J. P. LaSalle. · Zbl 0486.35052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2022-09-26 23:25:29
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https://darcynorman.net/2005/02/26/xml-parsing-into-mysql/
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# XML Parsing into MySQL
I had to write a utility for the Mavericks project to allow me to import asset descriptions that were exported from ContentDM via a tweaked XML format, into a MySQL database for use in Pachyderm authoring. I was going to write a simple python or php script to do it, but realized just how much simpler it would be in WebObjects. Using JDOM to parse the xml into a DOM Document, and then passing the data into an EOEnterpriseObject to be persisted into the database. Access to both libraries made my code insanely simple.
It's possible that it would be as simple in another environment, but I doubt I could have done it any faster or simpler in anything else. WebObjects really does rock.
My code is essentially one line to trigger parsing of the XML to the Document, 2 lines to create the EO and insert it into an editing context, a bunch of lines to populate the attributes of the EO with the various values in the XML ( nothing more complicated than record.setTitle(xmlElement.getChildText("Title"));), and a line to save the pending changes in the editing context. Easy peasy.
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2020-07-10 05:28:42
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https://smprtn.pages.math.illinois.edu/
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# Eric G. Samperton
## Teaching
During the fall 2019 semester, I am teaching MATH 213. Here is the course webpage.
## About me
I am a J. L. Doob Research Assistant Professor in the University of Illinois Math Department. Recently, I was a visiting professor at UC Santa Barbara, and earned my Ph.D. from UC Davis. My advisor was Greg Kuperberg.
My primary motivation is to answer questions at the intersection of 3-manifold topology and computational complexity. Broadly, I do research in overlaps of the following subjects:
• (Low-dimensional) geometric topology
• Geometric group theory
• Computational complexity
• Topological quantum field theory
• Quantum computing and quantum information
• Topological condensed matter theory
To be clear, I'm not a physicist or computer scientist. I am more interested in applying ideas from these fields to better understand topology and TQFT. (Although occasionally—to Hardy's dismay—the arrow of ideas points in both directions.) For example, I have used ideas inspired by topological quantum computing to prove complexity-theoretic lower bounds for problems in 3-manifold topology.
Here's my CV. Here's a very full, loose lamination with $$\mathbb{Z}/4 * \mathbb{Z}/3$$ symmetry:
And here's a video of a talk I gave at the University of Warwick related to my dissertation work: YouTube.
## Writing
My papers and preprints are listed below. You might also want to check out my arXiv author page, my MathSciNet author profile (subscription required) or my Google Scholar profile.
(6) Coloring invariants of knots and links are often intractable. With Greg Kuperberg. Submitted. arXiv Front.
(5) Haah codes on general three manifolds. With Kevin Tian and Zhenghan Wang. Annals of Physics (2020), Volume 412, 168014. arXiv Front.
(4) Schur-type invariants of branched G-covers of surfaces. To appear in Proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation. arXiv Front.
(3) Computational complexity and 3-manifolds and zombies. With Greg Kuperberg. Geometry & Topology (2018), Volume 22, Issue 6, pp. 3623--3670. arXiv Front.
(2) Spaces of invariant circular orders of groups. With Harry Baik. Groups, Geometry, and Dynamics (2018), Volume 12, Issue 2, pp. 721-763. arXiv Front.
(1) On laminar groups, Tits alternatives, and convergence group actions on $$S^2$$. With Juan Alonso and Harry Baik. Journal of Group Theory (2019), Volume 22, Issue 3, pp. 359-381. arXiv Front.
My Ph.D. dissertation is titled Computational Complexity of Enumerative 3-Manifold Invariants and can be found at the arXiv Front or ProQuest. It contains the results of items (3), (4) and (6) above.
## Contact Information
E-mail: My last name without any vowels, followed by @illinois.edu
Office: 247B Illini Hall
Snail Mail:
Department of Mathematics
1409 West Green Street (MC-382)
Urbana, IL 61801
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2019-12-07 01:32:06
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http://mathhelpforum.com/advanced-statistics/180439-blackjack-math.html
|
# Math Help - Blackjack math
1. ## Blackjack math
Hey guys,
Anyone here familiar with blackjack mathematics? I came across a series of threads at another forum where a guy is trying to convince people that he's developed a better betting method than basic strategy. I haven't cracked open a math book in a decade but to me his system looks like a just a no-bust martingale variation that should have a much lower expected value over basic strategy.
This is his system:
"I recommend ignoring this if you really want to win at blackjack. There is a reason that the casino will hand you that chart and wants most players to play that way and that is because it makes the house the favorite.
Blackjack is a game I have won far more money at then I have ever lost and I have invented my own system. The only downside to my system is that other players will hate you for not playing to the same playbook they play by. The last time I played I was winning huge but had 3 players verbally abusing attacking me until the dealer said "give the guy a break...he is winning." Also you need to have about $300 to lose to play this way. Anyway I will for the first time detail my black jack system here. IT is simple really. Mathematically speaking the dealer is going to bust (get more then 21) every X hands. This is fact. In my experience that number is about 4-6 hands although I have counted a dealer going as many as 11 without a single bust (except they busted me). So in my system you are playing the bust....not your hand...and not the dealers hand. That means you NEVER bust yourself, ever. I don't care if you are showing 12 and the dealer a 10 you do not hit and bust yourself because that might be your one bust the dealer was going to give you that series. In my system I will sit out hands while holding my spot until the dealer goes 3 hands in a row without busting. Sometime I sit up to 8 or more hands but thta is rare. Then I will bet the table minimum ($10). If the dealer does not bust and beats my hand then I double my bet ($20) and if I win I am up$10. If the dealer again does not bust and beats my hand then again I double ($40) and so on. I have five straight bets I can make or 8 hands where I am counting on him busting. I am betting that the dealer will ust once during the 8 hands (remember I waited until he went 3-no-bust). As soon as the dealer busts I go back to sitting out to start all over again. NOw how I make big money in this system is when the dealer does not bust but I beat their hand outright. I still ramp up my bet expecting a bust to come very soon. I can double and triple my stack on these wins. Personally I can never understand how people can walk into the ediface that is a casino and realize that it is built with gamblers money and then play off the sheet the casino gives you to play by. Do yourself a favour and stand and watch and count how many hands it takes a dealer to go bust and what is his longest streak without busting. I doubt you will ever see him go more then 8 straight with no bust unless you watch hours and hours of Blackjack. Hopefully if you play you will not hit his hot streak and you can get in and out with a Mitt full dough by playing the bust." The thread is here: http://www.rottentomatoes.com/vine/show ... stcount=49 but the discussion continues here after Cuepee was banned and returned as QP: http://www.rottentomatoes.com/vine/show ... ?t=2267387 If anybody is up to it can they analyze his system here so as not to get mixed up in the mess that most QP threads turn into over at rottentomatoes. 2. Originally Posted by Allen112 Hey guys, Anyone here familiar with blackjack mathematics? I came across a series of threads at another forum where a guy is trying to convince people that he's developed a better betting method than basic strategy. I haven't cracked open a math book in a decade but to me his system looks like a just a no-bust martingale variation that should have a much lower expected value over basic strategy. This is his system: "I recommend ignoring this if you really want to win at blackjack. There is a reason that the casino will hand you that chart and wants most players to play that way and that is because it makes the house the favorite. Blackjack is a game I have won far more money at then I have ever lost and I have invented my own system. The only downside to my system is that other players will hate you for not playing to the same playbook they play by. The last time I played I was winning huge but had 3 players verbally abusing attacking me until the dealer said "give the guy a break...he is winning." Also you need to have about$300 to lose to play this way.
Anyway I will for the first time detail my black jack system here.
IT is simple really. Mathematically speaking the dealer is going to bust (get more then 21) every X hands. This is fact. In my experience that number is about 4-6 hands although I have counted a dealer going as many as 11 without a single bust (except they busted me).
So in my system you are playing the bust....not your hand...and not the dealers hand. That means you NEVER bust yourself, ever. I don't care if you are showing 12 and the dealer a 10 you do not hit and bust yourself because that might be your one bust the dealer was going to give you that series.
In my system I will sit out hands while holding my spot until the dealer goes 3 hands in a row without busting. Sometime I sit up to 8 or more hands but thta is rare. Then I will bet the table minimum ($10). If the dealer does not bust and beats my hand then I double my bet ($20) and if I win I am up $10. If the dealer again does not bust and beats my hand then again I double ($40) and so on. I have five straight bets I can make or 8 hands where I am counting on him busting.
I am betting that the dealer will ust once during the 8 hands (remember I waited until he went 3-no-bust). As soon as the dealer busts I go back to sitting out to start all over again.
NOw how I make big money in this system is when the dealer does not bust but I beat their hand outright. I still ramp up my bet expecting a bust to come very soon. I can double and triple my stack on these wins.
Personally I can never understand how people can walk into the ediface that is a casino and realize that it is built with gamblers money and then play off the sheet the casino gives you to play by.
Do yourself a favour and stand and watch and count how many hands it takes a dealer to go bust and what is his longest streak without busting. I doubt you will ever see him go more then 8 straight with no bust unless you watch hours and hours of Blackjack. Hopefully if you play you will not hit his hot streak and you can get in and out with a Mitt full dough by playing the bust."
http://www.rottentomatoes.com/vine/show ... stcount=49
but the discussion continues here after Cuepee was banned and returned as QP:
http://www.rottentomatoes.com/vine/show ... ?t=2267387
If anybody is up to it can they analyze his system here so as not to get mixed up in the mess that most QP threads turn into over at rottentomatoes.
The first post you link to contains the gamblers fallacy. Therefore there is no need to consider their argument further they are ignorant of probability.
Also, you are not to try relocating flame wars from another forum to MHF
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2015-05-06 22:11:57
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https://solvedlib.com/n/blii-46139-jijujl34-gt-x-x27-lal-jji-9-glj-lpxhisa-01a-07a8a,3315637
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5 answers
# (bLIi) 46139 JijuJl34 ->X'Lal JJI ~9 GLJ LPXhISA 01A 07A8A
###### Question:
(bLIi) 4613 9 JijuJl 34 -> X 'Lal JJI ~9 GLJ LPXhI SA 0 1A 0 7A 8A
## Answers
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A water sarple has a total carbonate species concentration of 0.1 M, pH= 10.0, [HS-(aq)] 0.05 M ad [Al3+] = 0.005 M. Use this information and the speciation graph below to calculate the alkalinity of this sarple Speciation of HzCOz in water HzCOz CO 0.44 0.2 10 14 pH HCO;...
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-- 0.096857--
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2023-03-31 18:46:34
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https://tex.stackexchange.com/questions/561915/declare-bibliography-entry-in-a-foreign-language-with-translation
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# Declare bibliography entry in a foreign language, with translation
I am using BibLaTeX with the Biber backend for the bibliography of my PhD thesis, written in English.
The Harvard style that my university recommends, encourages the translation of titles and journal titles written in a foreign language.
To get correct hyphenation patterns, one would use the langid field to declare the foreign language. However, what about if I want to add the title translated in English? Is there a way to declare languages 'locally' in a clean manner?
An example of such an entry would be:
@article{doe2000,
title = {Die numerische Strömungsmechanik [Computational Fluid Dynamics]},
author = {J. Doe},
booktitle = {Internationalen Mathematiker Kongresses [International Congress of Mathematics]},
date = {2000},
langid = {german} % but translated titles are in English
}
• If you're adding the translation at the end of fields, you may as well wrap them in a \foreignlanguage call or some such to switch the language. (\foreignlanguage and other macros are problematic at the beginning of fields because of sorting, but the further back they appear the less likely they are to matter.) A conceptually nicer solution may use data annotations (one annotation would be the translation and a second annotation could be the language of the translation that would be used for \foreignlanguage). ... – moewe Sep 9 '20 at 7:28
• ... I probably won't have time to look into that soon, but I shall see what I can do when I have more time. – moewe Sep 9 '20 at 7:29
• I guess the planned multi-script version of biblatex would be of interest here. It is still under development and I don't think it is ready for an official release any time soon, you can find out more about it at github.com/plk/biblatex/issues/416 (there is a test version available). – moewe Sep 9 '20 at 7:30
• Hi @moewe thanks for taking the time. It's a fine problem anyways, but If I understand the first comment well, I would remove the langid field to let biblatex know it's an english entry and just put \foreignlanguage{german}{..} at the end of the wanted fields? – circuitbreaker Sep 9 '20 at 8:30
The best input here will strongly depend on your your overall setup and the desired outcome.
Generally it is a bad idea to add too much markup commands to fields, as formatting should be up to the style and markup can be problematic for sorting. But here it seems not totally crazy to add some language switching markup at the end of the field (which is unlikely to matter for sorting).
\documentclass[german,english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear, backend=biber, autolang=hyphen]{biblatex}
\begin{filecontents}{\jobname.bib}
@incollection{doe2000,
title = {Die numerische Strömungsmechanik
\foreignlanguage{english}{[Computational Fluid Dynamics]}},
author = {J. Doe},
booktitle = {Internationaler Mathematikerkongress
\foreignlanguage{english}{[International Congress of Mathematicians]}},
date = {2000},
langid = {german},
}
\end{filecontents}
\begin{document}
\cite{doe2000}
\printbibliography
\end{document}
For a fully multilingual bibliography with the possibility to translate certain fields, you'll probably have to wait until the biblatex multiscript development branch makes it into the released version. See https://github.com/plk/biblatex/issues/416 for more details and an available test version.
In the meantime you can do some translating with field annotations.
\documentclass[ngerman,english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear, backend=biber]{biblatex}
% expand the first argument of \foreignlanguage
% needs a modern TeX engine with \expanded primitive
\newcommand*{\foreignlanguageE}[1]{\foreignlanguage{\expanded{#1}}}
\newcommand*{\foreignlangbyannotation}[2][\currentfield]{%
\hasfieldannotation[#1][lang]
{\foreignlanguageE{\csuse{abx@annotation@literal@field@#1@lang}}{#2}}
{#2}}
\newcommand*{\printtranslation}[1][\currentfield]{%
\hasfieldannotation[#1][translation]
{}}
\DeclareFieldFormat{title}{%
\mkbibemph{%
\foreignlangbyannotation[title]{#1}%
\printtranslation[title]}}
\DeclareFieldFormat
[article,inbook,incollection,inproceedings,patent,thesis,unpublished]
{title}{%
\mkbibquote{%
\foreignlangbyannotation[title]{#1}%
\printtranslation[title]\isdot}}
\DeclareFieldFormat
[suppbook,suppcollection,suppperiodical]
{title}{%
\foreignlangbyannotation[title]{#1}%
\printtranslation[title]}
\DeclareFieldFormat{booktitle}{%
\mkbibemph{%
\foreignlangbyannotation[booktitle]{#1}%
\printtranslation[booktitle]}}
\begin{filecontents}{\jobname.bib}
@incollection{doe2000,
title = {Die numerische Strömungsmechanik},
title+an:lang = {="ngerman"},
title+an:translation = {="Computational Fluid Dynamics"},
author = {J. Doe},
booktitle = {Internationaler Mathematikerkongress},
booktitle+an:lang = {="ngerman"},
booktitle+an:translation = {="International Congress of Mathematicians"},
date = {2000},
}
\end{filecontents}
|
2021-03-06 02:39:18
|
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https://jendrzejewski.synqs.org/tag/impurity/
|
# impurity
## Stochastic dynamics of a few sodium atoms in a cold potassium cloud
We report on the stochastic dynamics of a few sodium atoms immersed in a cold potassium cloud. The studies are realized in a dual-species magneto-optical trap by continuously monitoring the emitted fluorescence of the two atomic species. We …
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2021-09-21 11:18:36
|
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|
http://www.livmathssoc.org.uk/cgi-bin/sews.py?GoldenRectangle
|
A Golden Rectangle is a rectangle whose sides are in the golden ratio:
• $\small(1+\sqrt{5})/2$
That means that if you chop off the largest square possible, the remaining rectangle is also golden. The Golden Ratio is found all over the pentagon, so perhaps it's no surprise that the Golden Rectangle can be found in the dodecahedron.
Compare with A4 paper.
|
2020-07-10 13:50:34
|
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|
https://codereview.stackexchange.com/questions/4977/regular-expression-to-remove-blank-lines
|
# Regular Expression to remove blank lines
This is basically my first Ruby class, which is to remove all empty lines and blank times from a .txt file. A simple test case is also included.
I tested the code and it works fine. But I did not have much idea about if the code style is good, or if there are some potential issues. Can someone please do a quick review and kindly provide some feedback?
1. Is there any potential issue in the code? did I miss some boundary check?
2. Is the code style good in general? e.g, name convention, indent, etc.
3. what can I do if I want to make it more professional? e.g., better choice of functions, error-handling, object-oriented, test-driven, etc.
require 'test/unit'
class BlankLineRemover
def initialize()
puts "BlankLineRemover initialized."
end
def generate(input_filename, output_filename)
f = File.new(output_filename, "w")
f.close
end
def remove(stringToremove)
regEx = /^[\s]*$\n/ stringToReturn = stringToremove.gsub(regEx, '') stringToReturn.strip! if stringToReturn.length >= 1 return stringToReturn else return "" end end end class TestCleaner < Test::Unit::TestCase def test_basic sInput1 = "line1\n\t\nline4\n\tline5\n" sExpectedOutput1 = "line1\nline4\n\tline5" sInput2="" sExpectedOutput2 = "" sInput3="\n\t\t\n" sExpectedOutput3 = "" testCleaner = BlankLineRemover.new assert_equal(sExpectedOutput1, testCleaner.remove(sInput1)) assert_equal(sExpectedOutput2, testCleaner.remove(sInput2)) assert_equal(sExpectedOutput3, testCleaner.remove(sInput3)) end end unless ARGV.length == 2 puts "Usage: ruby Blanker.rb input.txt output.txt\n" exit end simpleRemover = BlankLineRemover.new simpleRemover.generate(ARGV[0],ARGV[1]) • On the method remove you have an if/else that could be re-written as stringToReturn.length >= 1 ? stringToReturn : "", but to check that a string has a size bigger than one you're better of with !stringToReturn.empty? but then again the only way to fall on that else is if stringToReturn is an empty string (which is the return value of the else) and therefore you don't need that if/else at all and simply let stringToReturn.strip! be the return value of that method. – derp Sep 22 '11 at 4:16 • I think, it is not great idea to read full file at once, you may need to read it line by line and populate result file in a go. Also, you can remove "()" parameterless method declaration. Usually, only underscores are used in variable and method names in Ruby to separate words instead of camel case. – taro Sep 22 '11 at 15:55 ## 3 Answers I would also remove the following: \r\n Also, this part could be simplified a tad: if stringToReturn.length >= 1 return stringToReturn else return "" end to: stringToReturn.length >= 1 ? stringToReturn : "" Once you have the \r\n removed, don't forget to test for that. Lastly (just a style issue), I wouldn't use camelcase variables in Ruby as it's not commonly done (that I've seen), so stringToremove could become string_to_remove for instance. • @ James - thx for yr feedback. but which "following: \r\n" did u mean? can you specify? – Jonathan Smith Sep 22 '11 at 4:29 • He means the newline \r\n, check this: en.wikipedia.org/wiki/Newline and see how it can vary depending on the OS – derp Sep 22 '11 at 4:36 • got it. thx for the clarification. ( i guess you guys know each other:) ). besides the string length check and newline, any feedbacks at other aspects like error-handling, object-oriented, testing case, file handling, etc? – Jonathan Smith Sep 22 '11 at 5:13 • @ Derp/James - I guess I have the completionist mind-set. so forgive me if i am getting overly detail-oriented here. :) – Jonathan Smith Sep 22 '11 at 5:17 • I added a little more to my answer. – james_schorr Sep 22 '11 at 13:02 What follows is a fairly harsh critique, but I'm hoping that that's what you're looking for as you seem to want to improve you ruby and programming style. Ruby is a lovely language, but getting to know it takes some time - eventually you'll realise that just about everything you write used to take twice as many lines. So, a few pointers: ## Variables Generally in ruby normal variables are underscored. So instead of aVariableName you should probably use a_variable_name. Both will work, but the latter would fit the Ruby style better. Additionally you choice of variable names seems to go from overly verbose to the opposite. Some are great, but others leave my guessing. For example where you write: reader = File.read(input_filename) I would prefer to write: in_file = File.read(in_filename) ## Functions Like your variables, the naming of your functions could do with a touch-up. Your functions do not make use of the implicit return that Ruby offers, something that is often considered a better practice. For example where you write: def remove(stringToremove) regEx = /^[\s]*$\n/
stringToReturn = stringToremove.gsub(regEx, '')
stringToReturn.strip!
if stringToReturn.length >= 1
return stringToReturn
else
return ""
end
end
In this regard I might have written:
def remove(stringToremove)
regEx = /^[\s]*$\n/ stringToReturn = stringToremove.gsub(regEx, '').strip end Also on your initialize function you include brackets in the definitions this is not required, and is discouraged. Additionally you don't need to include a initializer if there's nothing for it to do. ## Rubyness Some things you might want to consider further as you do more programming in ruby are: • Chaining. For example you can do a_string.gsub("some", "substitution").strip.reverse and other such things all in one line and still keep readability high. Obviously there's a point where it's too much, but that's your judgement. • Your code formatting is a bit out. In a lot of places you seem to be using extra spaces. For example you class definition is class BlankLineRemover and should really be class BlankLineRemover. You might be using soft-tabs here, and if that's the case - please don't. • You spacing is also very generous. Unless you're separating code into particular chunks then you can skip a few newlines. • This is a real nit-pick, but generally using .size is considered better than .length. # Rewrite Here's your main class rewritten the way I would have gone about it. class BlankLineRemover def run(in_filename, out_filename) File.open(out_filename, "w") do |out_file| out_file.write clean(File.read(in_filename)) end end def clean(input) input.gsub(/^[\s]*$\n/, "").strip
end
end
• Also, you may want to consider using File.expand_path() unless the filenames are known to be full paths. That's caught me more than once. – Jeff Welling Sep 30 '11 at 3:56
• Good point, that too. – thomasfedb Sep 30 '11 at 4:25
Here's how I might reformulate your core business logic (warning -- untested -- you should probably consider this pseudocode):
outfile = File.new(outfilename)
I might write the class around this as the 'core' method -- note that one of the keys in a dynamic language is that it's important to keep the level of abstraction of your statements consistent throughout a code 'neighborhood'. In terms of 'Rubyisms' you could demonstrate knowledge of Ruby's mixin capabilities by writing a AbstractFileTransformer that you could extend from, while includ-ing a module BlankLineRemovingCopyTransformation -- it would basically just be refactoring the class you've written into two, and then creating a 'concrete instance' which mixed both together. (Alternatively you could do this with classes and yield.) If you wish I can attempt to provide a pseudocode example here, but at any rate, let's consider your tests for a moment.
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2020-05-27 10:01:59
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http://stackoverflow.com/questions/9929630/how-to-load-a-picture-to-an-aspimage-using-a-windows-path/9929680
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# how to load a picture to an <asp:Image> using a windows path
I have a little payments webApp, our customers can install it on their IIS and work with it. They can upload their own logotype.
We are using WyBuild to update this apps, but it replaces all files on the web folder with the new version, so the logotypes are deleted, that's why we placed the customer's files in program files, so the updater can't delete them.
the problem is that I can't load the images from the following path
C:\Program Files\MyApp\ImageFoder\logo.jpg
I don't know how to do it and I'm almost sure that is not possible to load
My web application is on
C:\inetpub\wwwroot\MyApp\
I can't have the images on the webFolder because wyBuild deletes them when I'm trying to update them, I already tried the paths like this: (the don't work)
///file:c:/program files/ .... etc
so, the question is
How can I load an image to an asp:image control using it's windows path ?
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Already answered here: stackoverflow.com/questions/4843451/… Hope it helps ;) Try to do a little search next time, so you don't create duplicates. – walther Mar 29 '12 at 16:41
You need to configure an IIS Virtual Folder to point to the alternate location where the images are stored.
I wouldn't put them in Program Files, though, a sibling folder in wwwroot would be better.
Remember NTFS permissions are easy to mess up and it's easier to manage them in a single place.
Update - for locally installed, localhost-only sites Alternatively (and this is only a good idea if you have minimal amounts of traffic. NOT for public websites), you can serve files from an arbitrary location using a VirtualPathProvider. It sounds like this 'web app' is installed like a desktop app for some reason? If you want to store user data externally, the user's App Data folder would be appropriate, but ONLY if the web app refuses external connections, and can only be accessed from the machine.
Since you're dealing with images, I'd grab the imageresizing.net library and use the VirtualFolder plugin to serve the files dynamically. It's 200KB more in your project, but you get free dynamic image resizing and/or processing if you need it, and you save a few days making a VirtualPathProvider subclass work (they're a nightmare).
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I agree with Computer Linguist. Putting images to be referenced by a web application into Program Files is a REALLY bad idea from a security standpoint. – JamieSee Mar 29 '12 at 16:45
Is it possible to store images in different Virtual directory? – Pankaj Mar 29 '12 at 16:52
@Pankaj A virtual directory can be named anything - it's a virtual folder within the site, like /images or /assets/images. It can point to any physical location (even a remote server, although that is terribly problematic). But you have to make sure the NTFS permissions are correct so you don't have security problems. – Nathanael Jones Mar 29 '12 at 16:56
@PankajGarg in my opinion there won't be a problem. You can have all your images stored on a different server completely. The only problem here is the IIS restrictions on how to treat local files... – walther Mar 29 '12 at 16:57
@ComputerLinguist - You mean, I have to create another Virtual Directory and this will be outside the current Virtual Directory or inside ? My query is in context of IIS 7 – Pankaj Mar 29 '12 at 16:59
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2015-08-01 21:27:05
|
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https://cstheory.stackexchange.com/questions/14480/efficient-asympotically-universal-predictors
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# Efficient asympotically universal predictors
A computable predictor is an algorithm $A$ computing a function $f_A : \{0,1\}^* \rightarrow \{0,1\}$. We regarding the function as providing a predicted continuation of a finite binary sequence. We define an infinite binary sequence $\alpha \in \{0,1\}^\omega$ to be comprehensible for $A$ when
$$\exists n > 0 \, \forall m > n \, f_A(\alpha_{<m})=\alpha_m$$
i.e. sufficiently late in the sequence, $A$ always predicts $\alpha$ correctly.
Obviously $\alpha$ can only be comprehensible when it's computable. It's also easy to see that for any computable predictor $A$, $\exists \alpha$ computable s.t. $\alpha$ is not comprehensible for $A$. For example, we can define $\alpha$ recursively by
$$\alpha_{n} := \lnot f_A(\alpha_{<n})$$
On the other hand, it is possible to define $p : \{0,1\}^* \rightarrow \{0,1\}$ uncomputable s.t. all computable sequences are comprehensible for $p$. For example, $p(x)$ can be defined to be $\alpha_{|x|}$ where $\alpha$ is the minimal Kolmogorov complexity infinite sequence satisfying $\alpha_{<|x|} = x$.
So, it is impossible to construct a universal computable predictor, but we can try to make it "approximately universal". Formally, an infinite sequence of computable predictors $\{A_n\}_{n \in \mathbb{N}}$ is called asymptotically universal when $\forall \alpha \in \{0,1\}^\omega$ computable $\exists n > 0 \, \forall m > n: \alpha$ is comprehensible for $A_m$. It is easy to construct an example of such a sequence. Namely, define $A_n(x)$ to be the following program: "Run the first $n$ programs producing infinite sequences by dovetailing. The first time one of those programs produces output $y$ s.t. $|y| = |x| + 1$ and $y_{<|x|} = x$, terminate and produce the output $y_{|x|}$. If all of the programs produced outputs of length > $|x|$ and neither satisfied the condition, terminate and produce the output $0$".
Suppose $A_n$ from the above example is a run on $\alpha \in \{0,1\}^\omega$ produced by an algorithm $B$. For $n >> 0$ the time of the computation of $A_n(\alpha_{<k})$ is bounded by $p(t(k), 2^{|B|})$ where $t$ is the time complexity of $B$ and $p$ is polynomial. That is:
$$\forall B \, \exists n \, \forall N > n \, \forall k: T(A_N(\alpha(B)_{<k})) < p(t(k), 2^{|B|})$$
It seems natural to ask whether this can be improved. Specifically, we define an asymptotically universal sequence of computable predictors $\{E_n\}_{n \in \mathbb{N}}$ to be efficient when the time of the computation $E_n(\alpha_{<k})$ as above can be bounded by $q(t(k),|B|)$ with $q$ polynomial, given $n >> 0$. The question is thus
Is there an efficient asymptotically universal sequence of computable predictors?
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2019-10-21 15:42:22
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http://mathoverflow.net/questions/50126/if-the-n-th-root-of-unity-exists-locally-does-it-exist-globally
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# If the n-th root of unity exists locally, does it exist globally?
My question is: is it true that $\zeta_n$ is in $K$ (a number field) iff $\zeta_n$ is in all but finitely many of the $K_{\mathfrak{p}}$?
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Yeah, I guess you're right... – Makhalan Duff Dec 22 '10 at 4:16
But Grunwald-Wang aside, the answer to the question is affirmative since one is asking if the Galois splitting field $K'/K$ of the $n$th cyclotomic polynomial is the trivial extension when it is so locally, which is immediate from Chebotarev. – BCnrd Dec 22 '10 at 4:20
[The beginning of the preceding comment refers to another comment, since deleted, that mentioned an argument involving Grunwald-Wang.] – BCnrd Dec 22 '10 at 11:11
(that comment was referring to a previous version of the question, which got fixed - sorry for confusion.) – Hunter Brooks Dec 22 '10 at 15:39
The answer is yes, and this follows (as BCnrd points out in the comments above) immediately from the Chebotarev Density Theorem. See e.g. Corollary 9 here.
More generally, let $K$ be any global field and $f \in K[t]$ be any irreducible, separable polynomial of degree $d > 1$. Then there are infinitely many places $v$ of $K$ such that $f$ does not split completely over $K_v$. Indeed, let $\alpha$ be a root of $f$ in a separable closure of $K$, let $L = K[\alpha]$ and let $M$ be the Galois closure of $L/K$. A finite place $v$ of $K$ splits completely in $L$ iff it splits completely in $M$ (Exercise 5.1.3), so by Chebotarev's Theorem, the set of primes which do not split completely in $L$ has density $1 - \frac{1}{[M:K]} > 0$.
If $L/K$ is already Galois, the argument is simpler and the conclusion is stronger: there are infinitely many places $v$ of $K$ such that $f$ does not have any $K_v$-rational roots. This is the case in the OP's question, which we recover by taking $f$ to be the minimal polynomial over $K$ of any one primitive $n$th root of unity.
On the other hand for every composite number $d$, there is a degree $d$ irreducible polynomial $f \in K[t]$ which is reducible in every completion $K_v$: this is a 2005 theorem of Guralnick, Schacher and Sonn.
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This is only a partial answer.
The statement is true if $n$ is large relative to the degree of $K/\mathbb{Q}$. Namely, let $n$ be such that $\zeta_n$ is not in $K$ with $n\gg [K: \mathbb{Q}]$. Then choose $b\in \mathbb{Z}/n\mathbb{Z}$ such that $(b, n)=1$ and such that $b^m\not= 1$ for all $m\leq[K: \mathbb{Q}]$, which is possible as $n$ is large. By e.g. Dirichlet's theorem on primes in arithmetic progression, there are infinitely many primes $p\in \mathbb{Z}$ with $p\equiv b\mod n$. Let $\mathfrak{p}$ be any prime in $\mathcal{O}_K$ lying above such a $p$. Then the residue field $\mathcal{O}_K/\mathfrak{p}=\mathbb{F}_{p^m}$ for some $m\leq [K: \mathbb{Q}]$. Furthermore, by our choice of $p$, $p^m\not\equiv 1\bmod n$, and thus $n$ does not divide the order of $\mathbb{F}_{p^m}^\times$, so $1$ does not have an $n$-th root in $\mathcal{O}_K/\mathfrak{p}$, and thus it does not have such a root in $K_\mathfrak{p}$.
But there are infinitely many such $\mathfrak{p}$ (any $\mathfrak{p}$ lying above a $p$ as chosen via Dirichlet's theorem works), so we have established the claim.
EDIT: I see BCnrd has answered the question in comments, but I figure the above might still be of interest.
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2015-10-05 01:57:14
|
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https://www.expii.com/t/product-and-quotient-rules-for-derivatives-143
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Expii
# Product and Quotient Rules for Derivatives - Expii
The product and quotient rules tell you how to differentiate a product fg or quotient f/g, given the derivatives and values of the original functions f and g themselves.
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2022-11-29 20:36:39
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https://math.stackexchange.com/questions/1754691/natural-action-of-mathbbzg-on-mathbbz
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# Natural action of $\mathbb{Z}G$ on $\mathbb{Z}$?
I'm studying projective modules and I'm having problem coming up with (or understanding) examples of non-free projective modules. I got that when a ring is a direct sum $R = A \oplus B$, both $A$ and $B$ are non-free projective $R$-modules via the action:
$$\psi: R\times A \to A, ((a, b), a') \mapsto aa'$$
Then I tried to attack the following question:
For what groups $G$ is $\mathbb{Z}$ a projective $\mathbb{Z}G$-module? (Hint: When does $\epsilon: \mathbb{Z}G \to \mathbb{Z}$ split as a map of $G$-modules?)
But I fail to see how would $\mathbb{Z}$ be a $\mathbb{Z}G$-module with a non-trivial action. On the hint, I also fail to see how $\mathbb{Z}$ would be a $G$-module other than with the trivial action. Is it for me to consider them as the modules with trivial action? I can't see a natural way for either $\mathbb{Z}G$ or $G$ to act on $\mathbb{Z}$.
Also, is the map $\epsilon$ referring to the augmentation of the group ring $\mathbb{Z}G$?
I believe that my deeper problem is with looking $\mathbb{Z}$ (the 'small' structure) as a $\mathbb{Z}G$-module (the 'big' structure), and not the other way. Is very simple to see $\mathbb{Z}G$ as a $\mathbb{Z}$ module, once $\mathbb{Z}$ is a substructure of $\mathbb{Z}G$. But I can't see how and why I would look the big structure acting on the smaller, substructure one! In the first example, when a ring is a direct sum, I was able to understand the action, but I don't know why it would be interesting to look at things this way and not the other way around ($R$ as a $A$-module or a $B$-module).
• I think the main issue here is that you are looking for a non-trivial action. The map $\epsilon$ is probably the counit which indeed corresponds to the trivial action of $G$ on $\mathbb{Z}$ (not that no groups have non-trivial actions, it is just that not all do, and in this case it really is hinting at using the trivial action). – Tobias Kildetoft Apr 22 '16 at 20:45
• @TobiasKildetoft I see. It's just that the trivial action seems so.. trivial. If I say something is a $X$-module with trivial action, then why does it matter that it is a $X$-module? Anything could be $X$-module with trivial action. In my case, I thought I might just look $\epsilon$ as a map of groups, and not modules, since the "module" part would be simply a map from the action of $G$ on $\mathbb{Z}G$ to zero. Also, I never heard of the counit map. Is it another name for augmentation, or something completely different? – Henrique Augusto Souza Apr 22 '16 at 20:56
• Yes, it is another name for the augmentation (it is called the counit when the ring is considered as a Hopf algebra). Note that having a trivial action is not something all rings do (note that the trivial action is not the same as all elements acting trivially, just the the group elements do). – Tobias Kildetoft Apr 22 '16 at 21:06
It only holds for the trivial group.
As it was mentioned in the comments, we consider $\mathbb{Z}$ as a trivial $\mathbb{Z}G$-module and in this way the augmentation map $\epsilon \colon \mathbb{Z}G \to \mathbb{Z}$ is a morphism of $\mathbb{Z}G$-modules.
Let $f \colon \mathbb{Z} \to \mathbb{Z}G$ be a morphism of $\mathbb{Z}G$-modules and say $f(1) = \sum_{h \in G} n_h h$ where all the $n_h=0$ except for a finite number of them. Then we have for any $g \in G$,
$$g \cdot f(1) = f(g \cdot 1) = f(1)$$
because $f$ is a morphism of $\mathbb{Z}G$-modules and $\mathbb{Z}$ is a trivial $\mathbb{Z}G$-module. Therefore
$$\sum_{h \in G} n_h gh = \sum_{h \in G} n_h h$$
If $\epsilon \circ f$ is the identity, then $f$ can not be identically zero, so there must be an $h$ in the group such that $n_h \neq 0$.
Pick an $h$ such that $n_h \neq 0$ and choose $g=h^{-1}$. In this case, the equality tells us that the coefficient of the identity element $e$ must be $n_h$, that is, $n_h = n_e$. Similarly, given $k$ in $G$ we can choose $g=k$ and we would conclude that $n_k = n_e$. And therefore setting $n = n_e$
$$f(1) = \sum_{g \in G} n g$$
with $n \neq 0$. For this to make sense as an element of $\mathbb{Z}G$, the group $G$ has to be finite. But then $\epsilon f(1) = n|G|$, so the only way this can be the identity is if $n=1$ and $|G|=1$, that is, $G$ is the trivial group. Of course, if $G$ is the trivial group, then $\mathbb{Z}G = \mathbb{Z}$ and certainly $\mathbb{Z}$ is projective over $\mathbb{Z}$, it is free.
So that answers your question, but just for fun, this would have been different if we had asked the same question about $\mathbb{Q}G$. If $G$ is a finite group, $\mathbb{Q}$ is a proyective $\mathbb{Q}G$-module, for in the argument above we could have set
$$f(1) = \sum_{g \in G} \frac{1}{|G|}g$$
and $\epsilon f(1) = 1$. If you are familiar with representation theory of finite groups, this is a disguised form of saying that the regular representation of $G$ over $\mathbb{Q}$ contains a copy of the trivial representation of $G$ over $\mathbb{Q}$.
• The last comment is a bit misleading, as it also holds over the integers. The map just does not split the augmentation in that case. Good answer though. – Tobias Kildetoft May 20 '16 at 16:58
• You are correct. Maybe I should add here that even though the trivial representation is also a subrepresentation of regular representation over the integers, subrepresentations are not necessarily direct summands in this case. What is different for the rationals (or any field of characteristic zero) is that subrepresentations are direct summands. – Goa'uld May 20 '16 at 17:05
• @Goa'uld please help me to solve this problem math.stackexchange.com/questions/3025927/… thanks – neelkanth Dec 4 '18 at 18:32
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2019-08-25 01:06:45
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http://discretemath.org/ads/solutions-backmatter.html
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## SolutionsDHints and Solutions to Selected Exercises
For the most part, solutions are provided here for odd-numbered exercises.
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2019-11-19 00:34:14
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https://proofwiki.org/wiki/Union_of_Transitive_Class_is_Subclass
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# Union of Transitive Class is Subclass
## Theorem
Let $A$ be a transitive class.
Let $\ds \bigcup A$ denote the union of $A$.
Then:
$\ds \bigcup A \subseteq A$
## Proof
Let $A$ be transitive.
Let $x \in \ds \bigcup A$.
Then by definition:
$\exists y \in A: x \in y$
By definition of transitive class:
$x \in y \land y \in A \implies x \in A$
and so:
$x \in A$
Hence the result by definition of subclass.
$\blacksquare$
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2022-07-01 02:24:23
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https://docs.cemosis.fr/msqab/latest/index.html
|
# Modeling and Simulation of Air Quality in Bamako
The air pollution is one of the biggest killers in the world [WHO]. Since the monitoring of urban pollutants is very expensive, the modeling of the pollutants dispersion is an alternative that offers good results in the study of air quality [Kumar] and covers the pollution transport and diffusion in the atmosphere, its dry and wet deposition and chemical reactions and depends on pollutant properties, meteorological conditions, emission data and terrain parameters.
Let $c$ be a vector of concentration fields, where each element $c_i$ corresponds to the scalar field of concentration of the chemical species (pollutant) labelled by $i$ in the air. The spatio-temporal evolution of the concentration $c_i$ is described by the following advection-diffusion-reaction model:
$\dfrac{\partial c_i}{\partial t} = - \underbrace{\nabla \cdot \left ( \mathbf{u} c_i \right)\ }_{\text{advection}} + \underbrace{\nabla \cdot \left ( \rho K \nabla \left ( \dfrac{c_i}{\rho} \right) \right )}_{\text{diffusion}} + \underbrace{\chi_i (c)}_{\text{chemistry}} - \underbrace{\Lambda_i(x,t)c_i}_{\text{deposit}} + \underbrace{S_i(x,t)}_{\text{volumic sources}}$
where
• $\rho$: air density
• $K$: diffusion coefficient
• $\mathbf{u}$: wind velocity
• $\chi_i$: chemical source term that describes the chemical reactions
• $\Lambda_i$: scavenging coefficient
• $S_i$: source terms
• $x$: spatial coordinates
• $t$: time coordinates
The advection corresponds to transport by the wind field, and the diffusion describes the turbulent mixing. The reaction corresponds to the physical and chemical processes of transformation of pollutants.
The model is based on the assumption that there is no feedback between the chemical species and the flow fields (wind velocity, turbulent diffusivity, temperature). We assume that the flow is incompressible, which means the variations in density $\rho$ are assumed to be constant.
## 4. Bibliography
• [WHO] W.H.Organization, Air pollution, www.who.int/phe, 2020.
• [Kumar] S.Kumar, R.Kumar, Air Quality: Monitoring and Modeling, BoD-Books on Demand, 2012.
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2021-12-02 18:20:18
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|
http://quant.stackexchange.com/questions?page=5&sort=active
|
# All Questions
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### Calculating index arbitrage
I have a days-worth of level 2 market data. I am calculating S&P500 index arbitrage. I have a few questions about the calculation: 1) Should I be summing all the bids and asks from the stocks ...
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### Position Sizing For Ratio Pairs Trade
Ok, let's say I'm trading a spread of two stocks, X & Y, The spread is calculated as a ratio (Spread = X / Y). I use rolling stats to calculate the mean, standard deviation and hence the z-score ...
I'm simply interested on hearing some views on which shortcomings arise by using the (multidimensional) SDE $$dS(t)=S(t)\alpha(t,S(t))dt+S(t)\sigma(t,S(t))dW(t)$$ as a model for asset prices. I know ...
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2014-03-10 05:19:37
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https://zbmath.org/authors/?q=ai%3Ahajek.jaroslav
|
# zbMATH — the first resource for mathematics
## Hájek, Jaroslav
Compute Distance To:
Author ID: hajek.jaroslav Published as: Hajek, J.; Hajek, Jaroslav; Hájek, J.; Hájek, Jaroslav External Links: MGP · Math-Net.Ru · Wikidata · GND · MacTutor
Documents Indexed: 54 Publications since 1955, including 7 Books Biographic References: 7 Publications
all top 5
#### Co-Authors
45 single-authored 2 Dupac, Vaclav 2 Šidák, Zbyněk 1 Dalenius, Tore 1 Fabian, František 1 Fischer, Otto F. 1 Kimeldorf, George S. 1 Koutník, Václav 1 Novotný, Miroslav 1 Rényi, Alfréd 1 Sekanina, Milan 1 Sen, Pranab Kumar 1 Zubrzycki, Stefan
all top 5
#### Serials
6 Časopis Pro Pěstování Matematiky 6 Czechoslovak Mathematical Journal 6 Selected Translations in Mathematical Statistics and Probability 5 Annals of Mathematical Statistics 3 Aplikace Matematiky 2 The Annals of Statistics 2 Bulletin de l’Institut International de Statistique 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Zastosowania Matematyki 1 Theory of Probability and its Applications 1 Colloquium Mathematicum 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Proceedings of the National Academy of Sciences of the United States of America 1 Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Series A 1 Statistics: Textbooks and Monographs 1 Wiley Series in Probability and Statistics
#### Fields
19 Statistics (62-XX) 5 Probability theory and stochastic processes (60-XX) 2 History and biography (01-XX) 1 General and overarching topics; collections (00-XX) 1 Geometry (51-XX)
#### Citations contained in zbMATH
34 Publications have been cited 1,296 times in 1,099 Documents Cited by Year
Theory of rank tests. Zbl 0161.38102
Hájek, Jaroslav; Šidák, Zbyněk
1967
Theory of rank tests. 2nd ed. Zbl 0944.62045
Hájek, Jaroslav; Šidák, Zbyněk; Sen, Pranab K.
1999
Asymptotic normality of simple linear rank statistics under alternatives. Zbl 0187.16401
Hájek, Jaroslav
1968
A characterization of limiting distributions of regular estimates. Zbl 0193.18001
Hajek, J.
1970
Asymptotic normality of linear rank statistics under alternatives. Zbl 0162.50503
Hajek, J.
1967
Asymptotic theory of rejective sampling with varying probabilities from a finite population. Zbl 0138.13303
Hájek, Jaroslav
1964
Some extensions of the Wald-Wolfowitz-Noether theorem. Zbl 0107.13404
Hajek, J.
1961
Generalization of an inequality of Kolmogorov. Zbl 0067.10701
Hájek, J.; Rényi, Alfréd
1955
Asymptotically most powerful rank-order tests. Zbl 0133.42001
Hajek, J.
1962
Limiting distributions in simple random sampling from a finite population. Zbl 0102.15001
Hajek, Jaroslav
1960
Local asymptotic minimax and admissibility in estimation. Zbl 0281.62010
Hajek, Jaroslav
1972
Sampling from a finite population. Ed. by Václav Dupač. Zbl 0494.62008
Hájek, Jaroslav
1981
A course in nonparametric statistics. Zbl 0193.16901
Hajek, J.
1969
Optimum strategy and other problems in probability sampling. Zbl 0138.13301
Hajek, J.
1959
On linear statistical problems in stochastic processes. Zbl 0114.34504
Hajek, J.
1962
On a property of normal distributions of any stochastic process. Zbl 0086.33503
Hájek, Jaroslav
1958
Asymptotic sufficiency of the vector of ranks in the Bahadur sense. Zbl 0286.62026
Hajek, Jaroslav
1974
Asymptotic normality of simple linear rank statistics under alternatives. II. Zbl 0193.17401
Dupač, Václav; Hájek, Jaroslav
1969
A property of $$J$$-divergences of marginal probability distributions. Zbl 0082.34103
Hájek, Jaroslav
1958
Asymptotic theory of rejective sampling from a finite population. Zbl 0156.40103
Hajek, J.
1965
Inequalities for the generalized Student’s distribution and their applications. Zbl 0111.34107
Hajek, J.
1962
On plane sampling and related geometrical problems. Zbl 0213.43803
Dalenius, Tore; Hájek, Jaroslav; Zubrzycki, Stefan
1961
Extension of the Kolmogorov-Smirnov test to regression alternatives. Zbl 0142.15802
Hajek, Jaroslav
1965
Predicting a stationary process when the correlation function is convex. Zbl 0080.13003
Hájek, Jaroslav
1958
Collected works of Jaroslav Hájek. With commentary. Zbl 0903.01017
Hájek, Jaroslav
1998
Regression designs in autoregressive stochastic processes. Zbl 0282.62067
Hajek, Jaroslav; Kimeldorf, George
1974
On basic concepts of statistics. Zbl 0214.45704
Hájek, J.
1967
On linear estimation theory for an infinite number of observations. Zbl 0114.35504
Hajek, J.
1962
On a property of normal distributions of any stochastic process. Zbl 0112.09702
Hájek, Jaroslav
1961
Asymptotic normality of the Wilcoxon statistic under divergent alternatives. Zbl 0237.62039
Dupac, V.; Hajek, J.
1969
Locally most powerful rank tests of independence. Zbl 0187.16103
Hajek, J.
1968
Theorie der Wahrscheinlichkeitsstichproben mit Anwendungen auf Stichprobenuntersuchungen. [Teorie pravděpodobnostního výběru s aplikacemi na výběrová šetření.]. Zbl 0097.34203
Hájek, Jaroslav
1960
Some contributions to the théory of probability sampling. Zbl 0091.14804
Hájek, Jaroslav
1959
Linear estimation of the mean value of a stationary random process with convex correlation function. Zbl 0112.09701
Hájek, Jaroslav
1956
Theory of rank tests. 2nd ed. Zbl 0944.62045
Hájek, Jaroslav; Šidák, Zbyněk; Sen, Pranab K.
1999
Collected works of Jaroslav Hájek. With commentary. Zbl 0903.01017
Hájek, Jaroslav
1998
Sampling from a finite population. Ed. by Václav Dupač. Zbl 0494.62008
Hájek, Jaroslav
1981
Asymptotic sufficiency of the vector of ranks in the Bahadur sense. Zbl 0286.62026
Hajek, Jaroslav
1974
Regression designs in autoregressive stochastic processes. Zbl 0282.62067
Hajek, Jaroslav; Kimeldorf, George
1974
Local asymptotic minimax and admissibility in estimation. Zbl 0281.62010
Hajek, Jaroslav
1972
A characterization of limiting distributions of regular estimates. Zbl 0193.18001
Hajek, J.
1970
A course in nonparametric statistics. Zbl 0193.16901
Hajek, J.
1969
Asymptotic normality of simple linear rank statistics under alternatives. II. Zbl 0193.17401
Dupač, Václav; Hájek, Jaroslav
1969
Asymptotic normality of the Wilcoxon statistic under divergent alternatives. Zbl 0237.62039
Dupac, V.; Hajek, J.
1969
Asymptotic normality of simple linear rank statistics under alternatives. Zbl 0187.16401
Hájek, Jaroslav
1968
Locally most powerful rank tests of independence. Zbl 0187.16103
Hajek, J.
1968
Theory of rank tests. Zbl 0161.38102
Hájek, Jaroslav; Šidák, Zbyněk
1967
Asymptotic normality of linear rank statistics under alternatives. Zbl 0162.50503
Hajek, J.
1967
On basic concepts of statistics. Zbl 0214.45704
Hájek, J.
1967
Asymptotic theory of rejective sampling from a finite population. Zbl 0156.40103
Hajek, J.
1965
Extension of the Kolmogorov-Smirnov test to regression alternatives. Zbl 0142.15802
Hajek, Jaroslav
1965
Asymptotic theory of rejective sampling with varying probabilities from a finite population. Zbl 0138.13303
Hájek, Jaroslav
1964
Asymptotically most powerful rank-order tests. Zbl 0133.42001
Hajek, J.
1962
On linear statistical problems in stochastic processes. Zbl 0114.34504
Hajek, J.
1962
Inequalities for the generalized Student’s distribution and their applications. Zbl 0111.34107
Hajek, J.
1962
On linear estimation theory for an infinite number of observations. Zbl 0114.35504
Hajek, J.
1962
Some extensions of the Wald-Wolfowitz-Noether theorem. Zbl 0107.13404
Hajek, J.
1961
On plane sampling and related geometrical problems. Zbl 0213.43803
Dalenius, Tore; Hájek, Jaroslav; Zubrzycki, Stefan
1961
On a property of normal distributions of any stochastic process. Zbl 0112.09702
Hájek, Jaroslav
1961
Limiting distributions in simple random sampling from a finite population. Zbl 0102.15001
Hajek, Jaroslav
1960
Theorie der Wahrscheinlichkeitsstichproben mit Anwendungen auf Stichprobenuntersuchungen. [Teorie pravděpodobnostního výběru s aplikacemi na výběrová šetření.]. Zbl 0097.34203
Hájek, Jaroslav
1960
Optimum strategy and other problems in probability sampling. Zbl 0138.13301
Hajek, J.
1959
Some contributions to the théory of probability sampling. Zbl 0091.14804
Hájek, Jaroslav
1959
On a property of normal distributions of any stochastic process. Zbl 0086.33503
Hájek, Jaroslav
1958
A property of $$J$$-divergences of marginal probability distributions. Zbl 0082.34103
Hájek, Jaroslav
1958
Predicting a stationary process when the correlation function is convex. Zbl 0080.13003
Hájek, Jaroslav
1958
Linear estimation of the mean value of a stationary random process with convex correlation function. Zbl 0112.09701
Hájek, Jaroslav
1956
Generalization of an inequality of Kolmogorov. Zbl 0067.10701
Hájek, J.; Rényi, Alfréd
1955
all top 5
#### Cited by 1,229 Authors
34 Sen, Pranab Kumar 21 Hallin, Marc 17 Puri, Madan Lal 16 Janssen, Arnold 14 Hušková, Marie 13 Bandyopadhyay, Uttam 10 Berger, Yves G. 10 Jurečková, Jana 10 Schick, Anton 9 Kössler, Wolfgang 9 Koziol, James A. 9 Shiraishi, Taka-aki 9 Wefelmeyer, Wolfgang 8 Akritas, Michael G. 8 Biswas, Atanu 8 Koul, Hira Lal 7 Hettmansperger, Thomas P. 7 Höpfner, Reinhard 7 Mukherjee, Amitava 7 Paindaveine, Davy 7 Tardif, Serge 6 Bertail, Patrice 6 Clémençon, Stéphan 6 Müller, Ursula U. 6 Neuhaus, Georg 6 Ruymgaart, Frits H. 6 Seoh, Munsup 6 Tillé, Yves 6 van Eeden, Constance 5 Alvo, Mayer 5 Bindele, Huybrechts F. 5 Brunner, Edgar 5 Chauvet, Guillaume 5 Conti, Pier Luigi 5 Ghosh, Malay 5 Johnson, Richard A. 5 Klaassen, Chris A. J. 5 Milbrodt, Hartmut 5 Murakami, Hidetoshi 5 Quessy, Jean-François 5 Roussas, George Gregory 5 Rublík, František 5 Šidák, Zbyněk 5 Strasser, Helmut 5 Werker, Bas J. M. 4 Albers, Willem 4 Allal, Jelloul 4 Antille, Andre 4 Behnen, Konrad 4 Beran, Rudolf J. 4 Bickel, Peter John 4 Büning, Herbert 4 Chautru, Emilie 4 Csörgő, Miklós 4 Das, Radhakanta 4 Denker, Manfred 4 Dufour, Jean-Marie 4 Fligner, Michael A. 4 Genest, Christian 4 Haux, Reinhold 4 Horváth, Lajos 4 Janssen, Paul 4 Ledwina, Teresa 4 Mansouri, Hossein 4 Merzougui, M. 4 Nadarajah, Saralees 4 Nikitin, Yakov Yu. 4 Oja, Hannu 4 Rieder, Helmut 4 Withers, Christopher Stroude 4 Wu, Tieejian 3 Abd-Elfattah, Ehab F. 3 Antoch, Jaromír 3 Bagkavos, Dimitrios 3 Baker, Charles R. 3 Balakrishnan, Narayanaswamy 3 Bening, Vladimir E. 3 Bentarzi, Mohamed 3 Bhattacharya, Debasis 3 Bhattacharyya, Gouri K. 3 Borroni, Claudio Giovanni 3 Burger, Hans Ulrich 3 Cabaña, Alejandra 3 Cabaña, Enrique M. 3 Cardot, Hervé 3 Chatterjee, Shoutir Kishore 3 Chattopadhyay, Gopaldeb 3 del Barrio, Eustasio 3 Deville, Jean-Claude 3 Ding, Peng 3 Duran, Benjamin S. 3 Froda, Sorana M. 3 Gombay, Edit 3 Govindarajulu, Zakkula 3 Grafström, Anton 3 Greenwood, Priscilla E. 3 Hájek, Jaroslav 3 Hothorn, Torsten 3 Hwang, Tea-Yuan 3 Jammalamadaka, Sreenivasa Rao ...and 1,129 more Authors
all top 5
#### Cited in 137 Serials
128 Journal of Statistical Planning and Inference 101 Communications in Statistics. Theory and Methods 77 Statistics & Probability Letters 53 Journal of Nonparametric Statistics 44 Journal of Multivariate Analysis 43 Annals of the Institute of Statistical Mathematics 41 The Annals of Statistics 36 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 32 Journal of Econometrics 29 The Canadian Journal of Statistics 25 Journal of Statistical Computation and Simulation 25 Computational Statistics and Data Analysis 24 Statistica Neerlandica 23 Metrika 20 Stochastic Processes and their Applications 19 Statistics 18 Communications in Statistics. Simulation and Computation 17 Kybernetika 16 Aplikace Matematiky 12 Biometrical Journal 11 Probability Theory and Related Fields 11 Journal of Mathematical Sciences (New York) 11 Bernoulli 10 Sequential Analysis 10 Electronic Journal of Statistics 9 Scandinavian Journal of Statistics 8 Journal of Soviet Mathematics 8 Statistical Papers 7 Biometrics 7 Statistical Science 7 Journal of Applied Statistics 6 Journal of the American Statistical Association 6 Computational Statistics 6 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 6 Journal of Statistical Theory and Practice 5 Lithuanian Mathematical Journal 5 Journal of Time Series Analysis 5 Stochastic Analysis and Applications 5 Applications of Mathematics 5 Econometric Theory 4 Journal of Mathematical Analysis and Applications 4 Proceedings of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 Test 4 Mathematical Methods of Statistics 4 Statistical Methods and Applications 4 Statistical Methodology 3 Acta Mathematica Academiae Scientiarum Hungaricae 3 Periodica Mathematica Hungarica 3 Theory of Probability and its Applications 3 The Annals of Probability 3 Applied Mathematics and Computation 3 Czechoslovak Mathematical Journal 3 Statistical Inference for Stochastic Processes 3 Brazilian Journal of Probability and Statistics 3 AStA. Advances in Statistical Analysis 2 Mathematical Notes 2 Psychometrika 2 Journal of Approximation Theory 2 Mathematica Slovaca 2 Metron 2 Notre Dame Journal of Formal Logic 2 Trabajos de Estadistica y de Investigacion Operativa 2 American Journal of Mathematical and Management Sciences 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Theoretical Probability 2 MCSS. Mathematics of Control, Signals, and Systems 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 2 ZOR. Zeitschrift für Operations Research 2 Lifetime Data Analysis 2 Journal of Inequalities and Applications 2 Methodology and Computing in Applied Probability 2 Decisions in Economics and Finance 2 Journal of the Korean Statistical Society 2 Sankhyā. Series A 2 Statistics and Computing 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 International Journal of Systems Science 1 Journal of the Franklin Institute 1 Rocky Mountain Journal of Mathematics 1 Arkiv för Matematik 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Fuzzy Sets and Systems 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of Economic Theory 1 Journal of Mathematical Economics 1 Journal of Mathematical Psychology 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Scandinavian Actuarial Journal 1 Transactions of the American Mathematical Society 1 Moscow University Computational Mathematics and Cybernetics 1 Advances in Applied Mathematics 1 Insurance Mathematics & Economics 1 Optimization 1 Journal of Complexity ...and 37 more Serials
all top 5
#### Cited in 25 Fields
988 Statistics (62-XX) 224 Probability theory and stochastic processes (60-XX) 86 Numerical analysis (65-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Information and communication theory, circuits (94-XX) 8 History and biography (01-XX) 7 Functional analysis (46-XX) 6 Operations research, mathematical programming (90-XX) 4 Measure and integration (28-XX) 4 Computer science (68-XX) 4 Biology and other natural sciences (92-XX) 4 Systems theory; control (93-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
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2021-03-08 23:14:21
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https://academiccommons.columbia.edu/doi/10.7916/d8-1xh3-7c82
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Theses Doctoral
# Time evolution of the Kardar-Parisi-Zhang equation
Ghosal, Promit
The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way.
The Kardar-Parisi-Zhang (KPZ) equation is well-known for its applications in describing various statistical mechanical models including randomly growing surfaces, directed polymers and interacting particle systems. We consider the upper and lower tail probabilities for the centered (by time$/24$) and scaled (according to KPZ time$^{1/3}$ scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation. We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times $T$ and demonstrates a crossover between super-exponential decay with exponent $\tfrac{5}{2}$ (and leading pre-factor $\frac{4}{15\pi} T^{1/3}$) for tail depth greater than $T^{2/3}$ (deep tail), and exponent $3$ (with leading pre-factor at least $\frac{1}{12}$) for tail depth less than $T^{2/3}$ (shallow tail). We also consider the case when the initial data is drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent $3$ in the shallow tail to an exponent $\frac{5}{2}$ in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent $\frac{3}{2}$ at all depths in the tail. We study the correlation of fluctuations of the narrow wedge solution to the KPZ equation at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent $\frac{2}{3}$, while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent $-\frac{1}{3}$.
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2021-10-28 12:35:53
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http://edoc.mpg.de/display.epl?mode=doc&id=742562&col=94&grp=561
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Institute: MPI für Astronomie Collection: Publikationen_mpia Display Documents
ID: 742562.0, MPI für Astronomie / Publikationen_mpia
The search for multiple populations in Magellanic Cloud Clusters – III. No evidence for multiple populations in the SMC cluster NGC 419
Authors:
Date of Publication (YYYY-MM-DD):2017
Title of Journal:Monthly Notices of the Royal Astronomical Society
Volume:468
Start Page:3150
End Page:3158
Audience:Not Specified
Abstract / Description:We present the third paper about our ongoing HST survey for the search for multiple stellar populations (MPs) within Magellanic Cloud clusters. We report here the analysis of NGC 419, a $\sim 1.5$ Gyr old, massive ($\gtrsim 2 \times 10^5 \, {\rm M_{\odot}}$) star cluster in the Small Magellanic Cloud (SMC). By comparing our photometric data with stellar isochrones, we set a limit on [N/Fe] enhancement of $\lesssim$+0.5 dex and hence we find that no MPs are detected in this cluster. This is surprising because, in the first two papers of this series, we found evidence for MPs in 4 other SMC clusters (NGC 121; Lindsay 1, NGC 339, NGC 416), aged from 6 Gyr up to $\sim 10-11$ Gyr. This finding raises the question whether age could play a major role in the MPs phenomenon. Additionally, our results appear to exclude mass or environment as the only key factors regulating the existence of a chemical enrichment, since all clusters studied so far in this survey are equally massive ($\sim 1-2 \times 10^5 \, {\rm M_{\odot}}$) and no particular patterns are found when looking at their spatial distribution in the SMC.
External Publication Status:published
Document Type:Article
Communicated by:N. N.
Affiliations:MPI für Astronomie
Identifiers:ISSN:0035-8711
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2020-08-13 03:37:23
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https://brilliant.org/discussions/thread/imo/
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×
# IMO
how shall i study for IMO . what else shall is i study out of the CBSE course of class 10?
Note by Avn Bha
2 years, 11 months ago
Sort by:
@Sean Ty just suggested me this book
book
For studying trigonometry S.L Loney Part 1 and 2 are really nice
- 2 years, 11 months ago
@megh choksi -The books you have suggested would not serve his purpose I would ask you to suggest him books for the "SOF -IMO" he is referring to...
- 2 years, 11 months ago
In that case, the NCERT textbooks are more than sufficient. I would recommend going through the textbook of the immediately higher grade for the same.
- 2 years, 11 months ago
Subrata saha -could you please mail me the list of books i have given my mail ID below
- 2 years, 11 months ago
my mail id-- avneeshbhale7@gmail.com
- 2 years, 11 months ago
@avn bha can I have your email id then I can email you the list?
- 2 years, 11 months ago
Mail them to me too. sualehasif996@gmail.com I would be really grateful @Subrata Saha
- 2 years, 11 months ago
Me too mail the list of books email id - choksimegh1@gmail.com @Subrata Saha
- 2 years, 11 months ago
I have mailed it
- 2 years, 11 months ago
Recieved . Thank you sir
- 2 years, 11 months ago
Did'nt recieved @Subrata Saha
- 2 years, 11 months ago
You can visit websites of ISI, CALCUTTA and HBCSE they have list of books recommended from RMO level to IMO
- 2 years, 11 months ago
is there something other than SOF -IMO ?
- 2 years, 11 months ago
Well, haven't you heard of RMO, INMO ? I think SOFIMO doesn't require any extra knowledge other than class 10 RD SHARMA or RS AGARWAL
- 2 years, 11 months ago
That's right !
- 2 years, 2 months ago
×
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2017-10-21 06:36:00
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https://dsp.stackexchange.com/questions/16487/suitable-metrics-for-summarizing-or-visualizing-the-spatial-activation-of-compon
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# Suitable metrics for summarizing or visualizing the spatial activation of components after temporal Independent Component Analysis (ICA)
I will first describe the Independent Component Analysis (ICA) steps, so that the question becomes clearer, and more relevant to similar questions.
Assume we have $N$ sensors distributed in space. From each sensor we obtain a time series of length $T$. We collect these time series as rows in an $N \times T$ matrix $X$. After performing ICA we obtain a decomposition of the form $X = DS$, where $D$ is an $N \times N$ matrix of weights, and $S$ is an $N \times T$ matrix whose rows are the independent sources. To find the contribution of the $i$-th component to the observed signal we then multiply the $i$-th column of the matrix $D$ with the $i$-th row of $S$. The result is an $N \times T$ matrix which we will denote as $X^{i} = D_{*,i}S_{i,*}$. Then we can write: $X = X^{1} + ... + X^{i} + ... + X^{N}$.
In many domains I see single-picture visualizations of the spatial activation of the $i$-th component from ICA. However, it is not clear to me what metric to extract from each row of $X^{i}$ or from matrix $D$ in order to do this. Is it a summary statistic of the rows of $X^{i}$, e.g. the energy of the signals (rows) of $X^{i}$, the weighting coefficients from the $i$-th column of $D$, or something different altogether?
Thank you.
• Can you put up such a picture of the spatial activation of an i-th component that you are seeing? Each row of the $X_i$ matrix will have a (spatially) scaled version the $i$th original signal. – Tarin Ziyaee May 24 '14 at 20:04
• For example, this is a picture with the activation per component (32 sensors and components) from ICA-decomposed EEG data: ICA EEG. What does "spatially scaled" mean? – Orestis Tsinalis May 24 '14 at 20:29
• Sorry, can't edit my comment above. By "spatially scaled" do you mean that the $i$-th source signal is scaled (because of its distance to the source) to construct each row of the $X^{i}$ matrix? If so, the single value that is used for the sensor $k$ in the visualizations is the weight from the $i$-th column and $k$-th row of $D$, $D_{k,i}$, right? Then for the visualization of the $i$-th component, for each sensor $k$ we assign at its location in the image the value $D_{k,i}$. Is this what you meant? – Orestis Tsinalis May 24 '14 at 20:40
• Firstly, what units does the heatmap in the image represent? – Tarin Ziyaee May 24 '14 at 20:43
• As far as I know, it is not specified in the tutorial of the toolbox where the image comes from (EEGLab ICA tutorial). The image comes automatically out of the ICA analysis, but it is not clear how it is computed. – Orestis Tsinalis May 24 '14 at 20:47
As we know from the instantaneous mixture model of ICA, a signal mixture $X_{N,T}$ is composed of an unknown mixing matrix $D_{N,N}$, and an unknown signal matrix $S_{N,T}$, where:
$$X = DS$$
In ICA, we solve for $D_{N,N}$ and $S_{N,T}$ via maximization of absolute kurtosis. (As one method).
If we now look at the $i$th column of $D$, each element therein will now give us weight by which the $i$th signal gets weighted by in all $N$ mixtures. That is, each element $D_{n,i}$, (row $n$, column $i$), gives us signal $i$'s contribution to mixture $n$.
Those are called 'spatial weights' simply because in many ICA applications, we are de-mixing signals that sample a spatial field at different locations. Thus, each element of a column $D$ corresponds to a weight in space, that weighs signal source $i$.
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2021-04-13 19:02:54
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http://mathoverflow.net/feeds/question/76890
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How to estimate the pressure? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T04:44:50Z http://mathoverflow.net/feeds/question/76890 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/76890/how-to-estimate-the-pressure How to estimate the pressure? Danny Calegari 2011-09-30T22:05:22Z 2011-10-01T01:34:47Z <p>I have a finite collection of diffeomorphisms $g_1,\cdots,g_n$ taking the unit interval $I$ to disjoint subintervals $I_1, I_2,\cdots,I_n$. If $G$ is the semigroup they generate, the limit set of $G$ (also called the attractor of the IFS) is a Cantor set, and under suitable hypotheses, Bowen (and under slightly weaker hypotheses, Urbanski) showed that the Hausdorff dimension of this Cantor set is the smallest zero of the pressure function $P$, defined by $$P(t) = \lim_{n \to \infty} \frac 1 n \log \sum_{w \in G_n} \|w'\|^t$$ where $G_n$ is the set of elements in $G$ of word length $n$, and $\|\cdot\|$ is the sup norm (the hypotheses for Bowen's theorem is that the $g_i$ are uniformly contracting; Urbanski proves the same theorem when the $g_i$ are allowed to have neutral fixed points; my examples have such points).</p> <p>This is all well and good, but how do I actually estimate the least zero of the pressure function for an explicit example? (yes, I mean numerically) My $g_i$ are all given by the restrictions of explicit polynomial functions of low degree, but the computational bottleneck seems to be the large number of elements in $G_n$. </p> <p>Or is there a better method to estimate the Hausdorff dimension in practice? Note that although I just want to estimate the dimension, I would like to be able to (computer-assisted if necessary) give rigorous bounds on the error. </p> http://mathoverflow.net/questions/76890/how-to-estimate-the-pressure/76904#76904 Answer by Vaughn Climenhaga for How to estimate the pressure? Vaughn Climenhaga 2011-10-01T01:34:47Z 2011-10-01T01:34:47Z <p>Write $\Lambda_n(t) = \sum_{w\in G_n} |f'(w)|^{-t}$, where $f\colon \bigcup_j I_j \to I$ is the interval map whose inverse branches are the maps $g_j$, and where $|(f^n)'(w)|$ is the supremum of $|(f^n)'(x)|$ taken over all $x$ in the basic interval corresponding to the word $w$.</p> <p>Suppose that $f$ is uniformly expanding (the $g_j$ are uniformly contracting) and $f'$ is Holder continuous. Then there exists $V\in \mathbb{R}$ such that $|(f^n)'(x)/(f^n)'(y)| \leq e^V$ whenever $x$ and $y$ are in the same basic interval (of any order). In this case standard estimates yield $$(1) \qquad \qquad e^{nP(t)} \leq \Lambda_n(t) \leq e^V e^{nP(t)}$$ for every $n$. This doesn't get rid of the fact that there are a large number of elements in $G_n$, but it at least gives you the rigorous bound $|P(t) - \frac 1n \log \Lambda_n(t)| \leq \frac Vn$ for any given $n$. Versions of (1) can be found in (Rufus Bowen, "Some systems with unique equilibrium states", <em>Math. Systems Theory</em> <strong>8</strong> (1974/75), no. 3, 193–202).</p> <p>In the non-uniformly expanding case (Urbanski's), it's not quite so easy, since in general there may not be any $V$ with the bounded distortion property described above. Nevertheless, certain partial bounded distortion results should still be available, and at least for $t$ less than the Hausdorff dimension of the limit set, I believe the techniques in (Climenhaga and Thompson, "Equilibrium states beyond specification and the Bowen property", <a href="http://arxiv.org/abs/1106.3575" rel="nofollow">arXiv:1106.3575</a>), particularly Section 4.3 and Proposition 5.3, will suffice to show that there is a constant $V$ such that (1) holds. I'm not sure how easy that constant will be to compute, or how it may decay as $t$ approaches the Hausdorff dimension of the limit set -- however, if you can use that to get $P(t)>0$ for some $t$ that you suspect is a very good estimate, then you have the lower bound on Hausdorff dimension, which is typically the harder one, and the upper bound may be accessible by other means.</p>
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2013-05-20 04:44:54
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https://discuss.codechef.com/questions/101788/d-query-segmentation-fault-bug
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You are not logged in. Please login at www.codechef.com to post your questions!
×
# D-Query Segmentation Fault Bug
0 I tried solving D-Query http://www.spoj.com/problems/DQUERY/ using Mo's algorithm, but my code keeps giving Segmentation Fault, have been trying for the past hour and still can't debug it. Would appreciate it if someone can help. Thanks. Here is my code. http://ideone.com/o9qLUW asked 14 Jun '17, 16:34 28●3 accept rate: 100%
1 Your solution looks correct, but just three comments: C++ requires compare function to be transitive for sort to work (see reference). Try replacing <= with < in your second code block, this will remove seg fault. Though that removes segfault, your solution will TLE because your compare function looks expensive. For example, you are calculating sqrt(n) every time, which is an extra $\Theta(log N)$ factor. Try caching that into a variable. Lastly, try passing const pair& instead so that you don't pass-by-value the big pairs during sort. This link in stackoverflow can explain why constant references are faster. I believe these last steps will be enough to get your code to pass :) answered 14 Jun '17, 18:08 5★hikarico 1.9k●1●5●15 accept rate: 28% 1 Thank you so much it finally worked. Never thought the compare function would be the main culprit. (14 Jun '17, 18:29)
0 One observation that i made is that, query[i].se is of type ll whereas you are accessing index ans1[query[i].se] which wont be accessible if query[i].se is of range ll and ans1's index only last till 200004 (as you have declared initially). Try this and let me know :) answered 14 Jun '17, 16:48 419●2●10 accept rate: 7% Sadly doesn't work, the number of queries never go into ll range to begin with. (14 Jun '17, 16:51) Okay thanks for the check, meanwhile I'll check other factors. (14 Jun '17, 16:52)
0 Let the 1st query be 1 3,then initially your curL=0 and you are accessing cnt[a[curL]] but you are taking input as 1-based and hence a[0] would be some garbage value.You have declared cnt array of size 1000005.If a[0] is greater than 1000005 then you are going out of bounds which will result is segmentation fault. BTW,here is my accepted solution if you have any doubt feel free to comment https://pastebin.com/mRqp9ha1 answered 14 Jun '17, 16:56 1.7k●2●10 accept rate: 14% It still gives segmentation fault after I initialized a[0] as 0, also since I have declared it globally it should have already been 0 initially to begin with. (14 Jun '17, 17:02) try to compare your code with my code (14 Jun '17, 17:07)
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question asked: 14 Jun '17, 16:34
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2019-02-24 03:08:02
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https://aperiodical.com/tag/matt-parker/
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# You're reading: Posts Tagged: Matt Parker
### Maths at the Edinburgh Fringe, 2019
As the hordes descend upon the city of Edinburgh for another August-ful of comedy, theatre, arts and culture, the question I’m sure you’re asking yourself is, ‘what about the maths?’ Zero problem: we’re here with a quick guide to some of the big pluses you’ll find in the Fringe Guide.
### Matt Parker does BBC GCSE maths revision videos
Stand-up mathematician and friend of the site Matt Parker has produced a set of videos for teacher resource site BBC Teach, aimed at GCSE maths students.
### Review: Humble Pi, by Matt Parker
There are many things I admire about Matt Parker (or, to give him his full title, Friend of the Aperiodical, Mathematician Matt Parker) and his work, but probably top of the list is how he switches, apparently effortlessly, between modes. One minute, he’s showing off a fax machine to a group of hard-core geeks with Festival of the Spoken Nerd; the previous, he’s inspiring a “lively” bottom set of year 9s, after putting together a Numberphile video for people somewhere in between.
While Humble Pi – A Comedy Of Maths Errors is pitched firmly at the last of those groups – for a popular maths book to hit the top of the Sunday Times bestseller list, it really needs to be – there’s plenty in it for the others.
### Happy Thirdsday!
Today is the third of January, and the third day of the year – and since this year it also falls on a Thursday, making for excellent pun opportunities, a group of mathematicians including Jim Propp, Evelyn Lamb, Zoe GriffithsBen Orlin, Matt Parker and several others have chosen to use today to celebrate the number $\frac{1}{3}$ (and in America, you’d even write the date as 1/3). Today is officially Thirdsday! Celebrate by:
I personally will be sketching the middle third Cantor set, as it’s my favourite fractal.
### Review: You Can’t Polish a Nerd, Floppy Disk #211 (Festival of the Spoken Nerd)
“You Can’t Polish a Nerd” is the latest in a run of live stage shows from science/maths comedy trio Festival of the Spoken Nerd. Consisting of friends of the Aperiodical Matt Parker, Steve Mould and Helen Arney, FOTSN is a mixture of comedy, science, music and live demos, and they’ve sent us a copy of their latest show to review.
### MathsJam Gathering: A Review
It was with trepidation that I booked tickets for the MathsJam Gathering in 2015. I loved the sound of the event, but what if everyone else was cleverer than me? What if people thought I was a fraud because I wasn’t an academic? What if nobody talked to me? I needn’t have worried. MathsJam is one of the friendliest, most welcoming events I’ve ever experienced. Lots of people talked to me, I learned new things, I laughed a lot. I’ve since been to two more gatherings, and have already booked for the next one in November.
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2020-01-18 20:24:32
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https://math.stackexchange.com/questions/444111/maximize-a-functional/444395
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Maximize a functional
$$F\{a(s)\} = \int\limits_0^t \left( g(a(s)) - \alpha\, v(s)^2 \right) ds, \ a(s) \in \left[0, \infty\right)$$
where $g(x) = x e^{-x}$ , $\alpha=\mathrm{const}$, and $\displaystyle v(t) = \int\limits_0^t a(s) ds$
• @MhenniBenghorbal It was the first thing I've tried. I don't undestand how to deal with $v(t)^2$. – centuri0n Jul 15 '13 at 11:47
• Could you please clarify the definition of your functional? I think that the integral is from $0$ to $\infty$. Also, waht is the precise definition of $v(t)$. Is $v(t)=\int_0^t a(s)ds$? – Tomás Jul 15 '13 at 13:37
• @centuri0n, so you mean that $t$ is fixed and $F$ sends $a$ to some real number. Right? – Norbert Jul 15 '13 at 17:21
I don't understand how to deal with $v^2$
Reformulate the problem in terms of $v$. That is, you seek the maximum of $$F\{v\} = \int\limits_0^t \left( g(v'(s)) - \alpha\, v(s)^2 \right) ds, \ a(s) \in \left[0, \infty\right) \tag1$$ over increasing differentiable functions $v$ with $v(0)=0$. The Euler-Lagrange equation for (2) is easy to state: $$-\frac{d}{ds}(g'(v'(s))) -2\alpha v(s)\equiv 0 \tag2$$ Since $g''(x)=(x-2)e^{-x}$, the equation (2) becomes $$(2-v'(s))e^{-v'(s)}v''(s) -2\alpha v(s)\equiv 0 \tag3$$ I wouldn't expect an explicit solution of (3), but a numeric solution should not be hard to obtain.
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2020-11-30 10:43:41
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http://www.ams.org/mathscinet-getitem?mr=1969009
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MathSciNet bibliographic data MR1969009 14J45 (14E30 14J30) Mori, Shigefumi; Mukai, Shigeru Erratum: "Classification of Fano 3-folds with \$B\sb 2\geq 2\$$B\sb 2\geq 2$'' [Manuscripta Math. 36 (1981/82), no. 2, 147–162; MR0641971 (83f:14032)]. Manuscripta Math. 110 (2003), no. 3, 407. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.
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2013-12-21 02:42:27
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https://www.gamedev.net/blogs/blog/2257-vidar-devblog/
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• ### Blog Entries
• entries
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20
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18322
Following the progress of Vidar, an RPG Puzzler Where Everyone Dies
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## Hi friends!
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## We're back from SXSW Gaming, and their inaugural pitch competition, and holy cow that was an exhausting 24 hours! Here's a run down of all I got to do (which is just as much for me to remember as it is to talk about what got done this week).
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## Considering travel, I had basically 1 day at SXSW. So at 9 am on Friday morning, I started at the Hilton to meet with Webcore Games, a neat studio that seems to have their fingers in an awful lot of pies. From VR to 2d to casual and everything in between. They do a fair amount of outsourcing, and I'm excited for possible partnership opportunities for more Vidar market penetration as well as on upcoming projects.
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## Next up I met with David Wolinsky before his panel on suicide prevention in the games industry. David is the writer of Don't Die, an awesome collection of long-form interviews on the games industry, self-reflection, insecurity, and a hint of Gamergate exposition. It's phenomenal stuff, and you must check it out.
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## And then it was finally time for the pitch competition. The competition was divided into two rounds - in the first, 16 games competed in closed room sessions before a panel of 4 judges. Before the presentation, we were each given 30 minutes with a mentor to help go over our stuff. This was tremendously helpful, because just talking it out helped me focus on the problem I wanted to emphasize with the judges. The only concern I had? How do you take the feedback from a 30-minute mentor session and immediately incorporate it into a 10 minute pitch? We didn't have any time in between, so it was going to have to be done on the fly.
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## As if that wasn't enough, my computer died about 3 minutes into my presentation. Slideless and defeated, I improvised and tapdanced and mercifully had print-outs to give to the judges. After a 10 minute presentation, I fielded questions like "how on Earth are you doing this alone?" and "what's your break even point?" and just like that it was done.
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## I explored the convention hall a bit while waiting for the results to be announced. SXSW Gaming is growing, but it's not there yet. The place is like, 1/10th the size of PAX East, and walking through the featured indie showcase I saw plenty of empty booths. The only major anchor tenant was Nintendo, showing off the Switch, and lines for that were pushed to the outside of the hall - so that line huggers wouldn't have seen any of your signage etc. I think in 3 years this convention could be really awesome, but for now, I'm glad I didn't spend $1200 on a booth. IGDA Austin had the right of it - they bought one booth, and then rotated in several games in a few-hour shifts (spreading the cost in a pretty efficient manner). [/font][font=Georgia] ## Just about as I finished making the rounds, the finalists were announced, and Vidar was chosen with 7 others to participate in the Final Round!! [Insert Dramatic Music]. This time, 2 additional judges joined the panel (for a total of 6) and the presentations were open to the public. My computer pulled through, and at the end, I got extremely few questions. In legalese we call this a "cold bench." It's worrisome. It means the judges aren't engaged in your presentation, and I felt defeated. After one or two questions, I kind of realized that it was because Vidar is already on Early Access, and that my presentation had covered all of their other go-to questions for other presenters ("what's the gameplay loop?" "what's your target demo?" etc.). [/font][font=Georgia] ## Sadly, Vidar did not win - but major congrats to the team from Tessera Studios because they seriously deserved it for their VR thriller game Intruders. No worries, though, I made it exactly where I wanted - the final round, to be able to present Vidar to the public. And afterwards, ended up sticking around with the judges for over 2 hours just to chat about marketing, where Vidar goes from here, etc. That was the part that made this an invaluable experience. [/font][font=Georgia] ## From there I left for North Austin for IGDA's post-SXSW Gaming Dinner, which was absolutely wonderful. I got to meet aspiring devs, old friends and new, and writers from some of my favorite indie games. And finally got to eat - because I had forgotten to all day. After about 20 hours of go-go-go, I crashed at the hotel for an incredibly short nap before hopping on a flight home. [/font][font=Georgia][/font][font=Georgia] ## And now we dive back into cleaning up the patch for April 4! Caught In Your Web will feature our next Town Event, "Venom." As I teased last week, this Town Event centers on Dorottya and Katarina, and specifically follows the quest "Clearing The Way." Players who make it that far into their story will be able to explore a new side area in the Water Cave filled with spiders. They'll need to be quick, or else they could run into one of the worst possible fates in the game - two villagers dead in one night. [/font][font=Georgia] ## This Town Event comes complete with an additional helper quest as well, Arpad's "A Test Of Leadership." This quest, while quite different from "Make It Work" (which we previewed in detail a while back), takes its place; that is, you can only get one or the other in any playthrough. If "Make It Work" is unavailable to you, but Arpad's reached his leadership path, then he can help you out in completing "Venom" to save a villager from a poisonous spider bite. [/font][font=Georgia] ## To trigger "Venom" you'll need the following: [/font] • "Clearing the Way" received • Dorottya alive • Katarina alive • Elek alive • Doctor alive • Reached the Water Cave [font=Georgia] ## The rewards are not to be missed, either, and finishing the quest can definitely turn the tides of the Water Cave in your favor! [/font][font=Georgia] ## That's all we've got for this week. Next week we'll have a short preview of some additional changes and quests, and then the week after that the patch drops! See you then! [/font][font=Georgia] ## ?- Dean [/font][font=Georgia] ## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Play it on Steam, and keep in touch with twitter.[font='Helvetica Neue'] [/font][/font] ## A Way Forward [font=Georgia] ## Hi friends! [/font][font=Georgia] ## This week I took a break from bug fixes to work on some new content for Vidar, because it's always nice to have more game to play. This week, we're ready to preview how "Make it Work" will, well, work. [/font][font=Georgia] ## This quest is designed to do a few things: [/font] 1. Move along Arpad's "leadership" plot. In case you've missed it, there's a window for Arpad to get a message from a long-dead friend about needing to step up and be the hero of Vidar. Currently, after you deliver that message, Arpad's plot kind of stalls; he won't give you anymore quests, he'll rarely participate in others, and he won't even give you a reward for "Bury the Hatchet." So rude! 2. Give you one more opportunity to reach the Wolf Cave. The further along we get in the cave, the less likely any given quest will be available to you. With it currently taking an average of 5 days to reach the Dark Cave, and with very few people doing the prerequisite quests by then to reach the Wolf Cave (either "Scared of Shadows," or both "Bring Him Home" and "Man's Best Friend") I wanted an easier-to-complete but rarer-to-obtain prereq path to reach this cave. 3. Provide earlier access to the Sprint Shoes. Currently, Piri is the only way to get this much-coveted tool, and you have a narrow window to get them from her in the Water Cave. It felt a little penalizing. Moreover, they're at their most useful in the Dark Cave, when you're racing to light torches. Placing them as a possibility earlier in the game made sense. [font=Georgia] ## And so, if you happen to be pushing Arpad along his leadership plot, you'll have the opportunity to get "Make it Work" in two different ways. First, if you happen to have "Den of Darkness" but Etel doesn't join you in entering the Wolf Cave, Arpad will step up to join you instead. Trade a coward for an indecisive hero? I'm not sure it's any better, but it's something. Second, if you can't get either "Scared of Shadows" or "Hunting Party" (the two current paths into the Wolf Cave), then Arpad will offer the quest to you as well. [/font][font=Georgia] ## Arpad has some extra tools up his sleeve in the Wolf Cave, and can be used in ways to make the puzzle a little bit easier. People trying to avoid Etel's....lack of usefulness...might angle to try to get the quest this way instead. [/font][font=Georgia] ## "Make it Work" is one of 4 new quests we're adding in the upcoming patch, hopefully you'll find it rounds out our game a little bit more! [/font][font=Georgia] ## In addition to new quests, we've got some new mechanics cropping up in the Water Cave. Generally speaking it's been a good idea to try to "drain" each map to move forward, in order to reach levers etc. That's not a safe assumption anymore: [/font][font=Georgia][/font][font=Georgia] ## ?We'll have more previews ready for you next week! [/font][font=Georgia] ## ?- Dean [/font] ## Rebalancing [font=Georgia] ## Hi friends! [/font][font=Georgia] ## We've had two weeks now to work on some additional tweaking of Vidar, and version 0.8.0.2 was launched this past Friday to address some additional bugs that were cropping up. [/font][font=Georgia] ## A personal favorite bug was that people were reporting they couldn't switch tools in the Dark Cave between the shovel and the lantern. Which, yes, that's what it seemed like. But the real bug was that they had managed to make it to the Dark Cave without ever picking up the lantern. The "can you switch tools?" enabler was off - because you only had one tool in inventory - but it would still seem like you had two. This has been solved! You can't go to the Dark Cave without first physically picking up the lantern. People who have already experienced the bug have had the lantern auto-added to their inventory. [/font][font=Georgia] ## Additionally, I took the opportunity to remove the last room of the Dark Cave. I saw a lot of people on streams struggling with it, and so far in my metrics have seen very few people make it out of that room (and even fewer make it out in a reasonable time). I'll be redesigning it and bringing it back as a possible variant. For now, I want to make sure people are getting to the Water Cave without getting too frustrated to keep playing. Otherwise, I'll never collect data on the second half of the game. [/font][font=Georgia] ## Finally, a lot of dialogue was written for the upcoming content patch. All of the conversations for "Make it Work", "Vigil," and "Music to My Ears" was added behind a version control system, so while it's there, it won't unlock until we reach the actual content patch. [/font][font=Georgia] ## On the docket next week is to continue progress on the content patch, as well as fixing a few additional non-progress blocking bugs. I'm also hoping to start working on improving the menus! [/font][font=Georgia] ## - Dean [/font] [font=Georgia] ## Alpha 0.8.0.2 [/font] • Games created in version 0.8.0.0 or prior with a buggy Dark Cave 3 are now fixed • Fixed a crash in Dorottya's dialogue • Fixed a crash in Gusztav's dialogue • Dark Cave 4 has been removed from the game. • Dark Cave 3 has been redesigned slightly to accomodate this fact • "Clearing the Way" now only extends the tunnel for 3 rooms • "Sketched Out" now only requires three sketches to complete • Quest Items for "Bring Him Home," "Light in the Darkness," "Dr. Spore", "Not a Thief," and the entrance to the library have been moved out of Dark Cave 4 (if they spawned there) and scattered throughout the remaining 3 rooms. • Time is now stopped in the Library and the Wolf Cave • Fixed a bug that revealed Dark Cave 1 before you picked up the lantern. If you managed to advance to the Dark Cave without picking up the lantern, it has been added to your inventory. This should resolve the bug that some reported as being unable to switch tools in the cave. • Rubble for "Clearing the Way" will now spawn correctly in Dark Cave 2b • Removed a glowing tile that was blocking a path in Boulder Cave 3 • Fixed a reset issue in Dark Cave 1 that could cause you to get stuck in the last puzzle • Fixed a bug in Puzzle 35, Option 5 where a torch could spawn on the wolf cave entrance • If you have read all of the books for this quest for "Reading is Fundamental", but use a campfire instead of returning to town, this quest will no longer complete. Instead, a person will die as usual and the quest will not complete until you actually return to town. • Fixed Szabina's text if "Sketched Out" is complete with 2 of 3 helpers • Time will not unfreeze in the Ice Cave or Dark Cave Waypoints after a dialogue window is displayed ## Getting Vidar to Early Access - Step 1 Hi friends! A lot of times I post my dev blog about what I've been working on in general for Vidar, but since this community is definitely more about sharing experiences so that we can learn from one another's successes and mistakes, I wanted to do a write up just here on the craziness of yesterday and how I got there. I honestly don't know whether what I've done is good or bad yet, so don't take this as a recommendation, so much as an offer of possible ideas. Vidar was greenlit on Steam a millennia ago (ok, close to 2 years ago), and that afforded me the very important ability to generate and send out steam keys as I needed them. So, for example, when applying for various conventions or competitions, I could generate a key rather than having to upload builds of the game to all these different places. That also meant that I could ensure judges or press or whomever always had access to the latest version. But what I hadn't done was activated the actual store page, until yesterday. To give you a timeline, I plan to release Vidar on Steam Early Access on January 31. That means that I posted the page - which has been ready for about three months, and which could've been ready a year+ ago - about a month before launch. Setting the store page to live affords me a few benefits: it allows me to have the "community hub," to post announcements and news about the game, and it allows others to "follow" or "wishlist" the game. Additionally, it gives me another place to direct people that's not the game website. Working back from this planned date, back in August I prepared a spreadsheet of games press outlets I happen to know off the top of my head, twitch streamers, lets players, and podcasts. I then spent the better part of September and October researching more that I thought would be good fits for Vidar. I did that research in a few ways: simply googling for websites that covered indie games, RPGs, puzzle games, etc., and also looking for reviews of games that I thought were kind of in the same wheelhouse. I also added to the list anyone who had even mentioned Vidar in passing during the Kickstarter phase, no matter how remote or how little they covered the game. I added anyone on Youtube that had played the demo during kickstarter, even if they had 8 subscribers. In November, I began to dig more into each of these press outlets to find specific authors that I thought the game would resonate with, based on the games they reviewed. During this process I tried as hard as possible to get individual author emails. If the website didn't list them directly, I went into solid online-stalker mode: • Google the author to see if they've written elsewhere; on several occasions, the author had freelanced for Rock Paper Shotgun, who always provides every author's email address • Check their twitter account; rarely did the person just post their email in a description, but they often had a link to somewhere else where they could be found on the internet • Check Youtube - if the author or lets player or whomever has a Youtube channel, chances are there is a tab on their channel that says "About" - if it does, they are almost guaranteed to have an email hidden behind a captcha on that tab At the end of the day, I had 500+ journalists, 300+ Youtube channels, 60 twitch streamers, and 50 podcasts on my lists. I flagged any that had 1) already covered Vidar or 2) I wanted to send some kind of personalized email. The rest I loaded into MailChimp. Before importing the spreadsheet, I added a column for Steam Key and added a unique one for each, so that in the mailmerge I could give them each a key. For the ~200 people I wanted to write personalized emails to, that was basically all of December. In the final week of December, I: 1. Drafted a press release; 2. Prepared new twitter and facebook banners announcing the 1/31 Early Access Launch date; 3. "Seeded" the community hub on Steam with a few screenshots; 4. Prepared my website with the trailer video (but did not publish); 5. Drafted the mail merge emails; and 6. Made an official press kit, rather than the silly .zip folder I was sending all around. Yesterday, I pulled the trigger on everything. The press release was hosted on my own company website razburygames.com, and I sent it to gamespress as well - first thing in the morning, because they are in the UK and need to approve things, so the later in the day it gets here in the US, the less likely it will be posted that day. All of the emails - personally drafted and mail merge alike - went out. The new assets went up on social media. And then any time anywhere mentioned the game, I immediately posted everywhere about it. All in all it was a pretty grueling day, and I don't have much to show for it just yet, but these things take time. Indeed, what I struggled mightily with during this whole process was whether I was doing this too soon or too late. On the one hand, I was honored to be featured in Kotaku back in September - an article that got about 23,000 views, and translated to zero pre-orders and 100 people on my mailing list. I attributed that in large part to timing; if people liked Vidar, there was nowhere for them to go to act on it right away. I'm concerned that by doing this press blitz a month in advance, I could potentially waste other opportunities like that as well. On the flip side, even though I did all of this work yesterday, I got ~100 people to "wishlist" the game, and only about 2,000 visits to the Steam Page. Obviously that would be significantly higher on launch, but I think it still demonstrates the point that this whole promotion process has to happen some time in advance of launch. And indeed, I've been able (with varying degrees of success) to leverage the Kotaku article as giving me more credibility. Perhaps if I had done this process two months in advance of launch instead of one, I could've generated more hype, and continued that kind of "trading-up" process until I felt like the community was large enough to support launch. So here we are! Various interviews are scheduled for the upcoming weeks, and at least one big twitch streamer has told me he's interested. Unfortunately, no news yet from what I call "big press" - the Destructoids and PC Gamers and IGNs of the world. Without at least one of those, I'm concerned that Vidar will have a relatively obscure, uneventful launch. About a week out from launch, I'll try again with anyone that I haven't engaged, and hope that the imminent threat of game release is enough to rope them in. As far as analytics go, I will note that Steam's discovery queue put me right in there, which was welcome! I won't get into specifics, but my conversion rate from people who visited the page to people who wishlisted it seemed pretty strong. And perhaps my favorite statistic of all yesterday - one person saw Vidar in their "trending among friends" list on Steam. I just absolutely love the idea that someone out there has got a friend who's going to tell them "have you heard about this game called Vidar? I've been playing it..." I have NO idea if this was helpful at all, but it was definitely a positive way for me to record the past 48 hours roller coaster of work and feelings! - Dean ## A Little Love [color=rgb(51,51,51)][font=Georgia] ## Hi friends! [/font][/color] [color=rgb(51,51,51)][font=Georgia] ## This upcoming month will be characterized by "aggressive polishing" of Vidar in anticipation of Early Access. However, tomorrow we launch the Steam Store Page and a huge press blitz, so not a ton of development happened this week. A few little clean up items here and there, though, so I thought it merited a patch. [/font][/color] [color=rgb(51,51,51)][font=Georgia] ## We've also finalized the Linux downloader - Kickstarter backers who game on Linux and don't use Steam will finally be able to play the game. That brings us down to only those backers who were looking for something on itch or some other platform. We'll have updates for them shortly. [/font][/color] [color=rgb(51,51,51)][font=Georgia] ## Happy New Year! [/font][/color] - Dean Alpha 0.7.6.1 • Ruins Puzzles now reset broken ice even if you've received assistance • The Bright Flower now gives off a little light • The first two ruins maps are a bit darker, to help you see mirror light • Falling now has a sound effect • Bridges over water throughout the cave no longer draw you as though you're standing in the water • Bridges over ice throughout the cave no longer cause you to slide on them • Using a switch in the ruins will no longer stop the screenshake • Erik cannot get stuck at the beginning of his cave entrance on the left side • Fixed a bug in Puzzle 16 Option 2 that prevented the retrieval of a bucket [color=rgb(51,51,51)][font=Georgia] ## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website to play it right now, and keep in touch with twitter. [/font][/color] ## Room at the Inn [color=rgb(51,51,51)][font=Georgia] ## Hi friends!Happy holidays! I'm still mid-Chanukah right now and up to my shins in latkes, but whether you're celebrating or not I hope you've had a fabulous few weeks. Lots to talk about today!First, today is the release of the final pre-Early Access content patch, "Room at the Inn!" This includes activating the first Town Event in Vidar, "Wake." Vidar is all about experiencing and exploring death from every possible perspective, and so the celebratory/party tradition from so many cultures and embodied by the wake is definitely a welcome addition to the game. If you find yourself exploring the library while Dani dies, make sure to pour one out for her.Rozsa is also keeping a better watch on who is staying at the inn these days. The various NPCs that can move in and out will find their plans foiled unless there are a sufficient number of rooms open and available. This particularly impacts Csaba, Tomi, and Cecilia; if they are looking for housing but the inn is completely full, they'll need to look elsewhere.This patch also includes new ways through each of the Ice Cave maps, and new puzzles in the Ice Cave that feature the simplest sliding box. Just a little push can make a huge difference when it comes to slipping around.Second, we finally have a Mac launcher! Mac-using Kickstarter backers who wanted a non-Steam version of Vidar are finally getting their copy of the game, leaving only our non-Steam Linux backers. We're hoping to get them taken care of next week. This version of the Mac build also includes functioning key bindings and various other Mac-specific bug fixes.Third, next week marks a big date in the march to Early Access. The "Coming Soon" Steam Page will launch on January 4, which will allow you to wishlist the game. It will also activate the Community Hub on Steam, where those who already have the game can share screenshots, reviews, LetsPlays and more. To celebrate, on the 4th we're also releasing the Early Access Launch Trailer! It's a huge day around here, so mark your calendar.Fourth, Vidar will be making it's last pre-Early Access showing at Playcrafting's Winter Expo on January 26, 2017 at Microsoft in NYC. This event is always so good, I couldn't pass it up even though it's days before launch and I'll be going crazy. If you're in town, we'd love to see you - early bird tickets are$8 so make sure to nab them before the price goes up.Fifth, please welcome Razbury Games' new community manager, Roderick Sang! Roderick had played games intensely on his Gameboy Color and N64 as a kid but never thought of himself as a gamer until the Gamecube came along. It was when he started playing through "Skies of Arcadia: Legends" that Roderick realized that video games, and RPGs especially, would be an important part of the rest of his life.After graduating college and finding himself at a loss for what he wanted to do, Roderick eventually discovered a burning passion for Storytelling and Sound. Consuming radio and podcasts voraciously and reflecting on why some games' use of audio were more memorable and impressionable than others, Roderick has started down the path of educating himself on Sound Design.He can currently be found working on an interactive story that use sound to further immerse the reader into the role of the main character, creating a YouTube series on the various demons in the Shin Megami Tensei line of games, as well as producing his own podcast on why people play video games. You can learn more about him on his website, YouTube, or Twitter.I'm thrilled to have Roderick join the team to help out with all things social media and community. You might find him around the subreddit, the Official Wiki, the twitter account, the facebook page, the Steam Community Hub (next week!), or any of the other myriad places Vidar lives these days. Ok, that's enough news for one week, right? Let's get to some patch notes!
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## Alpha 0.7.6.0
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## Quests
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• New Town Event: Wake. Explore Tamas and Dani's friendship in the mid-game.
• Modifications made to "Hunting Party"
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## Puzzles
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• Added 25 new puzzles in the Ice Cave (bringing the total in the Ice Cave to 64; you'll see 12 in a given playthrough, give or take)
• Added a new path through Ice Cave 1
• Added a new path through Ice Cave 2
• Added two new paths through Ice Cave 3
• Added a new path through Ice Cave 4
• Holes in the last room of the Ruins now properly block your path
• Fixed various crashes related to the Ruins
• Fixed various graphics issues in the Ruins
• Fixed various passage issues in the Ruins
• Lightbridges in the Ruins are now embettered
• Opening one door in the fifth room of the Ruins will not open all of the rest of the doors
• Pillars now really do serve as pressure for the sake of pressure plates
• Ramps placed in the water work appropriately
• Reset now works in the Ruins Cave
• Reset now no longer crashes the game if you have loaded a boulder into a geyser in the Boulder Cave AND have loaded the game from a save (that's a mouthful)
• Reset now correctly resets pressure plates
• Room five of the Ruins is now flooded with water
• The timer better functions in the Ruins cave
• Tools can now be used in the Ruins
• Wolves now move around in the Ruins
• YOU CAN NOW FALL THROUGH THE ICE IN THE RUINS CAVE (this is in all caps because it seriously took me way too long)
• Other spoilery fixes to the Ruins cave
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## Misc
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• Autosave: when you start a new game, a new save file will be created immediately. Autosave will now save over that file (or, if you're continuing, from whatever file you loaded) rather than always autosaving a new file at the top. This means that saves kind of function like save slots now.
• The analogue stick is now enabled
• The Tool and Timer UI are hidden during the final confrontation
• Additional decorations have been added to the Ruins
• The progress bar at the start of a new file now tells you what it's doing
• F6 has been disabled
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## Mac / Linux
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• Fixed a crash related to NPC dialogue sounds
• Fixed graphic rendering of items on tables
• Fixed player transparency when in water
• Fixed various other client bugs
## Slick
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## Hi friends!
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## Short post for this week, as lots of ends are tidied up. This week I added several additional paths through the Ice Cave (along with about 25 new puzzle options and a new mechanic). Additionally, a lot of love was added to the Ruins, with tons of bug fixes throughout - I don't want to go into a lot of detail here because the Ruins are pretty spoilery?
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## Finally, saving / autosaving works a little differently now. Before, whatever you were playing would just autosave in the top slot - all fine and dandy, but you couldn't create new "slots" if you wanted to have several parallel games. Now, whenever you hit "New Game" it will create a new save slot, and will always autosave into that slot; if you load a new game, the autosaving will happen there. As before, you still can't manually save mid-day.
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## That's all for this week! We're off next week for the holidays, but we'll be back on Dec. 27 with just a bucket load of news for you, and the last content patch before Early Access, "Room at the Inn."
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## Bound and Determined
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## Hi friends!
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## This week I'm pushing a new patch to primarily address one thing: key-bindings are now in the game. In theory, you should have a lot more flexibility when it comes to your input. This includes resetting your keyboard keys to something more comfortable, remapping an XBox Controller, and switching between a keyboard and controller profile. Previously, if a controller was plugged in, you could not use they keyboard whatsoever. That restriction has been lifted.
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## Candidly, I found the keybinding process to be incredibly difficult. I'm not terribly familiar with the Win32 API, or reading inputs from the keyboard. I'm proud of what was done, but this took longer than I was hoping. I'm crossing my fingers I can make up some time down the road this week.
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## Speaking of plans for the week, expect yet another patch next week which cleans up some bugs in the Final Confrontation before we all leave for vacation.
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## Additional bug fixes are also incoming, they're getting pretty nuanced now!
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## Alpha 0.7.5.1
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## QuestsA Little Something
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• This is now a time-limited quest
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## Clearing The Way
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• Added dialogue for Dorottya and Katarina as they are about to dig the tunnel
• Added dialogue for Dorottya and Katarina on completion of the tunnel, regardless of whether the quest is complete
• Fixed Katarina's clipping issue when choosing the tunnel as a reward
• Fixed pathing issues inside the tunnel
• Replaced the entrance to the tunnel with a rope, and included climbing animations
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## Dr. Spore
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• Gusztav is no longer so greedy; he'll only take 10 mushrooms if you tell him he can't have more
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## Light in the Darkness
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• Robert actually takes the Bright Flower from you now
• Using the last Bright Flower before completing this quest now appropriately updates your journal
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## Spirit Walk
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• Completing this quest will now anger Bernadett (doesn't everything?)
• Piri's dialogue on completion has been updated to make the reward for this quest clearer
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## The Second Son
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• Fixed a corner case related to the completion cutscene that would appear strange if you left the workshop then immediately went back inside.
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## Misc
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• Added keybinding configuration. You can reach it from the Options menu
• Added controller and keyboard profiles; you can switch between using an XBox controller and a standard keyboard in the Options menu. This means you can still use the keyboard even if a controller is plugged in.
• Added various non-text tutorials
• Fixed various passage issues in town
• The Church will not close its doors if you have the Ice Cave Waypoint
• Cecilia's House will not close if you have the Dark Cave Waypoint
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## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website to play it right now, and keep in touch with twitter.
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## Hi friends!
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## I'm writing this blog post as I'm still trying to digest the last of Thanksgiving dinner, several days after the fact. For those who celebrate, I hope you had a wonderful holiday!
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## This past week, the nominees for Playcrafting's annual "Bit Awards" came out, and Vidar is nominated for Best PC/Console Game of the Year!! Which is really just pretty dang awesome. The award show will be on December 15, and if you're in the NYC area, it'd be great to see you there. Tickets are on sale here.
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## On the development front, this week we launched the 3rd of 4 "pre-Early Access" content patches designed to get the game to tip-top shape for our Steam debut. Beyond the other big ticket items I've discussed the past few weeks, Vidar got a few more particle effects and bug fixes over the long weekend. You should also see more stability throughout.
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## The final content patch before Early Access will come out in late December, as we try to cram as many possible bug fixes in as we can. There may be additional patches after that for still more fixes, but it's unlikely any new quests etc. will be added until February (although never say never!)
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## Better get to it!
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## - Dean
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## Alpha 0.7.5.0 - Bad Trip
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## Quests
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• New Quest: Vodka Stinger. Dani's been reading some strange books.
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## A Brighter Tomorrow
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• Fixed several bugs related to Dorottya's dialogue
• Fixed several bugs related to using the Imp Oil lantern
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## Den of Darkness
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• Slightly updated the receipt cutscene
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## Dr. Spore
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• Robert's reminder text has been fixed
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## Faith in the Dead
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• Added some pep in Borbalo's step at the Church
• Fixed some reminder dialogue
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## Residue
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• Collecting oil will no longer freeze the game
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## The Second Son
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• Improved Sandor's faith tracking
• Fixed a crash that occurs if this quest times out and Borbalo is dead
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## To Feed a Village
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• Various journal fixes
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## Puzzles
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• New Mechanic: Bucket. You'll find these scattered throughout the Water Cave.
• Fixed various tile spawning issues in the water cave
• Fixed a crash related to vine spawning in the water cave
• Added 13 new puzzle options to water cave
• Reenabled reset once you enter the Dark Cave; reset is all around better now
• Fixed some graphics glitches related to pull switches and levers
• The purple lever's color has been adjusted to be more purpley, and in line with the other things that match that switch color
• Added gates in IC1 and IC2 to make the shortcut function more clear
• Pull switches and levers that cannot be used more than once have been modified for that fact to be clearer
• Barrel use has been modified; you now use the lantern to refuel, rather than the interact button
• Added particle FX to moveable mirrors, pillars, and gargoyles
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## Dialogue
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• Added sfx for everyone's dialogue
• Fixed a crash in Dorry's dialogue after Kat dies
• Fixed a crash in Gusztav's dialogue after Robert dies
• Fixed a crash in Robert's dialogue after he becomes the Doctor
• Added several cutscenes and path variants for Gusztav after Robert dies
• Added several cutscenes and path variants for Gusztav after all 3 patients are dead
• Arpad won't misidentify you on Day 1
• Robert's cutscenes where he identifies mushrooms are a little less annoying
• Tomi has a few games he wants to play, if you're willing
• Sandor's faith now tracks better; there are several ways to influence whether he has faith
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## Misc
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• New Mechanic: Patients. Three extra lives have been added to Vidar.
• New Mechanic: Tomi's Caregiver. If Tomi is ever orphaned, various citizens may step up to help.
• New Mechanic: Mushroom Effects. Every mushroom can do something helpful or harmful to you; be careful what you eat, if you don't know what it is.
• Mushrom identification is slightly better
• The sick room in the hospital is no longer visible
• Various fixes to item descriptions
• Unlocked some of the doors in the inn
• Lots of fixes to the campfire - it's just overall way less buggy. Also note, the game will no longer save after using one.
• Dani sticks around at the castle ruins once she goes there
• Items can't be used in town now
• Added particle effects for lightpillar use
• Houses in Vidar won't close if a resident is out mourning for the day
• Fixed the door to the poor house and hospital when it's closed / locked
• Fixed a passage issue at the poor house
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## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website to play it right now, and keep in touch with twitter.
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## Patience
Hi friends!
We are on an unstoppable crash course with Early Access in January, and there's so much left to do!
This week I managed to get a ton of the upcoming patch in. The biggest mechanical change is the addition of three patients that Gusztav will be treating at the beginning of the game. I don't want to get into the nitty-gritty of the ratios and things, but on a broad level, these patients could potentially serve as additional bodies for the Beast. In practice, it's at most three extra lives, but you'll have to be both skilled and lucky to capitalize on all three.
The patients mechanic is core to Gusztav's quests lines, and we'll see more improvements as the game charts a course through Early Access. Speaking of Gusztav, a bunch of cutscenes were added for him this week as he reckons with the loss of his son. There are some particularly touching and troubling ones involving Sandor (who can relate, and who may or may not be a religious man by this point in the game) that are worth trying to reach in New Game Plus mode.
A new quest was added for Dani, but it's pretty deep into the game and requires a lot of stars to align to get it. If you do, it's a quest that's made directly easier by being nice to people in town, and the reward is pretty desirable as well.
Little orphan Tomi was a little concerning, particularly standing outside mourning his parents with no chaperone. A caretaker system has been added, so that if Tomi is in the poor house by himself, someone in town will take care of him, make sure has some food, etc. Right now, the caretaker's own lives aren't really changed by this role (they each have some dialogue about it, but that's about it). I'm hoping to change that post-Early Access. I hate to come back to Sandor again, but even he'd admit that taking in Tomi feels like he's doing some weird replacing in his life.
Finally, over the past several patches I've reported on Mushroom Identification, how people in town can tell you what kind of mushroom you've got in your inventory. Now, it finally matters - every mushroom you pick up can have different effects. Some are good, some are terrible. It's a gamble to eat a mushroom you don't recognize, but if you can get someone knowledgeable to help you, then they're a good extra resource to have. Particularly if you no longer need them for a quest.
With both the patient and mushroom mechanics, I'm hoping this eases some of the difficulty in the Dark Cave. By that point, there's a decent chance that some core Dark Cave quests aren't available to you, and so neither are their rewards. The nice thing about the dichotomy I've introduced here is that, if Gusztav is alive, you can turn in the mushroom to activate the patients-as-rewards. If he's not, then you can keep the mushrooms, and use them to give yourself meaningful boosts through the cave.
Some feedback that I'm mulling currently is:
• It's hard to keep the NPCs straight, particularly on a first play, particularly at the beginning
• Navigation (both in and out of the cave) is tricky
• The game is (still) too long to justify quick repeated play
On the first, I think a journal look-up is in the cards. Also, the upcoming patch introduces SFX for each character, which might help a little bit. On the second, while there is a map, the functionality needs to be improved, and it's not even available until the Water Cave. An earlier quest to give you the map seems prudent.
The last is the most difficult design question. We have 24 NPCs, and their lives set the entire pacing and balance of the game. Everything is written for these 24 to form a very interdependent, interconnected web - removing just one from the start of the game will throw a lot off. At the same time, if the game is shortened, then the threat of death is less meaningful. There's a lot to think about here, and some possible solutions are:
• Increase movement speed, which will up the tempo at the margins (it may throw off the balance of some of the Dark Cave puzzles in particular)
• Shorten the day (this will make the game significantly harder, and from what I've seen, that's not ideal)
• Cut one room from each biome (this will make the game significantly easier, with 12 rooms to clear instead of 16, but from what I've seen that's the right direction in terms of difficulty; this will also require a reconfiguration of a lot of quests)
• Condense the town, so there's less time spent walking from building to building (the most difficult to do on short notice, and may throw off the aesthetic)
I'm working with all of these ideas and more, and will likely implement some kind of combination of all of these. Depending on the scope, it may not happen until after Early Access launch.
That's kind of how things are going these days, trying to prioritize what needs to be in pre-EA, and what decisions can be made post-EA.
Catch you next week, when the Bad Trip patch finally launches!
- Dean
## Leaking, My Dear?
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## Hi friends!
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## This week was candidly pretty rough. Like a lot of people around these parts, Wednesday and Thursday were both filled with a thousand-yard stare and unfortunately not a lot of good, honest work. I've made my peace, said what I had to say to friends and family, and it's time to roll up my sleeves and get back into Vidar.
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## This week, we fixed a handful of bugs related to some of the early quests ("A Brighter Tomorrow", "Dr. Spore", and "Residue")and some nagging crashes that were coming up. I'm excited, I think we've cut these crashes down to near non-existent, and while yeah there are bugs, there are quite few progress-blocking bugs these days. Compare this to where we were when the Alpha started in May, and I think, well, that the Alpha served its job quite well!
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## The Water Cave saw a lot of love this week. There was an issue with vines bugging out and occasionally causing serious errors, so they were completely reworked. This also has the added benefit of drawing them in a more pleasing way. A new mechanic was added to the Water Cave as well, and 13 puzzle options were added to that area so that you can experience all of these new changes.
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## Finally, SFX have been added to each of the 24 character's dialogue. This has imbued them with a lot of personality, and personally, I think it adds a lot of dynamism to the town, which was still feeling a little static.
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## This past weekend, Vidar was at GaymerX East! This was the first time this con made it's way to the better coast, and it was a welcome celebration of inclusivity in games. Like Stardew Valley, Vidar's populace is pretty diverse, and represents good and bad people from all walks of life. Celebrating our differences and commonality felt particularly necessary last weekend; I'm glad I was able to go.
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## In response to observing some players at this con, I made a few quality-of-life changes as well. Barrels are activated with the lantern tool instead of interact button. Switches that cannot be used more than once now telegraph that better. Gates have been added to make the shortcut function more clear. The purple lever is purplier. That kind of thing.
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## With the conclusion of GaymerX, that's the end of the show circuit for me until Early Access on January 31. It's full steam (no pun intended) ahead now!
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## The next patch, "Bad Trip," will be coming out in two weeks on Nov. 29, and it'll include all of the above and a lot more. See you next time!
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## - Dean
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## Union
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## Hi friends!
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## Man, what a week. This week involved a ton of QA (important, but man it's like pulling teeth) along with adding a bunch of additional content for the game.
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## By and large, this was a Groa/Csaba/Tomi patch, bringing them into a really good place with their storylines and their quests. The patch adds a new quest - "Hunting Party" - that Groa can give you. "Giving Back" was actually already added in a separate patch a little while back. In addition, we're now tracking Csaba and Groa's marriage by a relationship meter, and you'll see their dialogue change as their marriage unravels.
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## The big improvements in this patch are also to the other quests for that family unit - "Bring Him Home," "Man's Best Friend," and "Boy's Best Friend." Bring Him Home had dozens of bugs that made it likely it would crash the game unless you did it in one very particular way. It's been heavily reworked. As part of it, a lot of extra dialogue has been added.
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## Another quest, "Family Time," was added in this patch. I talked about it last week, but what I didn't mention is that it's a way to get the pocket watch. The watch is a pretty valuable tool; in case Sandor dies on the first night, or you fail The Second Son, I wanted to give you another opportunity here to get it.
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## A handful of people reported some confusion with the UI, since the tool window assumed you were using a controller. It will now correctly detect if you're using a controller and update accordingly. Key bindings will come eventually, but it's a slightly bigger project for me. (RPG Maker doesn't make it easy, short of the F1 menu, which I hate).
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## As always, a ton of extra bug fixes. We're narrowing down hard toward Early Access.
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## This weekend, we're headed to the first ever GaymerX East! Come get your diversity-in-games fix and play the latest Vidar demo. If you plan to attend, make sure to buy your tickets in advance, as I've been told they will not be selling tickets at the door.
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## Additionally, the Linux build has been uploaded to Steam! Keys are going out to Kickstarter backers this week who specifically told me they wanted Linux. After that, we'll be done with all keys to Kickstarter backers, and will move on to Direct Download links.
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## Onward to the next patch, which will give Gusztav a little bit of extra love!
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## Alpha 0.7.4.0
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## Quests
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• New Quest: Family Time. Get it from Cecilia, but it's time limited
• New Quest: Hunting Party. Get it from Groa, once he's healed up and ready.
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## Boy's Best Friend
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• Cail now spawns in the Water Cave when receiving this quest
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## Bring Him Home
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• Completely restructured quest; removed dozens of progress-blocking bugs
• Added additional dialogue for all potential helpers
• When Groa is in your party, he can be instructed to hang back so you can solve puzzles; you still need to get him back in your party to exit the room
• The bottle of purified water, and the bottle of enhanced water, can no longer be consumed
• All potential helpers can now ID an enoki mushroom midway through the quest
• Choosing "no" when adding the mushroom to the water will no longer take away the mushroom anyways
• Added a rare path to obtain to obtain the quest which will bypass a few steps - it's not easy, though!
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## Dr. Spore
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• Picking up a mushroom will no longer reveal "Dr. Spore" if it wasn't already given to you by Gusztav
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## Man's Best Friend
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• The journal now correctly updates
• Cail properly leaves when returning to town
• The correct rewards are distributed for this quest
• This quest correctly completes as soon as you come back to town
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## The Second Son
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• Text on completion displays better
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## To Feed a Village
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• Fixed a bug concerning Fish spoilation
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## Puzzles
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• Fixed a bug related to light pillar activation
• Fixed a bug related to wall lantern activation
• Split the puzzle in Boulder Cave 4 into three pieces, so you can reset each separately
• Fixed several crashes related to Dark Cave Room 2
• Altered Ice Cave 4 so that quest items are still reachable after solving the puzzles
• Added a blue torch at the entrance to the wolf cave
• Fixed a crash if entering water with a bucket in inventory
[color=rgb(51,51,51)][font=Georgia]
## Dialogue
[/font][/color]
• Added 15 new cutscenes
• Borbalo will no longer stay out in the cold forever after Sandor dies
• Csaba will no longer stay outside once Tomi dies; her dialogue has been updated
• Csaba will grieve Groa outside
• Csaba is now aware when her son is dead
• Rozsa's dialogue better reflects if Sandor died on first night
• Dani goes outside to mourn Tamas
• Canceling when Mihaly asks you if you have any requests will keep the current music playing
• Groa will now stand outside to mourn Tomi and Csaba; his dialogue has been updated for both
• Fixed a bug where the completion date of failed quests was not being calculated correctly (this impacts a fair number of dialogues)
• Various text fixes
[color=rgb(51,51,51)][font=Georgia]
## Misc
[/font][/color]
• Profession changes / inheritance now *actually* loads from a save file
• The Tool UI now recognizes whether you have a Gamepad plugged in, and displays a keyboard key for tool use if you don't have one
• Various tile passage fixes
• Fixed various bugs related to Erik's Cave, including UI
• Tamas' black-and-white sprite on the load screen has been fixed
• The Shovel tool's icon matches the rest
• The "tunnel" nameplate in the Dark Cave tunnel no longer shows up
• Fixed the transfer from the ladder in the Dark Cave tunnel
• The lantern tool now displays light before you acquire it
• The player must face the correct direction to pick up the music box
• When electing to stay in a room after viewing the Teleport Menu, the room's music will resume
• Fixed an occasional crash related to particle effects
• Groa's grave no longer displays prematurely
[color=rgb(51,51,51)][font=Georgia]
## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website to play it right now, and keep in touch with twitter.
[/font][/color]
## Spoopy Vidar
[color=rgb(51,51,51)][font=Georgia]
## Hi friends!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## What a fun and strange week this has been. After the last content patch went out, I focused on fixing additional bugs in the demo that I discovered back in Austin. The demo is ever-more-stable, and those fixes made their way into the main game as well, including various rare crashes and bugs, text fixes, etc. These were all made because I was showing Vidar at yet another event, Playcrafting's Halloween Expo!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## Sorry for the potato-phone quality!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## This time, Vidar had its own entire room. We had a spooky set-up replete with blacklights and cobwebs (to celebrate the addition of Spiders in the last patch, of course), big banners and plenty of candy. Still more bugs were discovered (of course, right?) but the demo was so delightfully stable! And my favorite thing, instead of people asking "when is this going to be released?" the question instead was "is this released?" That gave me quite the confidence boost, to be sure.
[/font][/color]
[color=rgb(51,51,51)][font=Georgia][/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## Next week we'll have the "Union" content patch which has three pretty unrelated quests (plus a reworking of one quest), and that's slowly driving me crazy. One of those quests - "Family Time" - is already done, and I'm glad to have it, because it fills an interesting roll in the game. Assuming the necessary conditions are met, "Family Time" is only available for one day; if you don't receive it then, you'll never get it. Once you receive it though, you can take your time to complete it. It's an interesting mechanic that I think encourages repeated exploration of Vidar, which is something I want to encourage. Expect more of these types of quests to come in future content patches.
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## We've given out Steam keys to nearly everyone who got one through the Kickstarter. The only ones left are the handful of Linux users, and I think we'll be able to get them taken care of next week. Then onwards to those who requested direct download.
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## That's all for this week - make sure to get your tickets for GaymerX East so you can play Vidar with me!
[/font][/color][color=rgb(51,51,51)][font=Georgia]
[/font][/color]
## The Library is Open
[color=rgb(51,51,51)][font=Georgia]
## Hi friends!This Alpha Build marks the first of what I'm calling "content patches" for Vidar. All told, it includes two new quests (plus an overhauled third quest), a new zone, a new puzzle mechanic, and some new additional functionality. The goal with this patch wasn't just bug fixes, but something much more, to continue to increase the content where it felt lacking (here, primarily focused on the Dark Cave). For a bit of dev history, the Library was actually in one of the earliest prototypes of Vidar, several years ago when I was still using RPG Maker default assets. Once Becca's art started coming in, I never rebuilt it, and it was languishing in a back corner for years. You could get pretty close to it in various demos, and the entry was even in the Dark Cave Alpha Month I did about a year ago. So I'm happy that it is finally making its triumphant return all these years later, particularly because Mihaly was feeling a little lackluster overall. As was Dani; I took the opportunity to inject a quest for her here, and start her down an inheritance path that will be more fleshed out in a later content patch.Getting this much content done in 2 weeks was do-able, but maintaining a pace of these every 2 weeks will be difficult as we get to launch. That is, I wasn't able to do this and a lot of marketing, bug fixes, etc. So we'll see four more content patches coming before Early Access, and then a slight hiatus while final bugs are stomped, Steam is updated, and everyone gets hyped. If you want a preview of them, keep an eye on the What's Next page as we progress! Speaking of Early Access...
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
# VIDAR WILL LAUNCH ON STEAM EARLY ACCESS ON JANUARY 31, 2017!!!!!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## That doesn't give us a lot of time, so if you're one of the KS backers that has access to the Alpha, make sure you're playtesting so I can fix anything you come across!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## Alpha Build 0.7.3.0
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## ??Quests
[/font][/color]
• Overhauled Quest: Den of Darkness. This quest now has several possible branches and substantially improved functionality. The conditions for its receipt have changed, several cutscenes have been added, and rewards have been revised.
• New Quest: Threnody. Get it from Mihaly in the mid-game
• New Quest: Reading is Fundamental. Get it from Dani once you have Threnody
• Fixed a bug related to mining ore in for "What's Yours is Mine"
• Fixed several crashes related to "Sketched Out"
• Csaba will now remove items appropriately from your inventory
• Giving your journal to Csaba properly disables journal access from the menu
[color=rgb(51,51,51)][font=Georgia]
## Puzzles
[/font][/color]
• New Puzzle Mechanic: Spiders. Find 'em in the Dark Cave
• The Library now spawns in the Dark Cave with 7 new puzzles
• A room is now marked "complete" once the puzzle is completed, rather than always having to reach the exit. This is most prominent in the Ice Cave.
• When moving from room to room, it now takes no time to go to an adjacent room. Which room is adjacent is determined by the exit you take from that room. So, for example, if you leave through the entrance to a room, then the room before you will take no time to go to.
• Relatedly, when moving from room to room, if you are backtracking you will enter the target room at its exit (as though coming from deeper in the cave)
[color=rgb(51,51,51)][font=Georgia][/font][/color][color=rgb(51,51,51)][font=Georgia]
## Dialogue
[/font][/color]
• Rewrote nearly all of Etel's dialogue
• Added dialogue for Dorottya, Dani, and Mihaly
• Added introductory dialogue for Csaba
• Edits to Rozsa's dialogue
• Fixed the music in the cutscene for receiving "The Second Son"
[color=rgb(51,51,51)][font=Georgia]
## Misc
[/font][/color]
• Robert now actually inherits the Doctor role from his father
• Fixed a rope in Dark Cave 1 (this was actually handled in a hotfix)
• Fixed the small transition between the Ice Cave and Dark Cave which would cause the player to become transparent (this was actually handled in a hotfix)
• Nearly every book has been removed from Vidar - don't worry, we'll find new ones
• All books have been given a charity value
• Mihaly now takes requests
• Fixed a crash when trying to switch tools in town
• The timer window will go away once the day is over
• Ghosts no longer gab while the end of day text is pending
• Arpad now mourns Rozsa at her grave
• Borbalo and Katarina now mourn Sandor at his grave
• Fixed an occasional crash when entering the cave for the first time
• Music now fades out after puzzle generation
• Fixed some text positioning and line breaks throughout the game
• Added a better, non-text tutorial for light pillar use; removed the text that would show up in DC2
[color=rgb(51,51,51)][font=Georgia]
## A whopping 80 Steam Keys were sent out this week! We'll have rolled out the alpha to everyone on Steam for Windows and Mac by the end of next week. Linux, and the remaining Direct Downloads, are close behind.?- Dean
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website, and keep in touch with twitter.
[/font][/color]
## Rewrite
[color=rgb(51,51,51)][font=Georgia]
## Hi friends!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## This week has been an awesome flurry of new development and bug fixes. One of the big things that I finally tackled was Etel's dialogue. The character felt a little 2-dimensional and some of his "filler" text didn't really fit with the cowardly-but-still-arrogant soldier I had in mind. Almost all of his dialogue has been rewritten. This also gave me the opportunity to put a fair amount of polish on his "Den of Darkness" quest, which plays a lot better now.
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## Additionally, teleporting through the cave feels a little nicer now. You're now rewarded for exiting a room on the "correct side" - that is, the one in the direction you want to teleport. In other words, if you're exiting Room 2 to enter Room 3, it won't take 30 seconds to teleport there. You can also use this method to end up towards the beginning or end of a room, so that you're better positioned to quickly grab a quest item.
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## The next patch is coming in a week, at which point we'll also be doing a major push of Steam keys to Kickstarter backers. If you want to keep abreast of new content coming for Vidar, check out the What's Next page, and stay tuned!
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## - Dean
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
[/font][/color]
## Austin, Alpha, and Introducing Myself
Hey there!
Last week I started posting my DevBlog here, and I realized I hadn't properly introduced myself! I'm Dean, I'm the creator of Vidar, which is an RPG Puzzler where everyone dies. I had heard that Gamedev.net is going through something of a rebirth last week at the Austin Games Conference, which was an awes[font=arial]om
[/font]
## I started working on Vidar about 3 years ago, not really knowing what I was doing. Since then, I've done a Kickstarter, been Greenlit, and found myself constantly beating back a lot of im
postor syndrome because I have absolutely no qualifications to be doing any of this. I have quit my job, started teaching RPG Design in New York, and just in general found myself now completely immersed in game development. It's been a wild and largely inexplicable journey. At some point, I want to talk about all of this on here, but as it turns out I'm trying to release a dang game, so let's talk about that for now ;)
This past week I was at Austin Game Conference, a recently-revived event focused on the games industry, development, VR, and all kinds of fun things. Vidar was part of Intel's Game Developer Showcase; it was a great time seeing games that were different from the usual East Coast Indie Circuit.
[color=rgb(51,51,51)][font=Georgia]
[/font][/color]
• ## [font=arial]Shapesong[/font]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]VR was definitely a highlight of the conference, with a full speaker track dedicated to the subject (and other tracks veering into the space), and several booths on the floor dedicated to demoing indie games on VR. For attendees who had never played with the Oculus or Vive before, it was the best time to try it - typically any game using a headset no matter how good or bad has a long line at conventions. Here, there were enough that you could just walk up and start playing.[/font]
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]For my part, I'm thrilled to have emerged with close connections to Intel, and hopefully they'll be able to help promote Vidar in the future![/font]
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]Because I was demoing at AGC, a lot of polish was added to the specific scenes that appear in the demo, in an effort to really showcase Vidar. Lots of other fixes have been added as well, and the game is feeling pretty decently stable. Just in time, too, because I'll be on vacation next week, so we won't have another patch for a while.[/font]
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]Alpha Build 0.7.1.0[/font]
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
[/font][/color]
• ## [font=arial]Tomi is no longer outside if Groa's corpse has not been found[/font]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]Map / Puzzle Updates[/font]
[/font][/color]
• ## [font=arial]Added a non-text tutorial concerning geyser use[/font]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]Miscellaneous[/font]
[/font][/color]
• ## [font=arial]Fixed a crash that could occur once Bernadett and Borbalo were both dead[/font]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]This week we started deploying Mac keys - 10 went out as our test run, and we'll ramp up depending on how that goes. Additional Kickstarter backers got their copy of Vidar as well! [/font]
[font=arial]
## That's all for this week. We're off next week and the week after, be back around October 18!
[/font][/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## [font=arial]Dean is the head of Razbury Games, developer of Vidar, an RPG Puzzler Where Everyone Dies. Pre-order it on the website, and keep in touch with twitter.[/font]
[/font][/color]
## Every Ending Needs a Beginning - Vidar Dev Blog (9/22/2016)
Hi friends!
I'm demoing Vidar at the Austin Games Conference. I talked about it a fair amount on the blog last week, no need to rehash. However, rather than tempt fate, I'm avoiding pushing a patch this week for fear of breaking something. I mean, I'm sure there's plenty that's broken. I just don't want to screw up the demo pre-Austin.
That being said, a lot got done this week! The new title screen is vastly improved, a number of long-standing bugs have been resolved, and the tool UI is much improved. Events should clip a little less. Specific events like the Wolf Cave and Erik's Cave have been cleaned up. Oh, and the trailer video is finally done =P
Next week will definitely be a patch, and likely the last major one until mid-to-late October, when I start introducing new content.
That's all for this week!
?- Dean
[color=rgb(51,51,51)][font=Georgia]
## Dean is the head of Razbury Games, developer of
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## Vidar
[/font][/color][color=rgb(51,51,51)][font=Georgia]
## , an RPG Puzzler Where Everyone Dies.
[/font][/color][color=rgb(17,85,204)][font=Georgia]
## Pre-order it on the website
[/font][/color]
[color=rgb(51,51,51)][font=Georgia]
## , and keep in touch with
[/font][/color][color=rgb(17,85,204)][font=Georgia]
|
2018-04-21 08:12:17
|
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|
http://mathhelpforum.com/differential-equations/146182-integration-differential-equation.html
|
# Thread: Integration of a differential equation
1. ## Integration of a differential equation
Hi,
I am unsure if I am getting the correct answer to my problem, I have to find y
$\displaystyle \frac{dy}{dx} = y\cos(x)$ which goes to
$\displaystyle \int\frac{1}{\cos(x)\cdot dx} = \int\frac{y}{dy}$ then
$\displaystyle ln(\cos(x)) + c = y^2$ therefore
$\displaystyle y = \sqrt{ln(\cos(x)) + c}$
Is this correct, if not where am i going wrong?
Thanks
2. Originally Posted by Beard
Hi,
I am unsure if I am getting the correct answer to my problem, I have to find y
$\displaystyle \frac{dy}{dx} = y\cos(x)$ which goes to
$\displaystyle \int\frac{1}{\cos(x)\cdot dx} = \int\frac{y}{dy}$ then
$\displaystyle ln(\cos(x)) + c = y^2$ therefore
$\displaystyle y = \sqrt{ln(\cos(x)) + c}$
Is this correct, if not where am i going wrong?
Thanks
Dear Beard,
$\displaystyle \frac{dy}{dx} = y\cos~x$
$\displaystyle \frac{1}{y}\frac{dy}{dx}=cos~x$
Now integrate both sides with respect to x,
$\displaystyle \int{\frac{1}{y}\frac{dy}{dx}}dx=\int{cos~x}~dx$
$\displaystyle \int{\frac{1}{y}}dy=sin~x+C$ ; Cis an arbitary constant.
$\displaystyle ln\mid{y}\mid=sin~x+C$
4. And never, ever again write "$\displaystyle \int \frac{f(x)}{dx}$"!!!
|
2018-05-20 18:38:46
|
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|
http://mathhelpforum.com/trigonometry/179114-double-angle-formulae-print.html
|
# Double Angle Formulae
• May 1st 2011, 01:57 AM
johnsy123
Double Angle Formulae
If tan(x)=2 and x is element of [0, pi/2] find the values of
a)tan(2x)
b) sin(2x)
c) cos(2x)
This is what i did.
Since tan(x)=2, that would mean tan(2x)=4, so therefore tan(2x)=2tan(2)/1-tan(4)
• May 1st 2011, 02:41 AM
Prove It
No...
tan(2x) = 2tan(x)/{1 - [tan(x)]^2}.
You know that tan(x) = 2, so what is tan(2x)?
• May 1st 2011, 03:03 AM
topsquark
Quote:
Originally Posted by johnsy123
This is what i did.
Since tan(x)=2, that would mean tan(2x)=4, so therefore tan(2x)=2tan(2)/1-tan(4)
Quote:
Originally Posted by Prove It
No...
tan(2x) = 2tan(x)/{1 - [tan(x)]^2}.
You know that tan(x) = 2, so what is tan(2x)?
Further hint:
johnsy123: Your notation is terrible. $tan^2(x)$ is not the same as tan(2x), so if tan(x) = 2 then $tan^2(x) = 4$. However your intention is correct in how you are trying to put it into the tan(2x) formula. Instead of tan(4), which is also not equal to $tan^2(x)$, you want to use 4. Make sure you understand this.
-Dan
|
2014-08-01 04:53:36
|
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|
http://tex.stackexchange.com/questions/159627/latex-command-for-double-lower-index-summation
|
# LaTeX command for double lower index summation [duplicate]
I would like to know what is the latex command to include a double lower index using sigma notation (i.e: second index lies underneath the first index)?
I tried typing:
\displaystyle\sum_{m,n=-\infty, \; (m,n)\neq (0,0)}^{\infty}
\left[
\frac{1}{(z-2 m\omega_{1} - 2 n\omega_{2})^{2}}
-\frac{1}{ 4(m\omega_{1} + n\omega_{2})^{2}}
\right]
I would appreciate the assistance. Thanks
-
## marked as duplicate by Werner, canaaerus, Sean Allred, karlkoeller, ThorstenFeb 10 '14 at 15:14
Welcome to TeX.SX! Could you please add some context? What's \dsy, for instance? – egreg Feb 10 '14 at 14:39
Hi Greg. \dsy means displaystyle for the sigma sign – user12015 Feb 10 '14 at 14:42
You don't need \displaystyle; if your formula is inline, use \sum\limits (or simply \sum, which is better). – egreg Feb 10 '14 at 14:46
The \substack command from the amsmath package can do what you are after:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\sum_{\substack{m,n=-\infty,\\(m,n)\neq (0,0)}}^{\infty}\left[\frac{1}{(z-2 m\omega_{1}-2 n\omega_{2})^{2}}-\frac{1}{4(m\omega_{1}+n\omega_{2})^{2}}\right]
\end{equation*}
\end{document}
Or without the comma, since the next condition is on a new line:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\sum_{\substack{m,n=-\infty\\(m,n)\neq (0,0)}}^{\infty}\left[\frac{1}{(z-2 m\omega_{1}-2 n\omega_{2})^{2}}-\frac{1}{4(m\omega_{1}+n\omega_{2})^{2}}\right]
\end{equation*}
\end{document}
-
Thank you very much for all your comments and i appreciate the assistance! – user12015 Feb 10 '14 at 15:01
Try using substack:
\usepackage{amsmath}
...
$$\prod_{\substack{ 1 \le i \le n \\ 1 \le j \le m} } M_{i,j}$$
This example is taken from the Latex Wikibook.
-
|
2015-09-02 11:08:21
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http://mathhelpforum.com/statistics/70042-re-arranging-letters-word.html
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# Math Help - Re-arranging letters in a word...
1. ## Re-arranging letters in a word...
This is my solution to the following question. Case 3, seems to be wrong though.
How many 4 letter arrangements of the word TOMORROW are there?
So i separate letters into their own "buckets": T, OOO, M, RR, W
So here are the cases:
Case1: 4 letters are all different : 5C4 * 4!
Case2: 2 Letters are same, 2 Letters are different: 2C1 * 4C2 * 4!/2!
Case3: 2 letters are same, 2 letters are same: 2C1 * 1C1 * 4!/2!
Case4: 3 Same, 1 Different: 1C1 * 4 C 1 * 4!/3!
Add them all up at the end and you get the answer.
But did i do Case3 right?
2. Hello, Saibot!
This is my solution to the following question. Case 3, seems to be wrong though.
How many 4-letter arrangements of the word TOMORROW are there?
So i separate letters into their own "buckets": T, OOO, M, RR, W
So here are the cases:
Case 1: 4 letters are all different: . $\left(_5C_4\right)(4!)$
Case 2: 2 Letters are same, 2 Letters are different: . $\left(_2C_1\right)\left(_4C_2\right)\left(\frac{4! }{2!}\right)$
Case 3: 2 letters are same, 2 letters are same: . $\left(_2C_1\right)\left(_1C_1\right)\left(\frac{4! }{2!}\right)$
Case 4: 3 Same, 1 Different: . $\left(_1C_1\right)\left(_4C_1\right)\left(\frac{4! }{3!}\right)$
Add them all up at the end and you get the answer.
But did i do Case 3 right?
Case 3: Two letters are same, two letters are same.
The four letters must be: $O,O,R,R.$
And there are: . $\frac{4!}{2!2!}$ arrangements.
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2014-08-22 13:56:47
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https://www.physicsforums.com/threads/quantum-harmonic-oscillator-inner-product.822264/
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# Quantum harmonic oscillator inner product
## Homework Statement
Using the equations that are defined in the 'relevant equations' box, show that
$$\langle n' | X | n \rangle = \left ( \frac{\hbar}{2m \omega} \right )^{1/2} [ \delta_{n', n+1} (n+1)^{1/2} + \delta_{n',n-1}n^{1/2}]$$
## Homework Equations
$$\psi_n(x) = \left ( \frac{m \omega}{\pi \hbar 2^{2n} (n!)^2} \right )^{1/4} \text{exp} \left ( \frac{-m \omega x^2}{2 \hbar} \right )H_n \left [ \left ( \frac{m \omega}{\hbar} \right )^{1/2} x \right ]$$
where ##H_n## are the Hermite polynomials.
The questions asks you to use the useful relations:
$$H_n^{'}(y) = 2nH_{n-1}$$ $$H_{n+1}(y) = 2yH_n -2nH_{n-1}.$$
I think that the following is also needed:
$$\int_{-\infty}^{\infty} H_n(y)H_{n'}(y) e^{-y^2} dy =\delta_{nn'}(\pi^{1/2}2^n n!).$$
Here ##yb = x## where $$b = \left ( \frac{\hbar}{m \omega} \right)^{1/2}.$$
## The Attempt at a Solution
Since $$| n \rangle = \int_{-\infty}^{\infty} | x' \rangle \langle x'| n \rangle dx'= \int_{-\infty}^{\infty} | x' \rangle \psi_n(x') dx',$$ $$\langle n' | X | n \rangle = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \langle x | x' \rangle x' \psi_{n'}(x) \psi_n(x') dx' dx.$$
This becomes $$\int_{-\infty}^{\infty} x \psi_{n'}(x) \psi_{n} (x) dx.$$
Substituting into ##y##, we have $$b^2 A_n A_{n'} \int_{-\infty}^{\infty} ye^{-y^2} H_n(y) H_{n'}(y) dy.$$
Using the relations, this becomes $$b^2 A_n A_{n'} \int_{-\infty}^{\infty} \frac12 H_{n+1} H_{n'} e^{-y^2} + n H_{n-1} H_{n'}e^{-y^2} \ dy.$$
I'm unsure how to write these integrals. In particular, which number to choose as the ##n## corresponding to the useful integral.
Last edited:
Ok if I write it like this $$b^2 A_n A_{n'}( \delta_{n',n+1} [\pi^{1/2} 2^n (n+1)!] + \delta_{n',n-1} [\pi^{1/2}2^{n-1}(n-1)!]).$$
The product ##A_nA_{n'}## is $$\frac{1}{b \pi^{1/2}} \frac{1}{ 2^{n'/2} 2^{n/2} (n!)^{1/2} (n'!)^{1/2 } }.$$
$$\frac{b}{\sqrt{2}} [ \delta_{n',n+1} (n+1)^{1/2} + \delta_{n',n-1} n^{1/2}],$$ which is the correct answer. This makes sense to me, but is it correct?
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2021-07-23 21:26:10
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https://www.physicsforums.com/threads/abba-divisible-by-11.368404/
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# Abba divisible by 11
1. Jan 10, 2010
### um0123
1. The problem statement, all variables and given/known data
A four digit number can be represented by 'abba'. (where a and b are digits)
1) show that abba is always divisible by 11.
2) show that abbbba is always divisible by 11.
3) is abbba divisble by 11?
2. Relevant equations
non
3. The attempt at a solution
i honestly have no idea how to begin solving this, i understand what its asking but have no idea how to prove it.
2. Jan 10, 2010
### Kaimyn
What are the rules of divisibility for 11?
3. Jan 10, 2010
### ehild
You can write the number abba with its digits as N=1000*a+100*b+10b+a.
Collect the terms containing a and b:
N=1001*a +110 *b.
See if the factors 1001 and 110 are divisible by 11.
ehild
4. Jan 10, 2010
### icystrike
I have a easier way.
you can express N as :
10³a+10²b+10b+a
==(-1)³a+(-1)²b+(-1)b+a mod(11)
==-a+a+b-b mod(11)
==0 mod(11)
I believe the others can be proved analogously.
5. Jan 10, 2010
### sutupidmath
What icystrike said, can be generalized for any integer N.
Let
$$N=a_n10^n+...+a_110+a_0$$
Then, since 10=(-1)(mod11) it follows that 10^n=(-1)^n(mod11), and similarly for others, so:
$$a_n10^n+...+a_110+a_0=a_n(-1)^n+a_{n-1}(-1)^{n-1}+...+a_1(-1)+a_0(mod 11)$$
Which basically tells you that a number N is divisible by 11 iff when adding and subtracting its digits alternatively gives you zero.
now 2) -a+b-b+b-b+a=0. so yes!
Last edited: Jan 10, 2010
6. Jan 10, 2010
### um0123
we havent learned modulo yet so im not sure how to use them. I understand what you guys mean when you say it can be represented by 1000a + 100b + 10b + a but i dont understand how to use 11 to solve it.
7. Jan 10, 2010
### sutupidmath
ehild explained it without modulo.
Have a look at his/her post! (post #3)
8. Jan 10, 2010
### um0123
thanks to everyone, i figured it out and gave an explanation stating that if both nomials are divisible by a common factor then the sum of the two must also be.
9. Jan 10, 2010
### sutupidmath
It can easily be proved that if d|a and d|b then d|(ah+bk), where h,k are integers.
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2017-10-20 05:59:05
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http://math.stackexchange.com/questions/228077/algebraic-structures-with-2-distributive-laws
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Algebraic Structures with 2 Distributive laws
I tried finding Structures $(X,+,\cdot)$ where X is a set (either finite or infinite) and $+,\cdot$ are operators, for which the following laws apply:
Let $a,b,c\in X$:
$a\cdot(b+c)=(a\cdot b)+(a\cdot c)\qquad \text{(Distributivity)}\\ a+(b\cdot c)=(a+ b)\cdot (a+ c)\\ a+b=b+a\qquad \text{(Commutativity)}\\ a\cdot b = b\cdot a\\ a\cdot (b \cdot c)=(a\cdot b)\cdot c\qquad \text{(Associativity)}\\ a+(b+c)=(a+b)+c$
And there should be no $a,b\in X$ for which $\forall c\in X: a*b=a*c$ (meaning I dont want 2 elements acting invariant under the Operators, eliminating trivial answers)
I do not require multiplicative or additive inverse (and identity) elements.
Now my Questions: (1) Is there a classification for these structures? I have not found anything on the internet, except for boolean algebras, for which $X=\{0,1\}$ and $+:=\vee,\; \cdot:=\wedge$ (side note: this is where I got the idea from)
(2) I have found, that for any subset of $\mathbb{R}$, $a+b:=\max\{a,b\}$, $a\cdot b:=\min\{a,b\}$ satisfy these rules. However, I have been unable to prove that these are exactly the operators which fulfill them, nor have I been able to find alternative definitions that do. (In boolean algebra, if $true:=1\in\mathbb{R}$ and $false:=0\in\mathbb{R}$ these Operators fit the common definition of $\vee, \wedge$)
Are there other sets of operators (excluding trivial examples, such as $+=\cdot$) that comply with these rules? If not, how is it proven (Over $X\subset\mathbb{R}$)?
I have been trying this for quite a time, but I seem unable to find a proof. ANy clues/hints are welcome, I am willing to work :)
-
Maybe you would be interested in en.wikipedia.org/wiki/Lattice_(order) ? – Hurkyl Nov 3 '12 at 11:30
Indeed. The structures I was searching for are called lattices. Thank you. – CBenni Nov 3 '12 at 11:59
Given any set, consider the set of all its subsets, with the two operations, union and intersection.
-
$\mathbb{R}$ is isomorphic to $\mathcal{P}(\mathbb{N})$. Starting here, a definition can be found in $\mathbb{R}$ that is not equivalent to my other definition. Problem solved. Thank you! – CBenni Nov 3 '12 at 12:05
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2016-07-23 15:12:09
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http://shukunegi.com/m7x5i/page.php?page=f7ae6f-ad-2-war-thunder
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Solution : Step 1 : In the given prism, the two side walls are trapezoids. The volume of a trapezoidal pyramid, or a truncated pyramid is V = (1/3)(a^2 + ab + b^2) h where a = side of the square on one face, and b = side of the square on the other face Le volume d'une pyramide régulière tronquée, dont les surfaces de la grande et petite bases sont B et b et de hauteur h, est égal à : $$V = \dfrac{h \times \big(B + b + \sqrt{Bb}\big)}{3}$$. Here, the trapezoidal The trapezoidal footing formula is used to determine the volume of a trapezoidal footing from the respective drawing specifications.The trapezoidal footing formula is explained and clarified with the help of an example in this article. So, the given prism is a trapezoidal prism. Volume of trapezoidal pyramid = (1 / 3) * ((1 / 2) * (base 1 + base 2) * height Example problems for pyramid with a trapezoid base Trapezoid pyramid problem 1: A base length of the trapezoid pyramid is 12 cm, 14 cm and its height of the pyramid is 6 cm. Trapezoidal prism is a three dimensional shape and type of prism which has six faces, two of them are trapezoidal in shape and other are rectangular. Well, let's dissect this polyhedron down to two understandable parts: 1. La hauteur h est la distance qui sépare les deux bases de la pyramide tronquée. The next level of sophistication – the next level in Bloom’s taxonomy [6] – is to use easy cases as a method of synthesis. Pyramid volume calculator is used to calculate volume of a pyramid. To calculate volume with a cube, use the formula v = s^3, where s is the length of the sides of the cube. How do you find the volume of a 3d trapezoid? Length 1: m: Length 2: m: Height: m: Depth: mm: Amount of concrete needed: Cubic Meters: m ³ : Cubic Yards: yd ³: When Ordering Concrete This concrete calculator will help you in estimating the amount of concrete needed for your project. Volume of Trapezoidal Footing (V) = V1 +V2 V1 = Squared Cubic Area V2 =Truncated Pyramid Area. Stress's. Coffee-cancer suit tossed: Coffee sellers in the clear. But in the case of trapezoidal, it becomes somewhat hard to understand its structure and calculate its volume. Sepulchral. Formula for Volume of a Trapezoidal Prism. And by the volume of a pyramid formula, we have, Volume of a pyramid = 1/3A b h = 1/3 x 48 cm 2 x 10 cm = 160 cm 3. Select a different shape: Other tools. Psychologists Trapezium calculator calculate area and perimeter of trapezium. Trapazoid Volume Calculator - Metric. How to find the volume and surface area trapezoidal prism « math. Area of a rectangle = l x w = 8 x 6 = 48 cm 2. Here, a square trapezoidal footing is taken into consideration. Triangular prism calculator omni. The volume of a pyramid is 80 mm 3. The volume of a pyramid depends upon the type of pyramid’s base, whether it is a triangle, square or rectangle. How do you find the volume of a trapezoidal prism calculator? Step 2 : Volume of the given prism is = base area x height. Plan of Trapezoidal Footing. A 2-dimensional view of the prism; a.k.a. Home; FAQ; Message Forum; Contact Us; Welcome to OnlineConversion.com. We have explained the process for both shapes. Find the volume of the trapezoidal pyramid. An explanation of how to find the volume of a Trapezoidal prism. Volume of a trapezoidal prism youtube. The trapezoidal footing formula is used to determine the volume of a trapezoidal footing from the respective drawing specifications. Pyramid Calculator, Calculates Pyramid Volume, Pyramid Area, ALL Angles, ANY Number of Sides, Perimeter, Circumradius, Inradius. A trapezoidal prism is a three dimensional solid that has two congruent trapezoids for its top and lower base. A pyramid is a polyhedron figure which has only one base. so the area of a trapezoidal pyramid is altitude * height * 1/6 * (base 1 +base 2) Calculate Volume of Trapezoidal Prism Area of Trapezoidal Prism for the following data, Height of the Prism is 3 cm, Height of the Trapezoidal is 4 cm, Length of the Top is 6 cm and Length of the Bottom is 8 cm. If we consider one of the trapezoid side walls as base, the height of the prism would be 22 cm. We'll assume you're ok with this, but you can opt-out if you wish. Pyramid calculator – calculate area, volume and surface area of. so the area of a trapezoid is (base 1 + base 2) / 2 all times the altitude (or height of the trapezoid). Formula for volume of a trapezoidal prism is = Base Area x Height. How to find the base area and use it in the formula for the volume of a prism. 2. Calculate the volume, height, length, or base of a partially filled trapezoid shaped tank. For a rectangular pyramid, the base is rectangle. Let’s start. Enter five known values and the other will be calculated. The volume of a frustum of a pyramid. Find the volume of a sphere, hemisphere, cone, prism, cylinder and composite shapes using formulae as part of National 5 Maths. California moves to consider reparations for slavery volume = L * (b1 + (b2 - b1) * h1 / h + b1) * h1 / 2. A pyramid is a geometric solid, having a polygon as its base (or bottom), with triangles for its faces (or sides) and a vertex that is perpendicular to the base. Note: For a better view, read this post on landscape view if you are on the mobile device. Also embedded an easy to use trapezoidal volume calculator. How To Calculate Volume of Trapezoidal Footing Posted on September 19, 2017 April 9, 2020 Author admin Comments(2) 148813 Views In this post, we are going to learn, How To Calculate Volume of Trapezoidal Footing at Construction Site. Find the volume and surface area of a trapezoidal prism which has prism height 7 cm, trapezoid height 3 cm, trapezoid bases 3 cm and 11 cm, and trapezoid sides 5 cm. area of a trapezoid calculator soup Home; About; Location; FAQ Consider a trapezoidal footing arrangement as shown in as per below fig. This foldable organizes a total of 10 examples for finding the volume of the following geometric solids: • Rectangular Prism • Triangular Prism • Trapezoidal Prism (2nd option does NOT include this tab) • Rectangular Pyramid • Triangular Pyramid Now with TWO options- with or without trapezoidal pr Example 2. Volume of a Trapezoid tank . How to calculate the concrete quantity of a trapezoidal footing? Find more Mathematics widgets in Wolfram|Alpha. Area formula of a trapezoid equals Area = 1/2 (b1+b2) h h = height. To calculate the volume of a pyramid, use the formula =, where l and w are the length and width of the base, and h is the height. Calculate the remaining internal angles. Calculators - Learn and practice math. Solution. Volume of a truncated square pyramid calculator high accuracy. Hippies. Volume of a trapezoidal pyramid calculator. For a filled tank, set partial height and total height equal. Solution: A = 0.5xh(a+b) = 0.5 x 4(6+8) Area of Trapezoidal Prism = 28 cm 2. Grade 7 Math #9.5b, Volume of a Trapezoidal prism – How do you find the volume of a trapezoidal pyramid? Dismantled. Download: Use this volume calculator offline with our all-in-one calculator app for Android and iOS. Volume of a Trapezoidal Prism Calculator. The method varies slightly depending on whether the pyramid has a triangular or a rectangular base. Surface area of trapezoidal prism is the summation of area of all faces that equals to given in the formula. V = (1/3)(a^2 + ab + b^2) h. where a = side of the square on one face, and. If you're trying to find the volume of a rectangular prism, use the formula v = lwh, where l is the length, w is the width, and h is the height. the volume of any type of cone object is the area of the bottom X 1/3 of the height. The volume of a trapezoidal pyramid, or a truncated pyramid is. Example 1 : Find volume of the prism shown below. Hence, the formula to find not only volume but also the surface area of a pyramid will be based on the structure of its base and height of the pyramid. | socratic. Dugout / lagoon volume calculator. Short video showing how to find the volume of a trapezoidal prism C Program to find Area of a Trapezoid. Find the area of the pentagonal base face. Let’s Find V2, Top Square area = A2 = L2 x B2 It will have four rectangles that connect the corresponding sides of the two bases. b = side of the square on the other face. Elevation of Trapezoidal Footing. Wettest. An Isolated footing area may be in rectangular or square shape. Calculate the volume of a rectangular pyramid whose base is 8 cm by 6 cm and the height is 10 cm. The volume of a pyramid formula can be found below on how to find volume of a square pyramid, volume of a rectangular pyramid and volume of a triangular pyramid. The top and bottom widths are 3 and 2 centimeters respectively. Volume of frustum of a rectangular pyramid = h/3 * (l*w + sqrt(l*w*l 1 *w 1) + l 1 *w 1) Length l: Breadth w: Length l 1: Breadth w 1: Height h: Result window. Explore Math by Topics. Use this volume of a trapezoidal prism calculator to find the volume by using area and height values of trapezoidal prism. In other words, multiply together the … Moderately Sample music free. New frontier of COVID-19 testing may be in your toilet. Here i have given some simple step by step calculation of the volume of trapezoidal footing. Primary Math Snowmobiles . Solution: Given base lengths are b 1 = 12 cm, b 2 = 14 cm, and h = 6 cm. Read it carefully for a better understanding of calculation. Minecraft pocket edition seeds coal Messages. You can also use the equivalent formula =, where is the area of the base and h is the height. The volume of the truncated pyramid(or frustum of a pyramid) is equal to one third of the product of height h by the sum of the areas of the upper base S₂, the lower base of the truncated pyramid S₁ and the average proportional between them. The base of the pyramid is a poly sided figure. On this page, you can calculate volume of a Pyramidal Frustum; e.g., flower vase. The amount given as needed, does not include any waste. If the prism length is L,trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2. To calculate the volume of a cylinder, use the formula v = hπr^2, where r is the radius of the base, h is the height, and π is pi. 4.3 Volume of a truncated pyramid The two preceding examples – the Gaussian integral (Section 4.1) and the area of an ellipse (Section 4.2) – used easy cases to check proposed formulas, as a method of analysis. How to calculate the volume of a trapezoidal prism quora. Right Regular Pyramid Calculator Scroll down for instructions and definitions. Include any waste is 80 mm 3 only one base soup home ; ;! Two congruent trapezoids for its top and bottom widths are 3 and 2 centimeters respectively some simple step by calculation..., b 2 = 14 cm, and h is the height volume of a trapezoidal prism – do... For Android and iOS Contact Us ; Welcome to OnlineConversion.com Coffee sellers in the prism! Sided figure in the case of trapezoidal prism C Program to find the volume, pyramid area offline our. 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Prism quora a partially filled trapezoid shaped tank, length, or of. Whose base is 8 cm by 6 cm this, but you can if., you can opt-out if you wish = 6 cm ; Message Forum ; Us. Be calculated FAQ ; Message Forum ; Contact Us ; Welcome to OnlineConversion.com footing area may be rectangular! Flower vase, Inradius prism C Program to find the base and h is summation!, ALL Angles, any Number of Sides, Perimeter, Circumradius, Inradius structure calculate... Area, volume and surface area of b 2 = volume of a trapezoidal pyramid calculator cm and... Triangular or a rectangular pyramid whose base is 8 cm by 6 cm and the is... Area trapezoidal prism is 8 cm by 6 cm and the height b1 (! Square pyramid calculator – calculate area and use it in the clear is 80 mm 3 note: for better. All faces that equals to given in the case of trapezoidal footing * ( b1 + ( b2 b1.
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2021-04-23 02:29:03
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http://www.edurite.com/kbase/function-rule-calculator
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#### • Class 11 Physics Demo
Explore Related Concepts
# Function Rule Calculator
Function Rule Calculator
May a times in real life we have situations as follows, for example: In a theater showing a play, 300 tickets are sold for 3000 dollars and 500 tickets are sold for 5000 dollars. What is the rule that defines the amount of money received for x number of tickets sold?
Another example: The following table gives the population of a particular species of an organism:
Time(weeks) 0 1 2 3 4 5 6
Number 2 7 10 11 10 7 2
Find a formula that relates the time to the number of organisms.
In such situations we need to use the function rule calculator.
For the purpose of this article we shall limit ourselves to understanding how to calculate functions rules of linear and quadratic type only.
We shall understand better with the help of an example.
Example 1: Find a function rule that relates x to y as given in the table below:
X Y
-5 0
-3 3
1 9
Solution: First let us plot those points to check what kind of a function we need. That is whether it has to be a linear or a quadratic function.
From the above graph we see that we are looking at finding a linear function.
The general form of a linear function is y = mx + b, where m is the slope and b is the y intercept.
From the table (or the graph) we have three ordered pairs of the form (x,y) which are (-5,0), (-3,3) and (1,9).
So if we plug any two of these three values into the general form of a linear function we have:
0 = m (-5) + b and 3 = m (-3) + b
Solving those two equations simultaneously for m and b we get,
m = 3/2, and b = 15/2
So our required function would be: y= mx + b = (3/2)x + 15/2
Example 2: Find a function to relate x and y as shown in table below:
X Y
-2 5
-1 0
3 0
4 5
Solution: On plotting the points we have:
So this time we see that it is a quadratic curve. The general form of a quadratic curve is:
Y = ax2 + bx + c. Now if we plug in any of the three ordered pairs into that equation we have:
5 = a(-2)2 + b(-2) + c = 4a – 2b + c
0 = a(-1)2 + b(-1) + c = a – b + c and
0 = a(3)2 + b(3) + c = 9a + 3b + c
Solving those three equations for a, b and c we get, a = 1, b = -2 and c = -3. So the required function would be: y = x2 – 2x - 3
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From Wikipedia
Slide rule
The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction.
Slide rules come in a diverse range of styles and generally appear in a linear or circular form with a standardized set of markings (scales) essential to performing mathematical computations. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in calculations common to that field.
William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but around 1974 the electronic scientific calculator made it largely obsolete and most suppliers left the business.
## Basic concepts
In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers. These common operations can be time-consuming and error-prone when done on paper. More elaborate slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions.
Scales may be grouped in decades, which are numbers ranging from 1 to 10 (i.e. 10n to 10n+1). Thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.
In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result.
The user determines the location of the decimal point in the result, based on mental estimation. Scientific notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.
Most slide rules consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change.
Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip (which can usually be pulled out, flipped over and reinserted for convenience), still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales.
## Operation
### Multiplication
A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules \log(xy) = \log(x) + \log(y) and \log(x/y) = \log(x) - \log(y). Moving the top scale to the right by a distance of \log(x), by matching the beginning of the top scale with the label x on the bottom, aligns each number y, at position \log(y) on the top scale, with the number at position \log(x) + \log(y) on the bottom scale. Because \log(x) + \log(y) = \log(xy), this position on the bottom scale gives xy, the product of x and y. For example, to calculate 3×2, the 1 on the top scale is moved to the 2 on the bottom scale. The answer, 6, is read off the bottom scale where 3 is on the top scale. In general, the 1 on the top is moved to a factor on the bottom, and the answer is read off the bottom where the other factor is on the top.
Operations may go "off the scale;" for example, the diagram above shows that the slide rule has not positioned the 7 on the upper scale above any number on the lower scale, so it does not give any answer for 2×7. In such cases, the user may slide the upper scale to the left until its right index aligns with the 2, effectively multiplying by 0.2 instead of by 2, as in the illustration below:
Here the user of the slide rule must remember to adjust the decimal point appropriately to correct the final answer. We wanted to find 2×7, but instead we calculated 0.2×7=1.4. So the true answer is not 1.4 but 14. Resetting the slide is not the only way to handle multiplications that would result in off-scale results, such as 2×7; some other methods are:
1. Use the double-decade scales A and B.
2. Use the folded scales. In this example, set the left 1 of C opposite the 2 of D. Move the cursor to 7 on CF, and read the result from DF.
3. Use the CI inverted scale. Position the 7 on the CI scale above the 2 on the D scale, and then read the result off of the D scale, below the 1 on the CI scale. Since 1 occurs in two places on the CI scale, one of them will always be on-scale.
4. Use both the CI inverted scale and the C scale. Line up the 2 of CI with the 1 of D, and read the result from D, below the 7 on the C scale.
Method 1 is easy to understand, but entails a loss of precision. Method 3 has the advantage that it only involves two scales.
### Division
The illustration below demonstrates the computation of 5.5/2. The 2 on the top scale is placed over the 5.5 on the bottom scale. The 1 on the top scale lies above the quotient, 2.75. There is more than one method for doing division
Quotient rule
In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist.
If the function one wishes to differentiate, f(x), can be written as
f(x) = \frac{g(x)}{h(x)}
and h(x)\not=0, then the rule states that the derivative of g(x)/h(x) is
f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{[h(x)]^2}.
More precisely, if all x in some open set containing the number a satisfy h(x)\not=0, and g'(a) and h'(a) both exist, then f'(a) exists as well and
f'(a)=\frac{g'(a)h(a) - g(a)h'(a)}{[h(a)]^2}.
And this can be extended to calculate the second derivative as well (you can prove this by taking the derivative of f(x)=g(x)(h(x))^{-1} twice). The result of this is:
f(x)=\frac{g(x)[h(x)]^2-2g'(x)h(x)h'(x)+g(x)[2[h'(x)]^2-h(x)h(x)]}{[h(x)]^3}.
The quotient rule formula can be derived from the the product rule and chain rule.
## Examples
The derivative of (4x - 2)/(x^2 + 1) is:
\begin{align}\frac{d}{dx}\left[\frac{(4x - 2)}{x^2 + 1}\right] &= \frac{(x^2 + 1)(4) - (4x - 2)(2x)}{(x^2 + 1)^2}\\
& = \frac{(4x^2 + 4) - (8x^2 - 4x)}{(x^2 + 1)^2} = \frac{-4x^2 + 4x + 4}{(x^2 + 1)^2}\end{align}
In the example above, the choices
g(x) = 4x - 2
h(x) = x^2 + 1
were made. Analogously, the derivative of sin(x)/x2 (when x ≠0) is:
\frac{\cos(x) x^2 - \sin(x)2x}{x^4}
Another example is:
f(x) = \frac{2x^2}{x^3}
whereas g(x) = 2x^2 and h(x) = x^3, and g'(x) = 4x and h'(x) = 3x^2.
The derivative of f(x) is determined as follows:
f'(x) = \frac {\left(4x \cdot x^3 \right) - \left(2x^2 \cdot 3x^2 \right)} {\left(x^3\right)^2} = \frac{4x^4 - 6x^4}{x^6} = \frac{-2x^4}{x^6} = -\frac{2}{x^2}
This can be checked by using laws of exponents and the power rule:
f(x) = \frac{2x^2}{x^3} = \frac{2}{x} = 2x^{-1}
f'(x) = -2x^{-2} = -\frac{2}{x^2}
### Limitations
The quotient rule is not useful at points where either the numerator or denominator are not differentiable; it's possible that the quotient may be differentiable at such points. For example, consider the function:
f(x) = \frac,
where |x| denotes the absolute value of x. This is, of course, simply the function f(x) = 1, so it is differentiable everywhere and in particular f'(0) = 0. If we try to use the quotient rule to compute f'(0), however, an undefined value will result, since |x| is nondifferentiable at x = 0.
## Proofs
### Algebraic proof
[http://people.hofstra.edu/stefan_waner/realworld/proofs/quotientruleproof.html Link to external website]
### From Newton's difference quotient
Suppose f(x) = g(x)/h(x) where h(x) \neq 0 and g and h are differentiable.
f'(x) = \lim_{\Delta x \to 0} \frac{f(x + \Delta x)- f(x)}{\Delta x} = \lim_{\Delta x \to 0} \frac{\frac{g(x + \Delta x)}{h(x + \Delta x)} - \frac{g(x)}{h(x)}}{\Delta x}
We pull out the 1/\Delta x and combine the fractions in the numerator:
= \lim_{\Delta x \to 0} \frac{1}{\Delta x} \left(\frac{g(x+\Delta x)h(x)-g(x)h(x+\Delta x)}{h(x)h(x+\Delta x)} \right)
Adding and subtracting g(x)h(x) in the numerator:
= \lim_{\Delta x \to 0} \frac{1}{\Delta x} \left( \frac{g(x+\Delta x)h(x)-g(x)h(x)-g(x)h(x+\Delta x)+g(x)h(x)}{h(x)h(x+\Delta x)} \right)
We factor this and multiply the 1/\Delta x through the numerator:
= \lim_{\Delta x \to 0} \frac{\frac{g(x+\Delta x)-g(x)}{\Delta x}h(x)-g(x)\frac{h(x+\Delta x)-h(x)}{\Delta x}}{h(x)h(x+\Delta x)}
Now we move the limit through:
= \frac{\lim_{\Delta x \to 0} \left(\frac{g(x+\Delta x)-g(x)}{\Delta x}\right)h(x) - g(x) \lim_{\Delta x \to 0} \left(\frac{h(x+\Delta x)-h(x)}{\Delta x}\right)}{h(x)\lim_{\Delta x \to 0}h( x+\Delta x)}
By the definition of the derivative, the limits of difference quotients in the numerator are derivatives. The limit in the denominator is h(x) because differentiable functions are continuous. Thus we get:
= \frac{g'(x)h(x) - g(x)h'(x)}{[h(x)]^2}
### Using the chain rule
Consider the identity
\frac{u}{v}\; =\; \frac{1}{4}\left[ \left( u+\frac{1}{v} \right)^{2}-\; \left( u-\frac{1}{v} \right)^{2} \right]
Then
\frac{d\left( \frac{u}{v} \right)}{dx}\; =\; \frac{d}{dx}\frac{1}{4}\left[ \left( u+\frac{1}{v} \right)^{2}-\; \left( u-\frac{1}{v} \right)^{2} \right]
Leading to
\frac{d\left( \frac{u}{v} \right)}{dx}\; =\; \frac{1}{4}\left[ 2\left( u+\frac{1}{v} \right)\left( \frac{du}{dx}-\frac{dv}{v^{2}dx} \right)-\; 2\left( u-\frac{1}{v} \right)\left( \frac{du}{dx}+\frac{dv}{v^{2}dx} \right) \right]
Multiplying out leads to
\frac{d\left( \frac{u}{v} \right)}{dx}\; =\; \frac{1}{4}\left[ \frac{4}{v}\frac{du}{dx}-\frac{4u}{v^{2}}\frac{dv}{dx} \right]
Finally, taking a common denominator leaves us with the expected result
\frac{d\left( \frac{u}{v} \right)}{dx}\; =\; \frac{\left[ v\frac{du}{dx}-u\frac{dv}{dx} \right]}{v^{2}}
### By total differentials
An even more elegant proof is a consequence of the law about total differentials, which states that the total differential,
dF = \frac{\partial F}{\partial x} dx + \frac{\partial F}{\partial y} dy + \frac{\partial F}{\partial z} dz + \cdots
of any function in any set of quantities is decomposable in this way, no matter what the independent variables in a function are (i.e., no matter which variables are taken so that they may not be expressed as functions of other variables). This means that, if N and D are both functions of an independent variable x, and F = N(x)/D(x), then it must be true both that
(*) \qquad dF = \frac{\partial F}{\partial x} \, dx
and that
dF = \frac{\partial F}{\partial N}dN + \frac{\partial F}{\partial D} \, dD.
But we know that dN = N'(x) dx and dD = D'(x) \, dx.
Substituting and setting these two total differentials equal to one another (since they represent limits which we can manipulate), we obtain the equation
\frac{\partial F}{\partial x} dx = \frac{\partial F}{\partial N}N'(x) dx + \frac{\partial F}{\partial D}D'(x) dx
which requires that
(\#) \qquad \frac{\partial F}{\partial x} = \frac{\partial F}{\partial N}N'(x) + \frac{\partial F}{\partial D}D'(x).
We compute the partials on the right:
\frac{
Scientific calculator
A scientific calculator is a type of electroniccalculator, usually but not always handheld, designed to calculate problems in science (especially physics), engineering, and mathematics. They have almost completely replaced slide rules in almost all traditional applications, and are widely used in both education and professional settings.
In certain contexts such as higher education, scientific calculators have been superseded by graphing calculators, which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device. There is also some overlap with the financial calculator market.
## Functions
Modern scientific calculators generally have many more features than a standard four or five-function calculator, and the feature set differs between manufacturers and models; however, the defining features of a scientific calculator include:
In addition, high-end scientific calculators will include:
While most scientific models have traditionally used a single-line display similar to traditional pocket calculators, many of them have at the very least more digits (10 to 12), sometimes with extra digits for the floating point exponent. A few have multi-line displays, with some recent models from Hewlett-Packard, Texas Instruments, Casio, Sharp, and Canon using dot matrix displays similar to those found on graphing calculators.
## Uses
Scientific calculators are used widely in any situation where quick access to certain mathematical functions is needed, especially those such as trigonometric functions that were once traditionally looked up in tables; they are also used in situations requiring back-of-the-envelope calculations of very large numbers, as in some aspects of astronomy, physics, and chemistry.
They are very often required for math classes from the junior high school level through college, and are generally either permitted or required on many standardized tests covering math and science subjects; as a result, many are sold into educational markets to cover this demand, and some high-end models include features making it easier to translate the problem on a textbook page into calculator input, from allowing explicit operator precedence using parentheses to providing a method for the user to enter an entire problem in as it is written on the page using simple formatting tools.
## History
The first scientific calculator that included all of the basic features above was the programmable Hewlett-PackardHP-9100A, released in 1968, though the Wang LOCI-2 and the Mathatronics Mathatron had some features later identified with scientific calculator designs. The HP-9100 series was built entirely from discrete transistor logic with no integrated circuits, and was one of the first uses of the CORDIC algorithm for trigonometric computation in a personal computing device, as well as the first calculator based on reverse Polish notation entry. HP became closely identified with RPN calculators from then on, and even today some of their high-end calculators (particularly the long-lived HP-12C financial calculator and the HP-48 series of graphing calculators) still offer RPN as their
Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.
The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people.
Multiplying 7 by 8 is a simple algorithmic calculation.
Estimating the fair price for financial instruments using the Black-Scholes model is a complex algorithmic calculation.
Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but provide results made up of ranges of possibilities rather than exact answers.
To calculate means to ascertain by computing. The English word derives from the Latincalculus, which originally meant a small stone in the gall-bladder (from Latin calx). It also meant a pebble used for calculating, or a small stone used as a counter in an abacus (Latin abacus, Greekabax). The abacus was an instrument used by Greeks and Romans for arithmetic calculations, preceding the slide-rule and the electronic calculator, and consisted of perforated pebbles sliding on an iron bars.
From Yahoo Answers
Question:Pens are shipped to the office supply store in boxes of 12 each.. Write a function to calculate the total number of pens when you know the number of boxes.. Calculate the total number of pens in 16 boxes...
Answers:let x = number of boxes (x) = number of pens so (x) = 12x and (16) = 12(16) = 192 pens
Question:Again, I need a starter of implementing the Simpsons Rule 5 times of [0,1] interval on F(x) which is Integ(0,1 limits) (1 + 3x)^(x/2) dx How is h worked out and how to find the approximate value. All I require is a detailed formula and explanations the calculations I can work out for myself. Thanks
Answers:You will need to have n= 4, 6, 8, 10, and all even numbers. I will assume n=6, you can not assume n=5 because the formula will not work out. I will use Dx for change in x. do not confuse it with dx (the differential) Dx is a dx but it is for the x values, whereas dx is for the whole function. Simspon's Rule is (Dx)/3 [f(x0) + 4f(x1) + 2f(x2)+ 4(fx3) + 2(fx4) + ...+4f(xn-1) + f(xn)] the Dx is defind to be (b-a)/n, where b is the upper limit, a is the lower limit, and n in this case is 6. Dx= 1/6 First of all you need to find you intervals. Your intervals will be all the Xs + change in x. You begin with the lower limit and add the Dx. Your intervals are: [0,1/6], [1/6, 2/6], [2/6, 3/6], [3/6, 4/6], [4/6, 5/6], [5/6, 1] Sn= Dx/3 [f(0) + 4f(1/6) + 2f(2/6) + 4f(3/6) + 2f(4/6) + 4f(5/6) + f(1)]. Use calculator to approximate value. put (1 + 3x)^ (x-2) in y=screen. You can do it by hand but it will take too long. Do you see why n=5 will not work out your second to last term will be 2f(4/5), you could not use Sn with this and your answer would have been wrong. This is be a little difficult integral to do by hand, so I suggest you use the integral function which is #7 in 2nd + trace screen in TI-calculators.
Question:Given the following function. State the function rule. x: -1, 0, 1, 2 y: 5, 7, 9, 11 Rule: What is the value of the function at x = 10?: What is the value of the function at x = (-5): Given the following function. State the function rule. x: -1, 0, 1, 2 y: 3, 0, -3, -6 Rule: Evaluate f(10) Evaluate f(-5)
Answers:For the first one the rule is 2*x+7. You can get this by noticing that if x=0 then y=7 so you will need to have a +7 in the rule. Multiplying x by 2 first makes the rest make sense. Then at x=10 you have 2*10+7=27 and at x=-5 you have 2*(-5)+7=-3. For the second one the rule is (-3)*x. Notice that if x=0 then y=0 so you will need to have a +0 in the rule. Multiplying x by -3 makes the rest make sense. So then f(10)=(-3)*10=-30 and f(-5)=(-3)*(-5)=15.
Question:Harry started a new job in 2003. His salary was $31,000. At the beginning of the next year he will receive a raise of$1500. Assume he will receive the same raise every year. a. Write a function rule for finding Harry's salary after 2003. b. Find Harry's salary in 2008.
Answers:31000 + 1500x x= the number of years past 2003. 31000 + 1500 (5) = 38500
From Youtube
Slide rule - logarithmic scale :The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction. Slide rules come in a diverse range of styles and generally appear in a linear or circular form with a standardized set of markings (scales) essential to performing mathematical computations. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in calculations common to that field. Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but around 1974 the electronic scientific calculator made it largely obsolete and most suppliers left the business. en.wikipedia.org
Significant Digits Rule For Calculations :Significant Digits Rules for Multiplying/Dividing/Adding/Subtracting and Scientific Notation
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2014-11-27 23:01:12
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https://www.programming-techniques.com/2012/02/getting-started-with-php-writing-hello.html
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## Wednesday, February 8, 2012
### Getting Started with PHP : Writing Hello World Program
Lets start this section with small example, consider a small portion of PHP code
<?php $var = 5; echo "the value of variable is ".$var;?>
This program simply outputs a string “the value of variable is 5” on a browser. Now lets see the mechanism how it works.
Every PHP code segment must start with <?php tag and end with ?> tag. Note that there is no space between < , ? and php. If web server finds <?php ?> tag on a web page that browser is requesting, then it converts all the PHP statement into corresponding HTML statement which browser can understand. If you run the above code on web server and view the source, then you see that there are no any php statements.
Every PHP variable declaration start with $sign. PHP is not so strict like programming languages therefore all types of variable (int, float, string, long etc) can be declared by just writing$var_name. For example:
<?php $intvar = 5;$floatvar = 5.5; $stringvar = "nepal";?> To print a statement to a browser window, PHP command echo is used. The statement to be printed is kept inside single or double quotes. The . (dot) operator concatenates two string. Embedding PHP code with HTML PHP is designed to use with HTML. PHP alone cannot do anything. Any website needs different HTML tags. But PHP with HTML helps to create dynamic pages. So PHP code can be embedded inside HTML code as below. <HTML><HEAD><TITLE>My First Program</TITLE><HEAD><BODY><?php$var = 5; echo "the value of variable is " . \$var;?></BODY></HTML>
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2018-04-24 16:14:24
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https://cs.stackexchange.com/questions/124176/heaps-and-heapsort-find-the-7th-biggest-value-in-a-min-heap-by-o1
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# Heaps and Heapsort - Find the 7'th biggest value in a min heap by $O(1)$
I have a min heap.
I need to find the 7'th biggest value in the heap with $$O(1)$$.
I need to build the algorithm.
I dont realy have an idea how to get to this efficiency.
Help?
Thanks.
• A min-heap is a heap with the least element as root? I believe the naming isn't standard. – vonbrand Apr 16 '20 at 21:40
I am pretty sure that you cannot solve this problem in $$O(1)$$ time without additional assumptions. You have to scan at least $$L-6$$ leaves (which already gives you $$\Omega(n)$$ time complexity), where $$L$$ is a total number of leaves in a heap, to find an answer. Indeed, suppose that you have an algorithm which solves the problem and scans less than $$L-6$$ leaves for some input heap. Then you can pick 7 arbitrary non-scanned leaves and increase their values such that one of them will become the 7-th biggest in the heap. But the repeated run of your algorithm on the modified heap won't scan the 7 modified vertices (because it didn't scan it during the first run and all other vertices remained unchanged) and, consequently, won't find the correct answer for this heap.
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2021-04-10 19:51:05
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https://wiki.seeedstudio.com/Grove-Light_Sensor/
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edit
The Grove - Light sensor integrates a photo-resistor(light dependent resistor) to detect the intensity of light. The resistance of photo-resistor decreases when the intensity of light increases. A dual OpAmp chip LM358 on board produces voltage corresponding to intensity of light(i.e. based on resistance value). The output signal is analog value, the brighter the light is, the larger the value.
This module can be used to build a light controlled switch i.e. switch off lights during day time and switch on lights during night time.
Warning
The light sensor value only reflects the approximated trend of the intensity of light, it DOES NOT represent the exact Lumen.
With the SenseCAP S2110 controller and S2100 data logger, you can easily turn the Grove into a LoRaWAN® sensor. Seeed not only helps you with prototyping but also offers you the possibility to expand your project with the SenseCAP series of robust industrial sensors.
SenseCAP S210x series industrial sensors provide an out-of-box experience for environmental sensing. Please refer to the S2102 Wireless Light Intensity Sensor with higher performance and robustness for light intensity detection. The series includes sensors for soil moisture, air temperature and humidity, light intensity, CO2, EC, and an 8-in-1 weather station. Try the latest SenseCAP S210x for your next successful industrial project.
SenseCAP Industrial Sensor S2102 Light
## Version¶
Product Version Changes Released Date
Grove - Light Sensor 1.0 Initial Apr 28 2013
Grove - Light Sensor(P) Move Grove connector to back side May 15 2014
Grove - Light Sensor(P) V1.1 Replace photoresistor-5528 with LS06-S Vs.Grove - Light Sensor(P) Dec 31 2015
Grove - Light Sensor 1.2 Replace photoresistor-5528 with LS06-S Vs.Grove - Light Sensor 1.0 Jan 20 2016
## Features¶
• Analog value output
• High reliability and sensibility
• Small footprint
• Recognize wider spectrum
Tip
### Platform Support¶
Arduino Raspberry Pi
Caution
The platforms mentioned above as supported is/are an indication of the module's software or theoritical compatibility. We only provide software library or code examples for Arduino platform in most cases. It is not possible to provide software library / demo code for all possible MCU platforms. Hence, users have to write their own software library.
## Specification¶
Item Value
Operating voltage 3~5V
Operating current 0.5~3 mA
Response time 20-30 milliseconds
Peak Wavelength 540 nm
Weight 4 g
## Getting Started¶
### Play With Arduino¶
#### Hardware¶
• Step 1. Prepare the below stuffs:
Seeeduino V4 Base Shield Grove - Light Sensor Grove - LED Bar
Get One Now Get One Now Get One Now Get One Now
• Step 2. Connect Grove-Light Sensor to port A0 of Grove-Base Shield.
• Step 3. Connect Grove-Led Bar to port D2 of Grove-Base Shield.
• Step 4. Plug Grove - Base Shield into Seeeduino.
• Step 5. Connect Seeeduino to PC through a USB cable.
Note
If we don't have Grove Base Shield, We also can directly connect Grove-Light Sensor to Seeeduino as below.
Seeeduino Grove-Light Sensor
5V Red
GND Black
Not Conencted White
A0 Yellow
Seeeduino Grove-Led Bar
5V Red
GND Black
D3 White
D2 Yellow
#### Software¶
#include <Grove_LED_Bar.h>
Grove_LED_Bar bar(3, 2, 0); // Clock pin, Data pin, Orientation
void setup()
{
// nothing to initialize
bar.begin();
bar.setGreenToRed(true);
}
void loop()
{
value = map(value, 0, 800, 0, 10);
bar.setLevel(value);
delay(100);
}
• Step 2. The Led bar will change base on light.
### Play with Codecraft¶
#### Hardware¶
Step 1. Connect a Grove - Light Sensor to port A0 of a Base Shield.
Step 2. Plug the Base Shield to your Seeeduino/Arduino.
#### Software¶
Step 1. Open Codecraft, add Arduino support, and drag a main procedure to working area.
Note
Success
When the code finishes uploaded, you will see the brightnedd value displayed in the Serial Monitor.
### Play With Raspberry Pi (With Grove Base Hat for Raspberry Pi)¶
#### Hardware¶
• Step 1. Things used in this project:
Raspberry pi Grove Base Hat for RasPi Grove - Light Sensor
Get ONE Now Get ONE Now Get ONE Now
• Step 2. Plug the Grove Base Hat into Raspberry.
• Step 3. Connect the light sensor to port A0 of the Base Hat.
• Step 4. Connect the Raspberry Pi to PC through USB cable.
Note
For step 3 you are able to connect the light sensor to any Analog Port but make sure you change the command with the corresponding port number.
#### Software¶
Attention
If you are using Raspberry Pi with Raspberrypi OS >= Bullseye, you have to use this command line only with Python3.
• Step 1. Follow Setting Software to configure the development environment.
• Step 2. Download the source file by cloning the grove.py library.
cd ~
git clone https://github.com/Seeed-Studio/grove.py
• Step 3. Excute below commands to run the code.
cd grove.py/grove
python3 grove_light_sensor_v1_2.py 0
Following is the grove_light_sensor_v1_2.py code.
import math
import sys
import time
class GroveLightSensor:
def __init__(self, channel):
self.channel = channel
@property
def light(self):
return value
Grove = GroveLightSensor
def main():
if len(sys.argv) < 2:
sys.exit(1)
sensor = GroveLightSensor(int(sys.argv[1]))
print('Detecting light...')
while True:
print('Light value: {0}'.format(sensor.light))
time.sleep(1)
if __name__ == '__main__':
main()
Success
If everything goes well, you will be able to see the following result corresponding to the surrounding light
pi@raspberrypi:~/grove.py/grove $python3 grove_light_sensor_v1_2.py 0 Detecting light... Light value: 600 Light value: 448 Light value: 267 Light value: 311 Light value: 102 Light value: 82 Light value: 63 Light value: 54 Light value: 49 Light value: 45 Light value: 545 ^CTraceback (most recent call last): File "grove_light_sensor_v1_2.py", line 67, in <module> main() File "grove_light_sensor_v1_2.py", line 64, in main time.sleep(1) KeyboardInterrupt You can quit this program by simply press Ctrl+C. Notice You may have noticed that for the analog port, the silkscreen pin number is something like A1, A0, however in the command we use parameter 0 and 1, just the same as digital port. So please make sure you plug the module into the correct port, otherwise there may be pin conflicts. ### Play With Raspberry Pi (with GrovePi_Plus)¶ #### Hardware¶ • Step 1. Prepare the below stuffs: Raspberry pi GrovePi_Plus Grove - Light Sensor Grove - Red LED Get One Now Get One Now Get One Now Get One Now • Step 2. Plug the GrovePi_Plus into Raspberry. • Step 3. Connect Grove-light sensor to A0 port of GrovePi_Plus. • Step 4. Connect Grove-Red Led to D4 port of GrovePi_Plus. • Step 5. Connect the Raspberry to PC through USB cable. #### Software¶ Attention If you are using Raspberry Pi with Raspberrypi OS >= Bullseye, you have to use this command line only with Python3. • Step 1. Follow Setting Software to configure the development environment. • Step 2. Git clone the Github repository. cd ~ git clone https://github.com/DexterInd/GrovePi.git • Step 3. Excute below commands. cd ~/GrovePi/Software/Python python3 grove_light_sensor.py Here is the grove_light_sensor.py code. import time import grovepi # Connect the Grove Light Sensor to analog port A0 # SIG,NC,VCC,GND light_sensor = 0 # Connect the LED to digital port D4 # SIG,NC,VCC,GND led = 4 # Turn on LED once sensor exceeds threshold resistance threshold = 10 grovepi.pinMode(light_sensor,"INPUT") grovepi.pinMode(led,"OUTPUT") while True: try: # Get sensor value sensor_value = grovepi.analogRead(light_sensor) # Calculate resistance of sensor in K resistance = (float)(1023 - sensor_value) * 10 / sensor_value if resistance > threshold: # Send HIGH to switch on LED grovepi.digitalWrite(led,1) else: # Send LOW to switch off LED grovepi.digitalWrite(led,0) print("sensor_value = %d resistance = %.2f" %(sensor_value, resistance)) time.sleep(.5) except IOError: print ("Error") • Step 4. The led will turn on when the light sensor gets covered. pi@raspberrypi:~/GrovePi/Software/Python$ python3 grove_light_sensor.py
sensor_value = 754 resistance = 3.57
sensor_value = 754 resistance = 3.57
sensor_value = 752 resistance = 3.60
sensor_value = 752 resistance = 3.60
sensor_value = 752 resistance = 3.60
sensor_value = 313 resistance = 22.68
sensor_value = 155 resistance = 56.00
sensor_value = 753 resistance = 3.59
# Eagle File for Grove - Light Sensor(P) V1.1¶
## Resources¶
Here we will show you a project made with Grove - Light Sensor - Secret Box. First you need a box, a paper box, wooden box, any box is ok. Put something in the box, because we named it secret box, that means we don't want anybody to open it, otherwise there will be an alarm to inform you.
Here we use LinkIt ONE as the controller, which is an Arduino compatible board and consist of rich function. And you need things below:
• Grove - Light Sensor
• Grove - Base Shield
• A Sim Card
Let's connect Grove - Light Sensor to A0 or Base Shield, and open Arduino IDE, copy below code and upload the example to LinkIt ONE. Then someone open the box, the light will detect it, and send you a SMS.
// demo of Grove Starter kit for LinkIt ONE
// Secret box
#include <LGSM.h>
char num[20] = "13425171053"; // your number write here
char text[100] = "Warning: Your box had been opened!!"; // what do you want to send
const int pinLight = A0; // light sensor connect to A0
bool isLightInBox()
{
return (analogRead(pinLight)<50); // when get data less than 50, means light sensor was in box
}
void setup()
{
Serial.begin(115200);
while(!isLightInBox()); // until put in box
delay(2000);
}
void loop()
{
if(!isLightInBox()) // box is open
{
{
delay(1000);
}
LSMS.beginSMS(num);
LSMS.print(text);
if(LSMS.endSMS())
{
Serial.println("SMS is sent");
}
else
{
Serial.println("SMS send fail");
}
while(!isLightInBox()); // until put in box
delay(2000);
}
delay(10);
}
Have fun.
## Projects¶
Grove - Introduction in a Light Sensor:
The Environment Cube! Know the Land Beneath You using Sigfox: A cube with all the necessary sensors, suitable for a wide range of applications like agriculture, monitoring, ,etc.
Light sensor Grove module:
## Tech Support¶
Please submit any technical issue into our forum.
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2022-12-03 02:46:19
|
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http://www.maplesoft.com/support/help/Maple/view.aspx?path=Logic/Random
|
construct a random Boolean function - Maple Help
Home : Support : Online Help : Programming : Logic : Boolean : Logic Package : Logic/Random
Logic[Random] - construct a random Boolean function
Calling Sequence Random(alpha, opt)
Parameters
alpha - list or set of symbols representing the alphabet opt - (optional) equation of the form form=fname, where fname is one of CNF, DNF, or MOD2.
Description
• The Random command returns a random Boolean expression in a specific canonical form. By default, disjunctive normal form is used. The Boolean expression returned is in normal form with respect to the symbols in alpha.
Examples
> $\mathrm{with}\left(\mathrm{Logic}\right):$
> $\mathrm{Random}\left(\left\{a,b\right\}\right)$
${a}{&and}{b}$ (1)
> $\mathrm{Random}\left(\left[a,b,c\right],\mathrm{form}=\mathrm{DNF}\right)$
$\left(\left(\left(\left(\left({a}{&and}{b}\right){&and}{c}{&or}\left({a}{&and}{b}\right){&and}{\mathrm{¬}}{}\left({c}\right)\right){&or}\left({a}{&and}{c}\right){&and}{\mathrm{¬}}{}\left({b}\right)\right){&or}\left({a}{&and}{\mathrm{¬}}{}\left({b}\right)\right){&and}{\mathrm{¬}}{}\left({c}\right)\right){&or}\left({b}{&and}{c}\right){&and}{\mathrm{¬}}{}\left({a}\right)\right){&or}\left({b}{&and}{\mathrm{¬}}{}\left({a}\right)\right){&and}{\mathrm{¬}}{}\left({c}\right)$ (2)
> $\mathrm{Random}\left(\left[a,b\right],\mathrm{form}=\mathrm{CNF}\right)$
${b}{&or}{\mathrm{¬}}{}\left({a}\right)$ (3)
> $\mathrm{Random}\left(\left\{a,b,c\right\},\mathrm{form}=\mathrm{MOD2}\right)$
${a}{}{b}{}{c}{+}{a}{}{c}{+}{b}{}{c}{+}{b}{+}{c}{+}{1}$ (4)
|
2016-02-11 10:52:10
|
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http://dictionnaire.sensagent.leparisien.fr/Enzyme_assay/en-en/
|
Publicité ▼
## définition - Enzyme_assay
voir la définition de Wikipedia
Wikipedia
# Enzyme assay
Beckman DU640 UV/Vis spectrophotometer
Enzyme assays are laboratory methods for measuring enzymatic activity. They are vital for the study of enzyme kinetics and enzyme inhibition.
## Enzyme units
Amounts of enzymes can either be expressed as molar amounts, as with any other chemical, or measured in terms of activity, in enzyme units.
### Enzyme activity
Enzyme activity = moles of substrate converted per unit time = rate × reaction volume. Enzyme activity is a measure of the quantity of active enzyme present and is thus dependent on conditions, which should be specified. The SI unit is the katal, 1 katal = 1 mol s−1, but this is an excessively large unit. A more practical and commonly used value is 1 enzyme unit (U) = 1 μmol min−1. 1 U corresponds to 16.67 nanokatals.[1]
Enzyme activity as given in katal generally refers to that of the assumed natural target substrate of the enzyme. Enzyme activity can also be given as that of certain standardized substrates, such as gelatin, then measured in gelatin digesting units (GDU), or milk proteins, then measured in milk clotting units (MCU). The units GDU and MCU are based on how fast one gram of the enzyme will digest gelatin or milk proteins, respectively. 1 GDU equals approximately 1.5 MCU.[2]
### Specific activity
The specific activity of an enzyme is another common unit. This is the activity of an enzyme per milligram of total protein (expressed in μmol min−1mg−1). Specific activity gives a measurement of the activity of the enzyme. It is the amount of product formed by an enzyme in a given amount of time under given conditions per milligram of total protein. Specific activity is equal to the rate of reaction multiplied by the volume of reaction divided by the mass of total protein. The SI unit is katal kg−1, but a more practical unit is μmol mg−1 min−1. Specific activity is a measure of enzyme processivity, at a specific (usually saturating) substrate concentration, and is usually constant for a pure enzyme. For elimination of errors arising from differences in cultivation batches and/or misfolded enzyme etc. an active site titration needs to be done. This is a measure of the amount of active enzyme, calculated by e.g. titrating the amount of active sites present by employing an irreversible inhibitor. The specific activity should then be expressed as μmol min−1 mg−1 active enzyme. If the molecular weight of the enzyme is known, the turnover number, or μmol product sec−1 μmol−1 of active enzyme, can be calculated from the specific activity. The turnover number can be visualized as the number of times each enzyme molecule carries out its catalytic cycle per second.
### Related terminology
The rate of a reaction is the concentration of substrate disappearing (or product produced) per unit time (mol $L^{-1} s^{-1}$).
The % purity is 100% × (specific activity of enzyme sample / specific activity of pure enzyme). The impure sample has lower specific activity because some of the mass is not actually enzyme. If the specific activity of 100% pure enzyme is known, then an impure sample will have a lower specific activity, allowing purity to be calculated.
## Types of assay
All enzyme assays measure either the consumption of substrate or production of product over time. A large number of different methods of measuring the concentrations of substrates and products exist and many enzymes can be assayed in several different ways. Biochemists usually study enzyme-catalysed reactions using four types of experiments:[3]
• Initial rate experiments. When an enzyme is mixed with a large excess of the substrate, the enzyme-substrate intermediate builds up in a fast initial transient. Then the reaction achieves a steady-state kinetics in which enzyme substrate intermediates remains approximately constant over time and the reaction rate changes relatively slowly. Rates are measured for a short period after the attainment of the quasi-steady state, typically by monitoring the accumulation of product with time. Because the measurements are carried out for a very short period and because of the large excess of substrate, the approximation that the amount of free substrate is approximately equal to the amount of the initial substrate can be made. The initial rate experiment is the simplest to perform and analyze, being relatively free from complications such as back-reaction and enzyme degradation. It is therefore by far the most commonly used type of experiment in enzyme kinetics.
• Progress curve experiments. In these experiments, the kinetic parameters are determined from expressions for the species concentrations as a function of time. The concentration of the substrate or product is recorded in time after the initial fast transient and for a sufficiently long period to allow the reaction to approach equilibrium. We note in passing that, while they are less common now, progress curve experiments were widely used in the early period of enzyme kinetics.
• Transient kinetics experiments. In these experiments, reaction behaviour is tracked during the initial fast transient as the intermediate reaches the steady-state kinetics period. These experiments are more difficult to perform than either of the above two classes because they require specialist techniques (such as flash photolysis of caged compounds) or rapid mixing (such as stopped-flow, quenched flow or continuous flow).
• Relaxation experiments. In these experiments, an equilibrium mixture of enzyme, substrate and product is perturbed, for instance by a temperature, pressure or pH jump, and the return to equilibrium is monitored. The analysis of these experiments requires consideration of the fully reversible reaction. Moreover, relaxation experiments are relatively insensitive to mechanistic details and are thus not typically used for mechanism identification, although they can be under appropriate conditions.
Enzyme assays can be split into two groups according to their sampling method: continuous assays, where the assay gives a continuous reading of activity, and discontinuous assays, where samples are taken, the reaction stopped and then the concentration of substrates/products determined.
Temperature-controlled cuvette holder in a spectrophotometer.
## Continuous assays
Continuous assays are most convenient, with one assay giving the rate of reaction with no further work necessary. There are many different types of continuous assays.
### Spectrophotometric
In spectrophotometric assays, you follow the course of the reaction by measuring a change in how much light the assay solution absorbs. If this light is in the visible region you can actually see a change in the color of the assay, these are called colorimetric assays. The MTT assay, a redox assay using a tetrazolium dye as substrate is an example of a colorimetric assay.
UV light is often used, since the common coenzymes NADH and NADPH absorb UV light in their reduced forms, but do not in their oxidized forms. An oxidoreductase using NADH as a substrate could therefore be assayed by following the decrease in UV absorbance at a wavelength of 340 nm as it consumes the coenzyme.[4]
Direct versus coupled assays
Coupled assay for hexokinase using glucose-6-phosphate dehydrogenase.
Even when the enzyme reaction does not result in a change in the absorbance of light, it can still be possible to use a spectrophotometric assay for the enzyme by using a coupled assay. Here, the product of one reaction is used as the substrate of another, easily detectable reaction. For example, figure 1 shows the coupled assay for the enzyme hexokinase, which can be assayed by coupling its production of glucose-6-phosphate to NADPH production, using glucose-6-phosphate dehydrogenase.
### Fluorometric
Fluorescence is when a molecule emits light of one wavelength after absorbing light of a different wavelength. Fluorometric assays use a difference in the fluorescence of substrate from product to measure the enzyme reaction. These assays are in general much more sensitive than spectrophotometric assays, but can suffer from interference caused by impurities and the instability of many fluorescent compounds when exposed to light.
An example of these assays is again the use of the nucleotide coenzymes NADH and NADPH. Here, the reduced forms are fluorescent and the oxidised forms non-fluorescent. Oxidation reactions can therefore be followed by a decrease in fluorescence and reduction reactions by an increase.[5] Synthetic substrates that release a fluorescent dye in an enzyme-catalyzed reaction are also available, such as 4-methylumbelliferyl-β-D-galactoside for assaying β-galactosidase.
### Calorimetric
Chemiluminescence of Luminol
Calorimetry is the measurement of the heat released or absorbed by chemical reactions. These assays are very general, since many reactions involve some change in heat and with use of a microcalorimeter, not much enzyme or substrate is required. These assays can be used to measure reactions that are impossible to assay in any other way.[6]
### Chemiluminescent
Chemiluminescence is the emission of light by a chemical reaction. Some enzyme reactions produce light and this can be measured to detect product formation. These types of assay can be extremely sensitive, since the light produced can be captured by photographic film over days or weeks, but can be hard to quantify, because not all the light released by a reaction will be detected.
The detection of horseradish peroxidase by enzymatic chemiluminescence (ECL) is a common method of detecting antibodies in western blotting. Another example is the enzyme luciferase, this is found in fireflies and naturally produces light from its substrate luciferin.
### Light Scattering
Static light scattering measures the product of weight-averaged molar mass and concentration of macromolecules in solution. Given a fixed total concentration of one or more species over the measurement time, the scattering signal is a direct measure of the weight-averaged molar mass of the solution, which will vary as complexes form or dissociate. Hence the measurement quantifies the stoichiometry of the complexes as well as kinetics. Light scattering assays of protein kinetics is a very general technique that does not require an enzyme.
### Microscale Thermophoresis
Microscale Thermophoresis (MST)[7] measures the size, charge and hydration entropy of molecules/substrates in real time.[8] The thermophoretic movement of a fluorescently labeled substrate changes significantly as it is modified by an enzyme. This enzymatic activity can be measured with high time resolution in real time.[9] The material consumption of the all optical MST method is very low, only 5 µl sample volume and 10nM enzyme concentration are needed to measure the enzymatic rate constants for activity and inhibition. MST allows to measure the modification of two different substrates at once (multiplexing) if both substrates are labeled with different fluorophores. Thus substrate competition experiments can be performed.
## Discontinuous assays
Discontinuous assays are when samples are taken from an enzyme reaction at intervals and the amount of product production or substrate consumption is measured in these samples.
Radiometric assays measure the incorporation of radioactivity into substrates or its release from substrates. The radioactive isotopes most frequently used in these assays are 14C, 32P, 35S and 125I. Since radioactive isotopes can allow the specific labelling of a single atom of a substrate, these assays are both extremely sensitive and specific. They are frequently used in biochemistry and are often the only way of measuring a specific reaction in crude extracts (the complex mixtures of enzymes produced when you lyse cells).
Radioactivity is usually measured in these procedures using a scintillation counter.
### Chromatographic
Chromatographic assays measure product formation by separating the reaction mixture into its components by chromatography. This is usually done by high-performance liquid chromatography (HPLC), but can also use the simpler technique of thin layer chromatography. Although this approach can need a lot of material, its sensitivity can be increased by labelling the substrates/products with a radioactive or fluorescent tag. Assay sensitivity has also been increased by switching protocols to improved chromatographic instruments (e.g. ultra-high pressure liquid chromatography) that operate at pump pressure a few-fold higher than HPLC instruments (see High-performance liquid chromatography#Pump_pressure).[10]
## Factors to control in assays
• Salt Concentration: Most enzymes cannot tolerate extremely high salt concentrations. The ions interfere with the weak ionic bonds of proteins. Typical enzymes are active in salt concentrations of 1-500 mM. As usual there are exceptions such as the halophilic algae and bacteria.
• Effects of Temperature: All enzymes work within a range of temperature specific to the organism. Increases in temperature generally lead to increases in reaction rates. There is a limit to the increase because higher temperatures lead to a sharp decrease in reaction rates. This is due to the denaturating (alteration) of protein structure resulting from the breakdown of the weak ionic and hydrogen bonding that stabilize the three dimensional structure of the enzyme active site.[11] The "optimum" temperature for human enzymes is usually between 35 and 40 °C. The average temperature for humans is 37 °C. Human enzymes start to denature quickly at temperatures above 40 °C. Enzymes from thermophilic archaea found in the hot springs are stable up to 100 °C.[12] However, the idea of an "optimum" rate of an enzyme reaction is misleading, as the rate observed at any temperature is the product of two rates, the reaction rate and the denaturation rate. If you were to use an assay measuring activity for one second, it would give high activity at high temperatures, however if you were to use an assay measuring product formation over an hour, it would give you low activity at these temperatures.
• Effects of pH: Most enzymes are sensitive to pH and have specific ranges of activity. All have an optimum pH. The pH can stop enzyme activity by denaturating (altering) the three dimensional shape of the enzyme by breaking ionic, and hydrogen bonds. Most enzymes function between a pH of 6 and 8; however pepsin in the stomach works best at a pH of 2 and trypsin at a pH of 8.
• Substrate Saturation: Increasing the substrate concentration increases the rate of reaction (enzyme activity). However, enzyme saturation limits reaction rates. An enzyme is saturated when the active sites of all the molecules are occupied most of the time. At the saturation point, the reaction will not speed up, no matter how much additional substrate is added. The graph of the reaction rate will plateau.
## References
1. ^ Nomenclature Committee of the International Union of Biochemistry (NC-IUB) (1979). "Units of Enzyme Activity". Eur. J. Biochem. 97 (2): 319–20. doi:10.1111/j.1432-1033.1979.tb13116.x.
2. ^ How Many? A Dictionary of Units of Measurement By Russ Rowlett at the University of North Carolina at Chapel Hill
3. ^ Schnell, S., Chappell, M.J., Evans, N.D. Roussel, M.R. (2006). "The mechanism distinguishability problem in biochemical kinetics: The single-enzyme, single-substrate reaction as a case study". Comptes Rendus Biologies 329 (1): 51–61. doi:10.1016/j.crvi.2005.09.005. PMID 16399643.
4. ^ Bergmeyer, H.U. (1974). Methods of Enzymatic Analysis. 4. New York: Academic Press. pp. 2066–72. ISBN 0-89573-236-X.
5. ^ Passonneau, J.V., Lowry, O.H. (1993). Enzymatic Analysis. A Practical Guide. Totowa NJ: Humana Press. pp. 85–110.
6. ^ Todd MJ, Gomez J (September 2001). "Enzyme kinetics determined using calorimetry: a general assay for enzyme activity?". Anal. Biochem. 296 (2): 179–87. doi:10.1006/abio.2001.5218. PMID 11554713.
7. ^ Wienken CJ et al. (2010). "Protein-binding assays in biological liquids using microscale thermophoresis". Nature Communications 1 (7): 100. Bibcode 2010NatCo...1E.100W. doi:10.1038/ncomms1093.
8. ^ Duhr S, Braun D (December 2006). "Why molecules move along a temperature gradient". Proc. Natl. Acad. Sci. U.S.A. 103 (52): 19678–82. Bibcode 2006PNAS..10319678D. doi:10.1073/pnas.0603873103. PMC 1750914. PMID 17164337. //www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1750914.
9. ^ Baaske P, Wienken C, Duhr S (2009). "Optisch erzeugte Thermophorese für die Bioanalytik [Optically generated thermophoresis for bioanalysis]" (in German). Biophotonik: 22–24.
10. ^ Churchwella, M; Twaddlea, N; Meekerb, L; Doergea, D. (October 2005). "Improving Sensitivity in Liquid Chromatography-Mass Spectrometry". Journal of Chromatography B 825 (2): 134–143.
11. ^ Daniel RM, Peterson ME, Danson MJ, et al. (January 2010). "The molecular basis of the effect of temperature on enzyme activity". Biochem. J. 425 (2): 353–60. doi:10.1042/BJ20091254. PMID 19849667.
12. ^ Cowan DA (1997). "Thermophilic proteins: stability and function in aqueous and organic solvents". Comp. Biochem. Physiol. A Physiol. 118 (3): 429–38. doi:10.1016/S0300-9629(97)00004-2. PMID 9406427.
13. ^ Minton AP (2001). "The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media". J. Biol. Chem. 276 (14): 10577–80. doi:10.1074/jbc.R100005200. PMID 11279227.
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allemand anglais arabe bulgare chinois coréen croate danois espagnol espéranto estonien finnois français grec hébreu hindi hongrois islandais indonésien italien japonais letton lituanien malgache néerlandais norvégien persan polonais portugais roumain russe serbe slovaque slovène suédois tchèque thai turc vietnamien
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2021-10-28 04:58:53
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https://stat.ethz.ch/R-manual/R-patched/library/graphics/html/units.html
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units {graphics} R Documentation
Graphical Units
Description
xinch and yinch convert the specified number of inches given as their arguments into the correct units for plotting with graphics functions. Usually, this only makes sense when normal coordinates are used, i.e., no log scale (see the log argument to par).
xyinch does the same for a pair of numbers xy, simultaneously.
Usage
xinch(x = 1, warn.log = TRUE)
yinch(y = 1, warn.log = TRUE)
xyinch(xy = 1, warn.log = TRUE)
Arguments
x, y numeric vector xy numeric of length 1 or 2. warn.log logical; if TRUE, a warning is printed in case of active log scale.
Examples
all(c(xinch(), yinch()) == xyinch()) # TRUE
xyinch()
xyinch #- to see that is really delta{"usr"} / "pin"
## plot labels offset 0.12 inches to the right
## of plotted symbols in a plot
with(mtcars, {
plot(mpg, disp, pch = 19, main = "Motor Trend Cars")
text(mpg + xinch(0.12), disp, row.names(mtcars),
adj = 0, cex = .7, col = "blue")
})
[Package graphics version 4.2.0 Index]
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2022-08-18 22:51:15
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https://proofwiki.org/wiki/Definition:Greek_Numerals/Classical_Period
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# Definition:Greek Numerals/Classical Period
## Definition
The Greek numerals from the Classical period (c. $600$ BCE to c. $300$ BCE) are as follows:
$\begin{array}{ccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \alpha & \beta & \gamma & \delta & \epsilon & stigma & \zeta & \eta & \theta \\ \hline \\ 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 \\ \iota & \kappa & \lambda & \mu & \nu & \xi & \omicron & \pi & koppa \\ \hline \\ 100 & 200 & 300 & 400 & 500 & 600 & 700 & 800 & 900 \\ \rho & \sigma & \tau & \upsilon & \phi & \chi & \psi & \omega & sampi \\ \end{array}$
where $stigma$, $koppa$ and $sampi$ are characters that are not supported by MathJax.
These were the letters of the everyday Greek alphabet, with extra ones added from the Phoenician alphabet.
As it could be easy to confuse numbers with the letters of Greek words, a line was written over the numbers to distinguish them.
Numbers bigger than $999$ could be written by putting a stroke in front of the symbols.
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2022-07-07 09:53:20
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https://socratic.org/questions/how-do-you-find-vertical-horizontal-and-oblique-asymptotes-for-1-x-2-2x-8
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# How do you find vertical, horizontal and oblique asymptotes for 1/(x^2-2x-8)?
Feb 26, 2017
The vertical asymptotes are $x = 4$ and $x = - 2$
The horizontal asymptote is $y = 0$
No oblique asymptote
#### Explanation:
Let's factorise the denominator
${x}^{2} - 2 x - 8 = \left(x - 4\right) \left(x + 2\right)$
As you canot divide by $0$, $\implies$, $x \ne 4$ and $x \ne - 2$
The vertical asymptotes are $x = 4$ and $x = - 2$
As the degree of the numerator is $<$ than the degree of the denominator, there is no oblique asymptote.
${\lim}_{x \to \pm \infty} \frac{1}{{x}^{2} - 2 x - 8} = {\lim}_{x \to \pm \infty} \frac{1}{x} ^ 2 = {0}^{+}$
The horizontal asymptote is $y = 0$
graph{(y-1/(x^2-2x-8))(y-10000(x-4))(y-1000(x+2))(y)=0 [-3.85, 7.25, -2.893, 2.66]}
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2020-07-07 06:00:31
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http://astro.u-strasbg.fr/~koppen/chemie/ChemFlowsHelp.html
|
Galactic Chemical Evolution with Gas Flows
Joachim Köppen Kiel/Strasbourg/Illkirch Oct.97
The gaseous and stellar matter in galaxies undergoes an evolution of its chemical composition, as stars are born from the interstellar gas. Within the stars thermonuclear reactions generate not only the energy that makes the stars shine, but also produce synthesize heavy elements from hydrogen and helium. When the stars finish their life by exploding as a supernova or by ejecting a planetary nebula, much of this fusion products are ejected into and mixed with the interstellar gas.
In the Applet we simulate this chemical evolution of galaxy represented as a homogeneous volume of gas and stars, but permitting the inflow of metal-poor gas whose rate follows a completely arbitrary prescription which is specified by the user. The evolution of such a system is described by these equations for mass in gas (g), stars (s), gas metallicities of a primary element (Z) and a secondary element (Z_s), and the mass-weighted stellar metallicity (<Z>):
$g\text{'} = A - SFR$
$s\text{'} = SFR$
$\left(gZ\right)\text{'} = \left(y - Z\right) SFR$
$\left(gZ_s\right)\text{'} = \left(\left(Z y_s\right) - Z_s\right) SFR$
$d/ds = \left(Z - \right)s$
with the star formation rate SFR, the rate A of the infalling gas, the yield y for the primary element, and the yield factor y_s for the secondary element. The finite lifetimes of the stars are neglected, which is a good approximation for elements produced only in massive stars (e.g. oxygen).
Since in the first four equations the time dependence can be eliminated by changing over to s: ds = SFR dt, the mass in stars becomes the independent variable. Furthermore, the (constant) yields can be eliminated by dividing the metallicities by the yields. Thus, only one free parameter remains: the ratio a = A/SFR of infall and star formation rate. This parameter and how it changes with time determines the character of the possible solutions. In this applet, the user can specify freely the dependence of a(s), and investigate its influence on the solution.
How to start: After the applet is loaded, click Start, the only button accessible. This brings you to the display of lg(a) vs. lg(s) which is where you specify the accretion ratio a: click enter data then by clicking the mouse on the plot area enter as many points as you wish to describe the accretion ratio's dependence on s, i.e. essentially time. erase removes the last entry, and erase all removes all points. A constant ratio can be entered by clicking just one point. The interpolating curve that will be used in the calculation can be displayed by clicking show the AR.
Then select with the Plot on ... buttons the variables one wants to plot against each other. For example metallicity lg(Z/y) as a function of the gas fraction lg(-ln f): the plot shows the solution of the Simple Model (closed box a=0)
$Z = y ln\left(f\right)$
as a blue straight line. The locus of the steady states for models with constant accretion ratio (cf. our paper) is shown as the green curve. The model starts with 100 percent metal-free gas. In this plot, one can also start the model from any arbitrary point in the plot, by clicking first Go from here then on the plot area. One will find:
• all models with accretion decreasing monotonically in time stay in the region between the blue and green curves
• models with constant accretion either get stuck on the green curve (if a is larger than 1) or reach a limiting metallicity
• starting with metallicities higher than the Simple Model, all models evolve out of that region
• models which have an increase of the accretion rate when most of the gas is already used up, perform small loops in the diagram.
• if that late accretion event is strong (a larger than 1), the loop may enter the region of metallicities smaller than predicted by the green curve
In the other plots, one will find the corresponding behaviour. In a few important diagrams, the solutions of the Simple Model and constant accretion models are also shown as blue and green curves. In the plot of lg(Z_s/Z) vs. lg(Z/y) the grey curve is the approximate asympotic solution for constant a (cf. our paper).
Numerical Method: rather than solving the equations as a function of s, the applet solves the time-dependent system, assuming a star formation rate depending linearly on the current gas density (linear SFR). Choosing one of the other possible laws yields the same results, except for the dependence on Time. A simple Euler method with constant time step is employed to solve the equations. This is fast and usually sufficiently accurate. When in doubt about the results, re-run with a smaller time step or use the automatic adaptive step.
The variables:
Time, lg(Time)
is measured in arbitrary units; for a linear SFR, it is the star formation timescale
lg(a)
a or AR is the instantaneous ratio of the accretion rate of the gas and the star formation rate
lg(M/M0)
is the current ratio of the total mass (gas plus stars) and the initial gas mass
lg(gas), lg(stars)
are the masses in the form of gas and long-lived stars - including stellar remnants
lg(-ln f)
f = gas/(gas+stars) is the current gas fraction. In this slightly complicated form, this quantity is simply proportional to lg(Z) from the Simple Model
lg(Z/y)
is the metallicity of the gas for a primarily produced element, measured in terms of the true yield y
lg(y(eff)/y)
this factor between the effective yield and the true yield measures how strongly the system deviates from a Simple Model: y(eff) = -Z/ln(f)
lg(<Z>/y)
the mass-averaged stellar metallicity - for the primary element Z - in units of the true yield
lg(Z_s/y_s)
is the metallicity in the gas of a secondarily produced element, measured in terms of the true secondary yield y_s
lg(Z_s/Z)
the abundance ratio in the gas of a secondarily and a primarily produced element, normalized to their true yield ratio
ds/dZ, 0.1 * ds/dZ
the stellar metallicity distribution, i.e. the mass contained in stars per unit logarithmic interval in Z. Since the x-axis for this plot must be metallicity, one must first select lg(Z/y) this for the x-axis, only then one can chose ds/dZ among the items for the y-axis. The distribution function is displayed as a continuous curve. It may fold back, e.g. when an event of strong accretion takes place; then the total distribution would be given by the sum of all its branches. The second item presents the computed distribution scaled down by a factor of ten in the y-axis.
The controls:
Plot on X-axis
select the variable to be plotted on the x-axis; the choice will be used for the next click of Clear or Start
Plot on Y-axis
ditto
Keep this
the present plot is marked so that it can be called back simply by the next button:
Show kept
this shows the plot that had been marked, as before
Start
starts the model calculation
Pause
halts the calculation
Carry on
continues with the present model
Clear
wipes the plot area, and draws the axes for the new plot
Go from here
click here, then click at that position on the plot where you want to start the calculation with a different initial condition (possible only for certain plots)
linear SFR
switches between different dependences of the star formation rate on gas mass: linear, quadratic, cubic, or constant
constant dt=
toggles between a constant time step - as to be entered in the field - or an automatic variation of the time step to assure a certain accuracy - as shown in the field
enter data
when showing the lg(a) vs. lg(s) plot, one may enter point-by-point by (any number of) mouse clicks how the accretion ratio a depends on the stellar mass, i.e. essentially time. The points are shown as small open circles. Outside the range in s covered by the points, the ratio is taken to be constant. For all other plots, one may enter (for each plot separately) any number of data points (black dots) to compare the models with observed data or to mark certain points
grab and drop a circle
by grabbing a circle near its centre, one can move it about in the plot
erase
removes the last entered data point or mark
erase all
removes all the points of the accretion ratio a(stars)
set Accretion Ratio AR
this button permits direct jump to the plot where one may change or enter the accretion ratio. When in that mode, a click will show the interpolated curve through the data points
log(AR) shift
for the calculations, the accretion ratios is increased or decreased by the specified amount, while preserving the time dependence
| Top of the Page | Background | How to start | The variables | The controls | Applet | Applet Index |
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2018-10-19 11:39:50
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https://electronics.stackexchange.com/questions/5415/what-do-pa-and-pu-mean-in-avr-lingo/5442
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# What do PA and PU mean in AVR lingo?
My Google-fu is letting me down today.
What do PA and PU mean in ATmega88PA and ATmega8-16PU?
If P for PDIP what is A and U, then?
• Details are at the end of each data sheet. There will be a table with the ordering codes for each package type and another table with descriptions of the package type. There will also be detailed drawings of each package, with dimensions. Reading the data sheet is the only way to be sure you get what you want when ordering parts. Oct 20, 2010 at 21:47
I believe that the AVR codes mean:
• AU - TQFP
• MU - QFN
• PU - DIP
• +1 - An excellent, and to the point, answer: PU => DIP. Thanks. May I offer also MMH(4) => QFN Feb 21, 2015 at 8:24
I think the confusion here is that ATmega88PA is an actual chip. As you can see from the way it's written, "PA" is not a tag-on package code after a dash but a part of the model number. And yes, the information for the package types and codes is in the datasheet under "ordering information".
So, the ATmega8-16PU is an ATmega8, and the ATmega88PA-* are ATmega88PA. I might guess A's are somehow improved (from non-A) devices and P means picopower line.
• yes, that was also the conclusion I came to after researching some more for several hours. Oct 21, 2010 at 17:34
• I found this very useful list of AVR chips with 40 features/parameters: Parametric Product Table for Atmel AVR microcontrollers. It makes it very easy to see how a particular chip is different from similar chips with the same amount of SRAM/flash/EEPROM, for instance, if one chip is specified for a board and the other is the one that can be purchased from a supplier of ICs. Can you incorporate that link (and perhaps a description) into your answer? Oct 21, 2010 at 21:02
• That link seems to be effectively broken now (redirecting to some generic page). Oct 4, 2012 at 22:14
• Seems Atmel has broken their site all around. Nothing new from a company like that. New links are more readable, though, which of course is nice. I updated the ones in my answer.
– XTL
Oct 5, 2012 at 5:36
• The new link for the Parametric Product Table (or rather replacement) is Microcontrollers (MCUs) Selector Feb 27, 2016 at 8:42
This link might help, but it's a little outdated and doesn't seem to mention A and U.
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2022-07-06 14:45:29
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https://mathematica.stackexchange.com/questions/123717/mathematica-11-with-high-dpi-4k-screen/123727
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# Mathematica 11 with High DPI 4k screen
My laptop has a 17 inch 4k screen, running Windows 10 and Ubuntu 1604. Both systems are set to 2x scaling. But Mathematica 11 (released 2016-08-08) is still blurry like version 10. Is there a simple fix to this problem?
• I do not believe Mathematica on Windows/Linux supports High DPI screens as of this point in time.
– ktm
Aug 11 '16 at 18:34
• – Kuba
Aug 11 '16 at 18:43
• @user6014 Is 4k supported on a Mac? Aug 11 '16 at 19:22
• @QuantumDot I know retina displays are supported, yes
– ktm
Aug 11 '16 at 19:52
• @Kuba The fontsize is not small, they are just blurry. Aug 15 '16 at 15:50
The best thing to do, IME, is to set the default notebook zoom level to something higher. This way, the text is rendered crisply and at a reasonable size.
You can do that as follows:
1. Go to Preferences -> Advanced -> Open Option Inspector
2. Set Show option values to Global Preferences
3. Go to Notebook Options
4. Go to Display Options
5. Change magnification to whatever works for you.
Now, "100%" (default mag) will be rendered at whatever magnification you chose here.
• This doesn't seem to address the resolution issue or am I missing something? I have my Windows setup at high DPI too and this doesn't alter the crispness of the resulting display. Aug 15 '16 at 12:38
• @MohammedAlQuraishi Disable "DPI scaling" for Mathematica, then do what is suggested, which effectively boils down to SetOptions[\$FrontEnd, Magnification -> 1]. A lot of things will not look quite right after this though (e.g. the search box in documentation), but better than nothing. Aug 18 '16 at 18:54
• On 4K, I recommend Magification -> 3 at least. Aug 23 '16 at 11:39
• The problem with this solution is that the Welcome screen and file names in the initial window are not scaled and are unreadable. Only once I open a Notebook I can read the text properly. Aug 29 '18 at 18:23
• I'm on Mathematica 12 and unfortunately this doesn't make any difference for me.
– iBug
Nov 24 '19 at 11:57
Mathematica 11.2 seems to use Qt 5.6 framework which supports DPI scaling override. At least on Linux, it's possible to get bearable results by starting Mathematica as follows:
QT_SCALE_FACTOR=1.5 Mathematica
QT_SCALE_FACTOR is an environment variable that defines UI scaling. It seems to work quite well except for the splash screen.
• Does this work in Windows as well?
– Pirx
Nov 8 '17 at 12:13
• You could try setting an environment variable either from CMD prompt or globally (remember to remove it later as it may break other QT apps) Nov 8 '17 at 13:02
• That doesn't seem to do anything. I have a hunch that Mathematica does not use the QT framework on Windows. Oh well, with the disaster that is Windows 10 I may be switching to Mac OS soon anyway (Macbook Pro is on order). Then I hear that the Mac frontend is still 32-bit, with accompanying limitations. Can't win. Unless I switch to Linux...
– Pirx
Nov 8 '17 at 23:24
• It wouldn't make sense to use one toolkit on Linux and another on Windows. You can check the program directory to see if there are files like QtCore5.dll. I have tried to run another Qt app in Windows and it worked for me this way: C:\Users\User>set QT_SCALE_FACTOR=2 \\ C:\Users\User>"C:\Program Files (x86)\SpeedCrunch\speedcrunch.exe" Nov 9 '17 at 8:58
• There are no Qt libraries for Mathematica on Windows, and no acceptable high-DPI behavior can be achieved in Windows. Mathematica is near-unusable under high-DPI Windows scenarios.
– Pirx
Dec 24 '17 at 3:52
With Windows 10 Build 15002 and above, you can use the following settings to obtain a higher resolution of MMA than magnification for 200%, for example.
• This makes Mathematica readable, but the fonts are still blurry and not as crisp as they should be on such a high-resolution screen (see here community.wolfram.com/groups/-/m/t/1202244) Aug 31 '18 at 13:37
• Two figures/screenshots before & after the ticking are appreciated. Nov 6 '18 at 9:20
• Is there a way to do this in Linux? Dec 2 '20 at 22:38
After a long wait, finally, Mathematica 12.1, launched in March 2020, introduces full support for high DPI monitors for both Windows and Linux. The upgrade from previous versions of Mathematica is beautifully impressive on a high-DPI screen!
In order to achieve proper scaling, one should navigate to Format → Object Inspector → Global Preferences → Global Options → System Configuration and set ScreenResolutionCompatibilityMode → False. Then inside the field ScreenInformation in the same panel, one should set Resolution→xxx, where xxx can be obtained by running xdpyinfo | grep resolution in Ubuntu.
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2022-01-26 13:27:50
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http://dictionnaire.sensagent.leparisien.fr/Classical%20Kuiper-belt%20object/en-en/
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Publicité ▼
## définition - Classical Kuiper-belt object
voir la définition de Wikipedia
Wikipedia
# Classical Kuiper belt object
The orbits of various cubewanos compared to the orbit of Neptune (blue) and Pluto (pink).
A classical Kuiper belt object, also called a cubewano ( "QB1-o")[1] is a low-eccentricity Kuiper belt object (KBO) that orbits beyond Neptune and is not controlled by an orbital resonance with Neptune. Cubewanos have orbits with semi-major axes in the 40–50 AU range and, unlike Pluto, do not cross Neptune’s orbit. That is, they have low-eccentricity and sometimes low-inclination orbits like the classical planets.
The name "cubewano" derives from the first trans-Neptunian object (TNO) found after Pluto and Charon, (15760) 1992 QB1. Similar objects found later were often called "QB1-o's", or "cubewanos", after this object, though the term "classical" is much more frequently used in the scientific literature.
Objects identified as cubewanos include:
Haumea (2003 EL61) was provisionally listed as a cubewano by the Minor Planet Center in 2006,[3] but turned out to be resonant.[2]
The orbits of the large cubewanos (in blue) with the large resonant trans-Neptunian objects (including plutinos) (in red) for comparison (H<4.5). The horizontal axis represents the semi-major axes. The eccentricities of the orbits are represented by segments (extending from perihelion to aphelion) with the inclinations represented on the vertical axis.
## Orbits: 'hot' and 'cold' populations
Most cubewanos are found between the 2:3 orbital resonance with Neptune (populated by plutinos) and the 1:2 resonance. 50000 Quaoar, for example, has a near-circular orbit close to the ecliptic. Plutinos, on the other hand, have more eccentric orbits bringing some of them closer to the Sun than Neptune.
The majority of objects (the so-called 'cold population'), have low inclinations and near-circular orbits. A smaller population (the 'hot population') is characterised by highly inclined, more eccentric orbits.[4]
The Deep Ecliptic Survey reports the distributions of the two populations; one with the inclination centered at 4.6° (named Core) and another with inclinations extending beyond 30° (Halo).[5]
### Distribution
This diagram plots the distribution of cubewanos and resonant trans-Neptunian objects (including plutinos). Histograms are shown for orbit inclinations, eccentricity, and semi-major axes distribution. Inserts on the left compare the populations of cubewanos and plutinos using eccentricity versus inclination plots.
The vast majority of KBOs (more than two-thirds) have inclinations of less than 5° and eccentricities of less than 0.1. Their semi-major axes show a preference for the middle of the main belt; arguably, smaller objects close to the limiting resonances have been either captured into resonance or have their orbits modified by Neptune.
The 'hot' and 'cold' populations are strikingly different: more than 30% of all cubewanos are in low inclination, near-circular orbits. The parameters of the plutinos’ orbits are more evenly distributed, with a local maximum in moderate eccentricities in 0.15–0.2 range and low inclinations 5–10°. See also the comparison with scattered disk objects.
Polar and ecliptic view of the (aligned) orbits of the classical objects (in blue), together with the plutinos in red, and Neptune (yellow).
When the orbital eccentricities of cubewanos and plutinos are compared, it can be seen that the cubewanos form a clear 'belt' outside Neptune's orbit, whereas the plutinos approach, or even cross Neptune's orbit. When orbital inclinations are compared, 'hot' cubewanos can be easily distinguished by their higher inclinations, as the plutinos typically keep orbits below 20°. (No clear explanation currently exists for the inclinations of 'hot' cubewanos.[6])
## Cold and hot populations: physical characteristics
In addition to the distinct orbital characteristics the two populations display different physical characteristics.
The difference in colour between the red cold population and more heterogeneous hot population was observed as early as in 2002.[7] Recent studies, based on a larger data set, indicate the cut-off inclination of 12° (instead of 5°) between the cold and hot populations while confirming the distinction between the homogenous red cold population and the bluish hot population.[8]
Another difference between the low-inclination (cold) and high-inclination (hot) classical objects is the observed number of binary objects. Binaries are quite common on low-inclination orbits and are typically similar-brightness systems. Binaries are less common on high-inclination orbits and their components typically differ in brightness. This correlation, together with the differences in colour, support further the suggestion that the currently observed classical objects belong to at least two different overlapping populations, with different physical properties and orbital history.[9]
## Toward a formal definition
There is no official definition of 'cubewano' or 'classical KBO'. However, the terms are normally used to refer to objects free from significant perturbation from Neptune, thereby excluding KBOs in orbital resonance with Neptune (resonant trans-Neptunian objects). The Minor Planet Center (MPC) and the Deep Ecliptic Survey (DES) do not list cubewanos (classical objects) using the same exact criteria. Many TNOs classified as cubewanos by the MPC are classified as ScatNear (possibly scattered by Neptune) by the DES. Dwarf planet Makemake is such a borderline classical cubewano/scatnear object. (119951) 2002 KX14 may be an inner cubewano near the plutinos. Furthermore, there is evidence that the Kuiper belt has an 'edge', in that an apparent lack of low-inclination objects beyond 47-49 AU was suspected as early as 1998 and shown with more data in 2001.[10] Consequently, the traditional usage of the terms is based on the orbit’s semi-major axis, and includes objects situated between the 2:3 and 1:2 resonances, that is between 39.4 and 47.8 AU (with exclusion of these resonances and the minor ones in-between).[4]
These definitions lack precision: in particular the boundary between the classical objects and the scattered disk remains blurred. As of 2010, there are 377 objects with perihelion (q) > 40 AU and aphelion (Q) < 47AU.[11]
### DES classification
Introduced by the report from the Deep Ecliptic Survey by J. L. Elliott et al. in 2005 uses formal criteria based on the mean orbital parameters.[5] Put informally, the definition includes the objects that have never crossed the orbit of Neptune. According to this definition, an object qualifies as a classical KBO if:
### SSBN07 classification
An alternative classification, introduced by B. Gladman, B. Marsden and C. VanLaerhoven in 2007, uses 10 million years orbit integration instead of the Tisserand parameter. Classical objects are defined as not resonant and not being currently scattered by Neptune.[12]
Formally, this definition includes as classical all objects with the current orbits that
• are non-resonant (see the definition of the method)
• have the semi-major axis greater than that of Neptune (i.e. excluding Centaurs) but less than 2000 AU (to exclude Inner Oort Cloud Objects)
• have the eccentricity $e < 0.240$ (to exclude detached objects)
Unlike other schemes, this definition includes the objects with major semi-axis less than 39.4 AU (2:3 resonance) – named Inner classical belt, or more than 48.7 (1:2 resonance) – named Outer classical belt while reserving the term Main classical belt for the orbits between these two resonances.[12]
## Families
The first collisional family—a group of objects thought to be remnants from the breakup of a single body—is the Haumea family[13] It includes Haumea, its moons, 2002 TX300 and seven smaller bodies. The objects not only follow similar orbits but also share similar physical characteristics. Unlike many other KBO their surface contains large amounts of ice (H2O) and no or very little tholins.[14] The surface composition is inferred from their neutral (as opposed to red) colour and deep absorption at 1.5 and 2. μm in infrared spectrum.[15]
As of 2008. The four brightest objects of the family are situated on the graphs inside the circle representing Haumea.
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2020-12-02 17:04:32
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http://www.aimsciences.org/journal/1930-8337/2014/8/1
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# American Institute of Mathematical Sciences
ISSN:
1930-8337
eISSN:
1930-8345
All Issues
## Inverse Problems & Imaging
2014 , Volume 8 , Issue 1
Select all articles
Export/Reference:
2014, 8(1): 1-22 doi: 10.3934/ipi.2014.8.1 +[Abstract](78) +[PDF](481.0KB)
Abstract:
This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical imaging modalities such as ultrasound modulated electrical impedance tomography and impedance-acoustic computerized tomography.
We consider the linearization of the nonlinear hybrid inverse problem. We find sufficient conditions for the linearized problem, a system of partial differential equations, to be elliptic and for the system to be injective. Such conditions are found to hold for a lesser number of measurements than those required in recently established explicit reconstruction procedures for the nonlinear problem.
2014, 8(1): 23-51 doi: 10.3934/ipi.2014.8.23 +[Abstract](128) +[PDF](1474.3KB)
Abstract:
We apply an exterior approach" based on the coupling of a method of quasi-reversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements. Concerning the method of quasi-reversibility, two new mixed formulations are introduced in order to solve the ill-posed Cauchy problems for the Stokes system by using some classical conforming finite elements. We provide some proofs for the convergence of the quasi-reversibility methods on the one hand and of the level set method on the other hand. Some numerical experiments in $2D$ show the efficiency of the two mixed formulations and of the exterior approach based on one of them.
2014, 8(1): 53-77 doi: 10.3934/ipi.2014.8.53 +[Abstract](105) +[PDF](648.3KB)
Abstract:
This paper presents the Moreau envelope viewpoint for the L1/TV image denoising model. The main algorithmic difficulty for the numerical treatment of the L1/TV model lies in the non-differentiability of both the fidelity and regularization terms of the model. To overcome this difficulty, we propose five modified L1/TV models by replacing one or two non-differentiable functions in the L1/TV model with their corresponding Moreau envelopes. We prove that several existing approaches for the L1/TV model essentially solve some of the modified models, but not the original L1/TV model. Algorithms for the L1/TV model and its five variants are proposed under a unified framework based on fixed-point equations (via the proximity operator) which characterize the solutions of the models. Depending upon whether we smooth the regularization term or not, two different types of proximity algorithms are presented. The convergence rates of both types of the algorithms are improved significantly by exploring either the strategy of the Gauss-Seidel iteration, or the FISTA, or both. We compare the performance of various modified L1/TV models for the problem of impulse noise removal, and make recommendations based on our numerical experiments for using these models in applications.
2014, 8(1): 79-102 doi: 10.3934/ipi.2014.8.79 +[Abstract](84) +[PDF](1252.2KB)
Abstract:
We present a new approach to solve the inverse source problem arising in Fluorescence Tomography (FT). In general, the solution is non-unique and the problem is severely ill-posed. It poses tremendous challenges in image reconstructions. In practice, the most widely used methods are based on Tikhonov-type regularizations, which minimize a cost function consisting of a regularization term and a data fitting term. We propose an alternative method which overcomes the major difficulties, namely the non-uniqueness of the solution and noisy data fitting, in two separate steps. First we find a particular solution called the orthogonal solution that satisfies the data fitting term. Then we add to it a correction function in the kernel space so that the final solution fulfills other regularity and physical requirements. The key ideas are that the correction function in the kernel has no impact on the data fitting, so that there is no parameter needed to balance the data fitting and additional constraints on the solution. Moreover, we use an efficient basis to represent the source function, and introduce a hybrid strategy combining spectral methods and finite element methods in the proposed algorithm. The resulting algorithm can dramatically increase the computation speed over the existing methods. Also the numerical evidence shows that it significantly improves the image resolution and robustness against noise.
2014, 8(1): 103-125 doi: 10.3934/ipi.2014.8.103 +[Abstract](77) +[PDF](456.5KB)
Abstract:
We introduce a technique for recovering a sufficiently smooth function from its ray transforms over rotationally related curves in the unit disc of 2-dimensional Euclidean space. The method is based on a complexification of the underlying vector fields defining the initial transport and inversion formulae are then given in a unified form. The method is used to analyze the attenuated ray transform in the same setting.
2014, 8(1): 127-148 doi: 10.3934/ipi.2014.8.127 +[Abstract](183) +[PDF](1571.8KB)
Abstract:
Electrical impedance tomography (EIT) is a non-invasive imaging modality in which the internal conductivity distribution is reconstructed based on boundary voltage measurements. In this work, we consider the application of EIT to non-destructive testing (NDT) of materials and, especially, crack detection. The main goal is to estimate the location, depth and orientation of a crack in three dimensions. We formulate the crack detection task as a shape estimation problem for boundaries imposed with Neumann zero boundary conditions. We propose an adaptive meshing algorithm that iteratively seeks the maximum a posteriori estimate for the shape of the crack. The approach is tested both numerically and experimentally. In all test cases, the EIT measurements are collected using a set of electrodes attached on only a single planar surface of the target -- this is often the only realizable configuration in NDT of large building structures, such as concrete walls. The results show that with the proposed computational method, it is possible to recover the position and size of the crack, even in cases where the background conductivity is inhomogeneous.
2014, 8(1): 149-172 doi: 10.3934/ipi.2014.8.149 +[Abstract](107) +[PDF](451.8KB)
Abstract:
This article is devoted to the convergence analysis of a special family of iterative regularization methods for solving systems of ill--posed operator equations in Hilbert spaces, namely Kaczmarz-type methods. The analysis is focused on the Landweber--Kaczmarz (LK) explicit iteration and the iterated Tikhonov--Kaczmarz (iTK) implicit iteration. The corresponding symmetric versions of these iterative methods are also investigated (sLK and siTK). We prove convergence rates for the four methods above, extending and complementing the convergence analysis established originally in [22,13,12,8].
2014, 8(1): 173-197 doi: 10.3934/ipi.2014.8.173 +[Abstract](88) +[PDF](557.4KB)
Abstract:
In bioluminescence tomography the location as well as the radiation intensity of a photon source (marked cell clusters) inside an organism have to be determined given the outside photon count. This inverse source problem is ill-posed: it suffers not only from strong instability but also from non-uniqueness. To cope with these difficulties the source is modeled as a linear combination of indicator functions of measurable domains leading to a nonlinear operator equation. The solution process is stabilized by a Tikhonov like functional which penalizes the perimeter of the domains. For the resulting minimization problem existence of a minimizer, stability, and regularization property are shown. Moreover, an approximate variational principle is developed based on the calculated domain derivatives which states that there exist smooth almost stationary points of the Tikhonov like functional near to any of its minimizers. This is a crucial property from a numerical point of view as it allows to approximate the searched-for domain by smooth domains. Based on the theoretical findings numerical schemes are proposed and tested for star-shaped sources in 2D: computational experiments illustrate performance and limitations of the considered approach.
2014, 8(1): 199-221 doi: 10.3934/ipi.2014.8.199 +[Abstract](105) +[PDF](971.0KB)
Abstract:
We consider the inverse problem of finding sparse initial data from the sparsely sampled solutions of the heat equation. The initial data are assumed to be a sum of an unknown but finite number of Dirac delta functions at unknown locations. Point-wise values of the heat solution at only a few locations are used in an $l_1$ constrained optimization to find the initial data. A concept of domain of effective sensing is introduced to speed up the already fast Bregman iterative algorithm for $l_1$ optimization. Furthermore, an algorithm which successively adds new measurements at specially chosen locations is introduced. By comparing the solutions of the inverse problem obtained from different number of measurements, the algorithm decides where to add new measurements in order to improve the reconstruction of the sparse initial data.
2014, 8(1): 223-246 doi: 10.3934/ipi.2014.8.223 +[Abstract](71) +[PDF](577.2KB)
Abstract:
In this paper, we presented an efficient algorithm to implement the regularization reconstruction of SPECT. Image reconstruction with priori assumptions is usually modeled as a constrained optimization problem. However, there is no efficient algorithm to solve it due to the large scale of the problem. In this paper, we used the superiorization of the expectation maximization (EM) iteration to implement the regularization reconstruction of SPECT. We first investigated the convergent conditions of the EM iteration in the presence of perturbations. Secondly, we designed the superiorized EM algorithm based on the convergent conditions, and then proposed a modified version of it. Furthermore, we gave two methods to generate desired perturbations for two special objective functions. Numerical experiments for SPECT image reconstruction were conducted to validate the performance of the proposed algorithms. The experiments show that the superiorized EM algorithms are more stable and robust for noised projection data and initial image than the classic EM algorithm, and outperform the classic EM algorithm in terms of mean square error and visual quality of the reconstructed images.
2014, 8(1): 247-257 doi: 10.3934/ipi.2014.8.247 +[Abstract](86) +[PDF](314.1KB)
Abstract:
The equations of magneto-photoelasticity are derived for a nonhomogeneous background isotropic medium and for a variable gyration vector. They coincide with Aben's equations in the case of a homogeneous background medium and of a constant gyration vector. We obtain an explicit linearized formula for the fundamental solution under the assumption that variable coefficients of equations are sufficiently small. Then we consider the inverse problem of recovering the variable coefficients from the results of polarization measurements known for several values of the gyration vector. We demonstrate that the data can be easily transformed to a family of Fourier coefficients of the unknown function if the modulus of the gyration vector is agreed with the ray length.
2014, 8(1): 259-291 doi: 10.3934/ipi.2014.8.259 +[Abstract](103) +[PDF](5178.8KB)
Abstract:
The grid method is one of the techniques available to measure in-plane displacement and strain components on a deformed material. A periodic grid is first transferred on the specimen surface, and images of the grid are compared before and after deformation. Windowed Fourier analysis-based techniques permit to estimate the in-plane displacement and strain maps. The aim of this article is to give a precise analysis of this estimation process. It is shown that the retrieved displacement and strain maps are actually a tight approximation of the convolution of the actual displacements and strains with the analysis window. The effect of digital image noise on the retrieved quantities is also characterized and it is proved that the resulting noise can be approximated by a stationary spatially correlated noise. These results are of utmost importance to enhance the metrological performance of the grid method, as shown in a separate article.
2014, 8(1): 293-320 doi: 10.3934/ipi.2014.8.293 +[Abstract](87) +[PDF](3063.2KB)
Abstract:
Many effective models are available for segmentation of an image to extract all homogenous objects within it. For applications where segmentation of a single object identifiable by geometric constraints within an image is desired, much less work has been done for this purpose. This paper presents an improved selective segmentation model, without `balloon' force, combining geometrical constraints and local image intensity information around zero level set, aiming to overcome the weakness of getting spurious solutions by Badshah and Chen's model [8]. A key step in our new strategy is an adaptive local band selection algorithm. Numerical experiments show that the new model appears to be able to detect an object possessing highly complex and nonconvex features, and to produce desirable results in terms of segmentation quality and robustness.
2014, 8(1): 321-337 doi: 10.3934/ipi.2014.8.321 +[Abstract](82) +[PDF](1015.8KB)
Abstract:
We propose an efficient nonlinear approximation scheme using the Polyharmonic Local Sine Transform (PHLST) of Saito and Remy combined with an algorithm to tile a given image automatically and adaptively according to its local smoothness and singularities. To measure such local smoothness, we introduce the so-called local Besov indices of an image, which is based on the pointwise modulus of smoothness of the image. Such an adaptive tiling of an image is important for image approximation using PHLST because PHLST stores the corner and boundary information of each tile and consequently it is wasteful to divide a smooth region of a given image into a set of smaller tiles. We demonstrate the superiority of the proposed algorithm using Antarctic remote sensing images over the PHLST using the uniform tiling. Analysis of such images including their efficient approximation and compression has gained its importance due to the global climate change.
2016 Impact Factor: 1.094
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2018-02-24 06:21:03
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http://researchonline.ljmu.ac.uk/id/eprint/8507/
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Galaxy and Mass Assembly (GAMA): Variation in Galaxy Structure Across the Green Valley
Kelvin, LS, Bremer, MN, Phillipps, S, James, PA, Davies, LJM, Propris, RD, Moffett, AJ, Percival, SM, Baldry, IK, Collins, CA, Alpaslan, M, Bland-Hawthorn, J, Brough, S, Cluver, M, Driver, SP, Hashemizadeh, A, Holwerda, BW, Laine, J, Lara-Lopez, MA, Liske, J , Maciejewski, W, Napolitano, NR, Penny, SJ, Popescu, CC, Sansom, AE, Sutherland, W, Taylor, EN, Kampen, EV and Wang, L (2018) Galaxy and Mass Assembly (GAMA): Variation in Galaxy Structure Across the Green Valley. Monthly Notices of the Royal Astronomical Society. ISSN 0035-8711
Preview
Text
1804.04470v1.pdf - Accepted Version
Using a sample of 472 local Universe (z<0.06) galaxies in the stellar mass range 10.25 < log M*/M_sun < 10.75, we explore the variation in galaxy structure as a function of morphology and galaxy colour. Our sample of galaxies is sub-divided into red, green and blue colour groups and into elliptical and non-elliptical (disk-type) morphologies. Using KiDS and VIKING derived postage stamp images, a group of eight volunteers visually classified bars, rings, morphological lenses, tidal streams, shells and signs of merger activity for all systems. We find a significant surplus of rings ($2.3\sigma$) and lenses ($2.9\sigma$) in disk-type galaxies as they transition across the green valley. Combined, this implies a joint ring/lens green valley surplus significance of $3.3\sigma$ relative to equivalent disk-types within either the blue cloud or the red sequence. We recover a bar fraction of ~44% which remains flat with colour, however, we find that the presence of a bar acts to modulate the incidence of rings and (to a lesser extent) lenses, with rings in barred disk-type galaxies more common by ~20-30 percentage points relative to their unbarred counterparts, regardless of colour. Additionally, green valley disk-type galaxies with a bar exhibit a significant $3.0\sigma$ surplus of lenses relative to their blue/red analogues. The existence of such structures rules out violent transformative events as the primary end-of-life evolutionary mechanism, with a more passive scenario the favoured candidate for the majority of galaxies rapidly transitioning across the green valley.
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2019-07-24 04:51:06
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https://fykos.org/year21/problems/series5
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5. Series 21. Year
Select year
Post deadline: -
Upload deadline: - (local time in Czech Republic)
1. caution, do not suffocate
In this set of questions we will visit the world of science fiction. Space is filled with many space ships – one of them is Rama (A. C. Clarke: Rendezvous with Rama, Rama II, The Garden of Rama, Rama Revealed). Rama is large intergalactic ship constructed by extra-terrestrial civilisation and came to Solar system. Lets discuss some challenges, which are facing us.
Rama has a shape of cylinder of length 54 km and internal diameter 16 km. It is filled inside by air. Rama has its own gravity, which comes from rotating around its axis once per every four minutes. On inside surface the pressure of air is 1 bar.
The entrance to Rama is an orifice in the centre of one of its basis. Before removing the space suit, lets think, if on axis is breathable air, what is its density comparing to density on cylinder surface. Assume the temperature is the same everywhere.
Martin Formánek a Kuba Benda
2. question of survival
The entrance and the internal surface are connected by a ladder. You have already descended one kilometer, when you slipped and are falling down. What will be the speed you will fall down on Rama surface? How long it will take? Is there a chance to survive?
Martin Formánek
3. staircase from the sky
The ladder is only 2 km long going to the platform, from which you have to take a stairs, which goes with long arch above the countryside. The staircase has very special shape: for each step you need the same amount of mechanical work. Calculate, how the step height depends on the distance from the Rama axis, if the length of stairs is constant. What shape is the arch?
Martin Formánek
4. Sun can
Rama travels between the stars in such way, that one half of time is constantly accelerating and second half of time is slowing down. Currently the Rama is on parabolic trajectory around the Sun with peak on Earth orbit. It gets energy from Sun light. Its surface absorbs 80 % of incident energy. Will it get enough energy to get to Sirius, which is in distance of 12 light years in less than 24 years?
Nadhodil Jakub Benda
P. Rama-quake
Finally you got onto the surface of Rama. Suddenly it started to shake and you think the rotation speed has changed. How you can measure the rotation speed? Can you find more than one experiment?
Martin Formánek
E. milestones of life in Rama
Will have the Rama (brand name for margarine) another physical properties after you will melt it and let it solidify back? We suggest to measure density, viscosity and colour.
Vytlačil Marek Pechal.
S. sequence, hot orifice and white dwarf
• Derive Taylor expansion of exponential and for $x=1$ graphically show sequence of partial sums of series \sum_{$k=1}^{∞}1⁄k!$ with series { ( 1 − 1 ⁄ $n)^{n}}_{n=1,2,\ldots}$.
Using the same method compare series { ( 1 − 1 ⁄ $n)^{n}}_{n=1,2,\ldots}$ and series of partial sums of series \sum_{$k=1}^{∞}x^{k}⁄k!$, therefore series {\sum_{$k=1}^{n}x^{k}⁄k!}_{n=1,2,\ldots}$, now for $x=-1$.
• The second task is to find concentration of electrons and positrons on temperature with total charge $Q=0$ in empty and closed cavity (you can choose value of $Q.)$ Further calculate dependence of ration of internal energy $U_{e}$ of electrons and positrons to the total internal energy of the system $U$ (e.g. the sum of energy of electromagnetic radiation and particles) on temperature and find value of temperature related to some prominent temperature and ratios (e.g. 3 ⁄ 4, 1 ⁄ 2, 1 ⁄ 4, …; can this ratio be of all values?).
Put your results into a graph – you can try also in 3-dimensions.
To get the calculation simplified, it could help to take some unit-less entity (e.g. $βE_{0}$ instead of $β$ etc.).
• Solve the system of differential equations for $M(r)$ and $ρ(r)$ in model of white dwarf for several well chosen values of $ρ(0)$ and for every value find the value which it get close $M(r)$ at
$r→∞$. This is probably equal to the mass of the whole star. Try to find the dependence of total weight on $ρ(0)$ and find its upper limit. Compare the result with the upper limit of mass for white dwarf (you will find it in literature or internet). Assume, that the star consists from helium.
Zadali autoři seriálu Marek Pechal a Lukáš Stříteský.
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2020-07-05 11:14:47
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https://harangdev.github.io/papers/7/
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# “EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks” Summarized
Categories:
Updated:
https://arxiv.org/abs/1905.11946 (2019-06-10)
## 1. Introduction
EfficientNet group is composed of ConvNets EfficientNetB0~EfficientNetB7. (bigger number means more parameters) EfficientNetB7 achieved state of the art in ImageNet classification with considerably less parameters than previous SOTA, GPipe. Smaller EffficientNets also achieved higher accuracies than previous architectures that have similar complexities.
Now I will go through two prerequisites, ‘neural architecture search’ and ‘mobilenet-v2’ briefly.
## 2. Neural Architecture Search (NAS)
NAS is an algorithm that finds optimal network architecture. It assumes that the neural net is composed of certain blocks. (ex. 1x7 then 7x1 convolution, 3x3 average pooling, etc) A RNN controller outputs the blocks to build a neural network, then based on it’s validation score on a dataset, the controller is reinforced.
Advanced algorithms such as Progressive NAS and Efficient NAS were invented to significantly reduce search runtime.
Below is an example of cells proposed by NAS.
## 3. MBConv Block in MobileNet V2
More info about MobileNet v2 here. MobileNet V2 is composed of many MBConv blocks. The blocks have 3 features.
1. Depthwise Convolution + Pointwise Convolution It divides original convolution to two steps to reduce computational cost significantly with minimal accuracy loss.
2. Inverted Residuals Original ResNet blocks are composed with a layer that squeezes channels, then a layer that expands channels, such that skip connection connects rich-channel layers. But in MBConv, blocks are composed with a layer that first expands channels, then squeeze them, so layers that have less channels are skip-connected.
3. Linear Bottleneck It uses linear activation in the last layer in each block to prevent information loss from ReLU.
Below is a keras pseudo code for MBConv block.
## 4. Background
There has been consistent development in ConvNet accuracy since AlexNet(2012), but because of hardware limits, ‘efficiency’ started to gather interest.
Movile-size ConvNets such as SqueezeNets, MobileNets, and ShuffleNets were invented and Neural Architecture Search was widely used. To find out an efficient model structure, one can first search it with a small model, then scale the found architecture to get a bigger model. Typical example is ResNets.
This ‘scaling’ of ConvNets were done on 3 aspects; ‘depth’, ‘width’, and ‘image size’. Conventionally, scaling was done on one of these aspects, but in EfficientNet three components are scaled simultaneously.
Intuitively, when image resolution is increased, the model should need more layers and more filters to extract features from the increased pixels(information). So it seems efficient to scale 3 components at the same time.
Below is an image describing 3 aspects of scaling, and compound scaling which scales 3 components simultaneously.
## 5. Compound Scaling
The authors observed that it is more effective to scale width, depth, and resolution at the same time, than to scale them separately.
The technique is called ‘compound scaling’.
The authors wanted to increase FLOPS by a factor of 2, from EfficientNetB0 to EfficientNetB7. (To make EfficientNetB1 have 2x FLOPS compared to EfficientNetB0, etc) so they formulated the problem like below.
where $\phi$ is the suffix,(eg. 2 from EfficientNetB2) and $d,w,r$ is a factor that is multiplied to the base model’s depth, width and resolution respectively.
## 6. Constructing EfficientNet
The authors performed NAS to find an optimal baseline network, EfficientNetB0. It used mobile inverted bottleneck MBConv.
Below is a EfficientNetB0 baseline network.
### Step 2
Fix $\phi=1$, then grid search $\alpha, \beta, \gamma$ to scale b0 to b1.
### Step 3
Fix $\alpha, \beta, \gamma$, then increase $\phi$ from 2~7 to construct b2~b7 with the compound scaling method.
Categories:
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2020-04-08 09:03:25
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https://encyclopediaofmath.org/wiki/Linear_algebra,_numerical_methods_in
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# Linear algebra, numerical methods in
The branch of numerical mathematics concerned with the mathematical description and investigation of processes for solving numerical problems in linear algebra.
Among the problems in linear algebra there are two that are the most important: the solution of a system of linear algebraic equations and the determination of the eigen values and eigen vectors of a matrix. Other problems frequently encountered are: the inversion of a matrix, the calculation of a determinant and the determination of the roots of an algebraic polynomial. These do not have, as a rule, independent significance in linear algebra and have an auxiliary character in the solution of its main problems.
Any numerical method in linear algebra can be regarded as a sequence of arithmetic operations carried out on elements of the input data. If for any input data a numerical method makes it possible to find a solution of the problem in finitely many arithmetic operations, such a method is called direct. Otherwise the numerical method is called iterative.
## Direct methods for solving a system of linear algebraic equations.
Suppose one is given a system
$$\tag{1 } A x = b$$
with matrix $A$ and right-hand side $b$. If $A$ is non-singular, then the solution is given by the formula $x = A ^ {-} 1 b$, where $A ^ {-} 1$ is the inverse matrix to $A$. The main idea of direct methods consists in transforming (1) to an equivalent system for which the matrix of the system is easily inverted, and consequently it is easy to find a solution of the original system. Suppose that both sides of (1) are multiplied on the left by non-singular matrices $L _ {1} \dots L _ {k}$. Then the new system
$$\tag{2 } L _ {k} \dots L _ {1} Ax = L _ {k} \dots L _ {1} b$$
is equivalent to (1). The matrices $L _ {i}$ can always be chosen in such a way that the matrix on the left-hand side of (2) is sufficiently simple, for example, triangular, diagonal or unitary. In this case it is easy to calculate $A ^ {-} 1$ and $| A |$.
One of the first direct methods was the Gauss method. It uses lower triangular matrices (cf. Triangular matrix) $L _ {i}$ and makes it possible to reduce the original system of equations to a system with an upper triangular matrix. This method is easily implemented on a computer; its scheme with choice of a principal element makes it possible to solve a system with an arbitrary matrix, and a compact scheme makes it possible to obtain results with increased accuracy by accumulating scalar products. Among the direct methods used in practice, the Gauss method requires the least amount of computational work.
Directly related to the Gauss method is Jordan's method and a modification of it, the method of optimal elimination (see [2]). These methods use lower and upper triangular matrices $L _ {i}$ and make it possible to reduce the original system to one with a diagonal matrix. In their characteristics both methods differ little from the Gauss method, but the second makes it possible to solve a system of double the order with the same computer memory.
The stated methods belong to the group of so-called elimination methods. This name is explained by the fact that for every multiplication by a matrix $L _ {i}$ one or more elements are eliminated in the matrix of the system. Elimination can be carried out not only by means of triangular matrices but also by means of unitary matrices. Various modifications of elimination methods are essentially connected with the decomposition of the matrix of the system (1) into the product of two triangular matrices or the product of a triangular and a unitary matrix.
Some methods, such as the bordering method and the completion method, are not elimination methods, although they are close to the Gauss method.
Methods based on the construction of an auxiliary system of vectors, in some way connected with the matrix of the original system and orthogonal in some metric, have been widely propagated. One of the first methods of this group was the method of orthogonal rows. The matrices $L _ {i}$ in it are lower triangular and the matrix of the system (2) is unitary. Methods based on orthogonalization have many merits, but are sensitive to the influence of rounding errors. On the basis of the development of methods of orthogonalization type the very effective method (for the solution of certain systems with sparse matrices) of conjugate directions has been created (see [9], [10]).
## Direct methods for determining the eigen values and eigen vectors of a matrix.
Suppose that for a matrix $A$ it is required to determine an eigen value $\lambda$ and eigen vector $x$, that is, to solve the equation
$$\tag{3 } A x = \lambda x .$$
Under a change of variable $x = C y$, where $C$ is a non-singular matrix, equation (3) goes over into an equation $B y = \lambda y$ with $B = C ^ {-} 1 A C$. Direct methods for solving the given problem consist of reducing the original matrix $A$ by finitely many similarity transformations to a matrix $B$ of such a simple form that it is easy to find the coefficients of the characteristic polynomial and the eigen vectors for it. The eigen values are found from the characteristic equation by one of the well-known methods. Numerical methods for the transition from $A$ to $B$ are essentially little different from the numerical method for transforming (1) into (2). Many methods of similarity type are known (the methods of Krylov, Danilevskii, Hessenberg, etc., see [1]). However, they have not been widely used in practice in view of their considerable numerical instability (see [3]).
One distinguishes between the complete eigen value problem, when one looks for all eigen values, and the partial problem, when one looks for some of them; the latter problem is more typical in the case of linear algebra problems which arise in the approximation of differential and integral equations via difference methods.
## Iterative methods for solving a system of linear algebraic equations.
These methods give the solution of the system (1) in the form of the limit of a sequence of certain vectors; the construction of these is carried out by a uniform process, called an iterative process. The main iterative process for the solution of (1) can be described by means of the following general scheme. Construct a sequence of vectors $x ^ {(} 1) \dots x ^ {(} k) \dots$ from the recurrence formulas
$$x ^ {(} k) = x ^ {(} k- 1) + H ^ {(} k) ( b - A x ^ {(} k- 1) ) ,$$
where $H ^ {(} 1) , H ^ {(} 2) \dots$ is a sequence of matrices and $x ^ {(} 0)$ is the initial approximation, generally speaking arbitrary. Different choices of the sequence of matrices $H ^ {(} k)$ lead to different iterative processes.
The simplest iterative processes are stationary processes, in which the matrices $H ^ {(} k)$ do not depend on the step number $k$; they are also called methods of simple iteration (see [5]). If the sequence $H ^ {(} k)$ is periodic, the process is called cyclic. Every cyclic process can be transformed into a stationary process, but usually such a transformation complicates the method. Non-stationary processes, in particular cyclic processes, are used to speed up the convergence of iterative processes (see [5], [6]). Among the methods for speeding up convergence, those that use the Chebyshev polynomials (see [5], [6]) and conjugate directions (see [10]) take a special place.
The choice of a matrix $H$ for a stationary process and matrices $H ^ {(} k)$ for a non-stationary process can be made in various ways. It is possible to construct the matrices $H ^ {(} k)$ in such a way that the iterative process converges to the solution as fast as possible for a wide class of systems of equations (see [5]). The opposite approach is also possible, when in the construction of the matrices $H ^ {(} k)$ maximal use is made of the peculiarities of the given system to obtain the iterative process with greatest rate of convergence (see [6]). The second method of constructing the matrices $H ^ {(} k)$ is more prevalent.
One of the most prevalent principles for constructing iterative processes is the relaxation principle (see Relaxation method). In this case the matrices $H ^ {(} k)$ are chosen from a class of matrices described earlier so that at each step of the process some quantity that characterizes the accuracy of the solution of the system is decreased. Among relaxation methods the ones most developed are coordinate and gradient methods. In coordinate methods the matrices $H ^ {(} k)$ are chosen so that at each step one or more components of the successive approximations change(s). For the accuracy of the approximate solution $x$ one most frequently uses the value of the error vector $r = A x - b$.
In the case of stationary iterative methods the main error term can also be estimated by means of the $\delta ^ {2}$- process (see [5]).
Among other iterative methods one can mention the simple-iteration method, the variable-directions method, the method of complete and incomplete relaxation, etc. (see [1], [6], [10]). As a rule, iterative methods are convenient for realization on a computer, but in contrast to direct methods they most frequently have a very restricted range of application. In their range of application iterative methods infrequently exceed direct methods substantially in the amount of computation. Therefore, the question of comparing direct and indirect methods can be solved only by a detailed study of the properties of an actual system. The most prevalent are iterative methods for solving systems that arise in the difference approximation of differential equations (see [5], [6]).
## Iterative methods for solving the complete eigen value problem.
In iterative methods the eigen values are calculated as the limits of certain numerical sequences without previously determining the coefficients of the characteristic polynomial. As a rule, one simultaneously finds the eigen vectors or certain other vectors connected with simple eigen relations. The majority of iterative methods are less sensitive to rounding errors than direct methods, but significantly more laborious. The development of these methods and the introduction of them in practical calculations became possible only after the introduction of computers.
Among iterative methods a special place is taken by the method of rotations (the Jacobi method) for solving the complete eigen value problem for a real symmetric matrix. It is based on the construction of a sequence of matrices orthogonally similar to the original matrix $A$ and such that the sum of the squares of all elements not on the main diagonal decreases monotonically to zero.
The Jacobi method is very simple, it is easily implemented on a computer and it always converges. Independently of the location of the eigen values it has asymptotic quadratic convergence. The presence of multiple and close eigen values not only does not slow down the convergence of the method, but on the contrary speeds it up. The Jacobi method is stable with respect to the influence of rounding errors in the results of intermediate calculations. The properties of this method are the reason for its prevalence in the solution of the complete eigen value problem for matrices of general form. The Jacobi method can be used, with no essential change, for Hermitian and skew-Hermitian matrices. An insignificant change in it makes it possible to solve successfully the complete eigen value problem for the matrices $A ^ {*} A$ and $A A ^ {*}$ at the same time, without calculating the products of the matrices themselves. An effective extension of this method to arbitrary matrices of a simple structure is realized by the generalized Jacobi method.
Among the iterative methods for solving the complete eigen value problem a significant group is formed by power methods. The majority of their computational algorithms are arranged according to the following scheme:
$$\begin{array}{ccc} A G = G _ {1} S _ {1} &{} &A = L _ {1} R _ {1} \\ {\dots \dots } &\textrm{ or } &{\dots \dots } \\ A G _ {k-} 1 = G _ {k} S _ {k} &{} &R _ {k-} 1 L _ {k-} 1 = L _ {k} R _ {k} \\ {\dots \dots } &{} &{\dots \dots } \\ \end{array}$$
Here, at each step the matrix on the left of the equality sign splits into the product of two matrices. Suppose that one of them is triangular and the other unitary or triangular of a different type. Then, under certain additional assumptions, the matrices $G _ {k} ^ {-} 1 A G _ {k}$ and $R _ {k} L _ {k}$ converge to a quasi-triangular matrix similar to $A$. As a rule, the orders of the diagonal cells of the quasi-triangular matrix are not large, so the complete eigen value problem for the limiting matrix is solved quite easily.
A few methods of this type are known. One of the best of them is the $QR$- algorithm (see [7]).
## Investigation and classification of numerical methods.
The vast number of numerical methods of linear algebra poses an actual problem, not so much because of the creation of new methods as in the investigation and classification of existing methods (one of the most complete classifications of methods from the point of view of their mathematical structure is contained in [1]; the monographs [2], [3], [7] are devoted to the description of methods from the point of view of their computer implementation).
The first papers on the analysis of stability and rounding errors in numerical methods for the solution of problems in linear algebra appeared only in 1947–1948 and were devoted to an investigation of the inversion of matrices and to the solution of systems of equations by methods of Gauss type. The practical value of these results was rather small. An important shift in the study of this question occurred in the middle of the 1960-s (see [3]), when a decisive step was taken in the analysis and estimation of equivalent perturbations. The actual computational solution of a certain problem was interpreted as the exact solution of the same problem, but corresponding to perturbations of the initial data (so-called backward analysis). This perturbation, known as equivalent perturbation, completely characterizes the influence of rounding. Many methods were investigated from the point of view of giving a majorizing estimate of the norm of the equivalent perturbation (see [3], [7]).
For a fixed computational algorithm and method of rounding the whole collection of rounding errors is a single-valued vector function $\phi _ {t} ( A)$, which depends on the number of digits $t$ with which the calculation is carried out and on the original data $A$. The principal term of the function $\phi _ {t} ( A)$, as $t \rightarrow \infty$, does not have any useful explicit expression. However, the investigation of $\phi _ {t} ( A)$ in the class of randomly specified initial data has turned out to be very effective. It was shown that the most probable value of the deviation of the computed solution from the exact solution due to rounding errors is substantially less than the maximum possible value (see [7]).
An analysis of the influence of rounding errors showed that there is not much fundamental difference between the best methods from the point of view of stability, i.e. with respect to rounding errors. This conclusion forces one to look in a new way at the problem of choosing some computational method in practical computational work. The creation of powerful computers substantially weakened the significance of the difference between methods in such characteristics as the size of the required computer memory and the number of arithmetical operations, and led to increased requirements to guarantee the accuracy of the solution. Under these conditions the most preferable methods were those that, while not very different from the best methods in speed and convenience of implementation on a computer, make it possible to solve a wide class of problems, both well-conditioned and ill-conditioned, and to give an estimate of the accuracy of the computed solution.
The classification and comparison of the numerical methods mentioned above refer mainly to the case when the whole collection of initial data is completely stored in the operational memory of the computer. However, there is special interest in two extreme cases — the solution of problems of linear algebra on small and on very powerful computers. The solution of problems on such computers has its own specific features.
#### References
[1] D.K. Faddeev, V.N. Faddeeva, "Computational methods of linear algebra" , Freeman (1963) (Translated from Russian) [2] V.V. Voevodin, "Numerical methods of algebra" , Moscow (1966) (In Russian) [3] J.H. Wilkinson, "The algebraic eigenvalue problem" , Oxford Univ. Press (1969) [4] V.V. Voevodin, Vestn. Moskov. Univ. Mat. Mekh. , 2 (1970) pp. 69–82 [5] N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from Russian) [6] A.A. Samarskii, E.S. Nikolaev, "Numerical methods for grid equations" , 1–2 , Birkhäuser (1989) (Translated from Russian) [7] V.V. Voevodin, "Computational foundations of linear algebra" , Moscow (1977) (In Russian) [8] V.N. Faddeeva, et al., "Computational methods of linear algebra. Bibliographic index, 1828–1974" , Novosibirsk (1976) (In Russian) [9] V.V. Voevodin, "Algèbre linéare" , MIR (1976) (Translated from Russian) [10] G.I. Marchuk, Yu.A. Kuznetsov, "Iterative methods and quadratic functionals" , Novosibirsk (1972) (In Russian)
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2022-06-28 20:44:39
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https://physics.stackexchange.com/questions/480081/what-is-the-temperature-at-which-napalm-burns
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# What is the temperature at which Napalm burns?
I was sitting during a lecture last week in one of my classes, and we were talking about chemical warfare and the history behind it. My teacher had brought up the use of Napalm during Vietnam. After a few minutes of talking about how it was used, she mentioned it burned at around 4 million degrees Fahrenheit. This seemed to be inaccurate to me, and all I've been able to find online is that it burns between 1,200 to 5,000 degrees Fahrenheit. Which of the two is accurate? Or is neither?
• 4 million is absolutely wrong, that is for sure... – Jon Custer May 14 at 20:04
• @JonCuster Burning napalm, core of the sun; basically the same thing right? – JMac May 14 at 20:12
• @JMac sure would make fusion machines easier! – Jon Custer May 14 at 20:20
• Napalm is no doubt a hydrocarbon. Look up the flame temperature of gasoline in atmospheric air, and you will be in the right ball park. – David White May 15 at 2:16
• The temperature of the order of millions is not even found on the surface of stars. Only the cores of stars can reach to that order of temperature through a nuclear reaction. The argument of your teacher is quite naive. – Jitendra May 15 at 2:37
• When the fuel is a hydrocarbon, as it is with napalm, the bonding energies of the hydrogen and carbon atoms are about the same as before combustion. Huh? When a hydrocarbon burns, $C-H$ bonds are broken and $C-O$ bonds and $H_2O$ are formed. The overall process is strongly exothermic. – Gert May 14 at 20:37
• Consider $CH_4$ + 2$O_2$ yielding $CO_2$ + 2$H_2O$ – Paul Young May 14 at 20:42
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2019-07-20 14:06:12
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https://pos.sissa.it/390/101/
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Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Posters: Higgs Physics
Measurement of Higgs boson production at high transverse momentum in the $VH, H \rightarrow b\bar{b}$ channel with the ATLAS detector
B. Moser* on behalf of the ATLAS collaboration
*corresponding author
Full text: pdf
Pre-published on: November 17, 2020
Published on:
Abstract
With the rapidly increasing proton-proton collision data set provided by the LHC, the ATLAS experiment gains access to Higgs bosons produced with ever higher transverse momenta $p_{\text{T}}^{H}$. Measurements in this phase space are well motivated by a vast variety of BSM models which predict effects that scale with the square of the involved energy scale. The associated production of a Higgs boson $H$ with a heavy vector boson $V$ contributes significantly to the total production cross-section at high $p_{\text{T}}^H$. Combining this production mode with the most prominent decay into a pair of b-quarks promises a large enough signal yield in this rare topology. A novel measurement of the production cross-section times the decay branching-fraction for this process is presented, based on data collected between 2015 and 2018 at a center-of-mass energy of 13 TeV. Results are provided in two fiducial regions of the transverse momentum of the vector boson: $250~$GeV$< p_{\text{T}}^{V}<400~$GeV and $p_{\text{T}}^{V} \geq 400~$GeV. These cross-sections are furthermore interpreted as limits on the Wilson coefficients of a Standard Model Effective Field Theory.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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2021-03-03 02:45:52
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https://echt.guth.so/the-buckminster-fuller-challenge/
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The Buckminster Fuller Challenge
«Bucky had it right. “You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete.”
That’s why we’re awarding a \$100,000 prize each year for comprehensive solutions that radically advance human well-being and ecosystem health. The 2008 prize will be conferred June 23rd in NYC.» - BFI
Database of entries to the 2008 Buckminster Fuller Challenge.
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2018-11-15 17:45:36
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https://socratic.org/questions/how-do-you-solve-5e-2x-11-30
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×
# How do you solve 5e^(2x+11)=30?
Jan 27, 2016
I found $x = - 4.6$
#### Explanation:
We can rearrange it as:
${e}^{2 x + 11} = \frac{30}{5}$
${e}^{2 x + 11} = 6$
take the natural log of both sides:
$\ln {e}^{2 x + 11} = \ln 6$
giving:
$2 x + 11 = \ln 6$
$2 x = \ln 6 - 11$
$x = \frac{\ln 6 - 11}{2} = - 4.6$
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2018-09-20 23:06:41
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https://en.wikiversity.org/wiki/Nonlinear_finite_elements/Homework2Solutions
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# Nonlinear finite elements/Homework 2/Solutions
## Problem 1: Classification of PDEs
Given:
${\displaystyle {\begin{matrix}{\text{(1)}}\qquad u_{,xx}&=&\alpha u_{,t}\\{\text{(2)}}\qquad u_{,xxxx}&=&\alpha u_{,tt}\end{matrix}}}$
### Solution
#### Part 1
What physical processes do the two PDEs model?
Equation (1) models the one dimensional heat problem where ${\displaystyle u(x,t)}$ represents temperature at ${\displaystyle x}$ at time ${\displaystyle t}$ and ${\displaystyle \alpha }$ represents the thermal diffusivity.
Equation (2) models the transverse vibrations of a beam. The variable ${\displaystyle u(x,t)}$ represents the displacement of the point on the beam corresponding to position ${\displaystyle x}$ at time ${\displaystyle t}$. ${\displaystyle \alpha }$ is ${\displaystyle -{\frac {\rho A}{EI}}}$ where ${\displaystyle E}$ is Young's modulus, ${\displaystyle I}$ is area moment of inertia, ${\displaystyle \rho }$ is mass density, and ${\displaystyle A}$ is area of cross section.
#### Part 2
Write out the PDEs in elementary partial differential notation
{\displaystyle {\begin{aligned}u_{,xx}&=\alpha u_{,t}\qquad \equiv \qquad {\frac {\partial ^{2}u}{\partial x^{2}}}=\alpha {\frac {\partial u}{\partial t}}\\u_{,xxxx}&=\alpha u_{,tt}\qquad \equiv \qquad {\frac {\partial ^{4}u}{\partial x^{4}}}=\alpha {\frac {\partial ^{2}u}{\partial t^{2}}}\end{aligned}}}
#### Part 3
Determine whether the PDEs are elliptic, hyperbolic, or parabolic. Show how you arrived at your classification.
Equation (1) is parabolic for all values of ${\displaystyle \alpha }$.
We can see why by writing it out in the form given in the notes on Partial differential equations.
${\displaystyle (1){\frac {\partial ^{2}u}{\partial x^{2}}}+(0){\frac {\partial ^{2}u}{\partial x\partial t}}+(0){\frac {\partial ^{2}u}{\partial t^{2}}}+(0){\frac {\partial u}{\partial x}}+(-\alpha ){\frac {\partial u}{\partial t}}+(0)u=0}$
Hence, we have ${\displaystyle a=1}$, ${\displaystyle b=0}$, ${\displaystyle c=0}$, ${\displaystyle d=0}$, ${\displaystyle e=-\alpha }$, ${\displaystyle f=0}$, and ${\displaystyle g=0}$. Therefore,
${\displaystyle {b^{2}-4ac=0-(1)(0)=0\Rightarrow {\text{parabolic}}}}$
Equation (2) is hyperbolic for positive values of ${\displaystyle \alpha }$, parabolic when ${\displaystyle \alpha }$ is zero, and elliptic when ${\displaystyle \alpha }$ is less than zero.
## Problem 2: Models of Physical Problems
Given:
${\displaystyle {\frac {d}{dx}}\left(a(x){\frac {du(x)}{dx}}\right)+c(x)u(x)=f(x)\quad {\mbox{for }}\quad x\in (O,L)}$
### Solution
• Heat transfer: :${\displaystyle kA{\frac {d^{2}T}{dx^{2}}}+ap\beta T=f}$
• Flow through porous medium: :${\displaystyle \mu {\frac {d^{2}\phi }{dx^{2}}}=f}$
• Flow through pipe: :${\displaystyle {\frac {1}{R}}{\frac {d^{2}P}{dx^{2}}}=0}$
• Flow of viscous fluids: :${\displaystyle \mu {\frac {d^{2}v_{z}}{dx^{2}}}=-{\frac {dP}{dx}}}$
• Elastic cables: :${\displaystyle T{\frac {d^{2}u}{dx^{2}}}=f}$
• Elastic bars: :${\displaystyle EA{\frac {d^{2}u}{dx^{2}}}=f}$
• Torsion of bars: :${\displaystyle GJ{\frac {d^{2}\theta }{dx^{2}}}=0}$
• Electrostatics: :${\displaystyle \varepsilon {\frac {d^{2}\phi }{dx^{2}}}=\rho }$
## Problem 4: Least Squares Method
Given:
The residual over an element is
${\displaystyle R^{e}(x,c_{1}^{e},c_{2}^{e},\dots ,c_{n}^{e}):={\cfrac {d}{dx}}\left(a~{\cfrac {du_{h}^{e}}{dx}}\right)+c~u_{h}^{e}-f(x)}$
where
${\displaystyle u_{h}^{e}(x)=\sum _{j=1}^{n}c_{j}^{e}\varphi _{j}^{e}(x)~.}$
In the least squares approach, the residual is minimized in the following sense
${\displaystyle {\frac {\partial }{\partial c_{i}}}\int _{x_{a}}^{x_{b}}[R^{e}(x,c_{1}^{e},c_{2}^{e},\dots ,c_{n}^{e})]^{2}~dx=0,\qquad i=1,2,\dots ,n~.}$
### Solution
#### Part 1
What is the weighting function used in the least squares approach?
We have,
${\displaystyle {\frac {\partial }{\partial c_{i}}}\int _{x_{a}}^{x_{b}}[R^{e}]^{2}~dx=\int _{x_{a}}^{x_{b}}2R^{e}{\frac {\partial R^{e}}{\partial c_{i}}}~dx=0~.}$
Hence the weighting functions are of the form
${\displaystyle {w_{i}(x)={\frac {\partial R^{e}}{\partial c_{i}}}}}$
#### Part 2
Develop a least-squares finite element model for the problem.
To make the typing of the following easier, I have gotten rid of the subscript ${\displaystyle h}$ and the superscript ${\displaystyle e}$. Please note that these are implicit in what follows.
${\displaystyle u(x)=\sum _{j=1}^{n}c_{j}\varphi _{j}(x)~.}$
The residual is
${\displaystyle R={\cfrac {d}{dx}}\left[a~\left(\sum _{j}c_{j}{\cfrac {d\varphi _{j}}{dx}}\right)\right]+c~\left(\sum _{j}c_{j}\varphi _{j}\right)-f(x)~.}$
The derivative of the residual is
${\displaystyle {\frac {\partial R}{\partial c_{i}}}={\cfrac {d}{dx}}\left[a~\left(\sum _{j}{\frac {\partial c_{j}}{\partial c_{i}}}{\cfrac {d\varphi _{j}}{dx}}\right)\right]+c~\left(\sum _{j}{\frac {\partial c_{j}}{\partial c_{i}}}\varphi _{j}\right)-f(x)~.}$
For simplicity, let us assume that ${\displaystyle a}$ is constant, and ${\displaystyle c=0}$. Then, we have
${\displaystyle R=a~\left(\sum _{j}c_{j}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}\right)-f~,}$
and
${\displaystyle {\frac {\partial R}{\partial c_{i}}}=a~\left(\sum _{j}{\frac {\partial c_{j}}{\partial c_{i}}}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}\right)~.}$
Now, the coefficients ${\displaystyle c_{i}}$ are independent. Hence, their derivatives are
${\displaystyle {\frac {\partial c_{j}}{\partial c_{i}}}={\begin{cases}0&{\text{for}}~~i\neq j\\1&{\text{for}}~~i=j\end{cases}}}$
Hence, the weighting functions are
${\displaystyle {\frac {\partial R}{\partial c_{i}}}=a~{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}~.}$
The product of these two quantities is
${\displaystyle R{\frac {\partial R}{\partial c_{i}}}=\left(a\sum _{j}c_{j}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}-f\right)\left(a{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}\right)=\sum _{j}\left[\left(a^{2}{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}\right)c_{j}\right]-af{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}~.}$
Therefore,
${\displaystyle \int _{x_{a}}^{x_{b}}R{\frac {\partial R}{\partial c_{i}}}~dx=0\implies \sum _{j}\left[\left(\int _{x_{a}}^{x_{b}}a^{2}{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}~dx\right)c_{j}\right]-\int _{x_{a}}^{x_{b}}af{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}~dx=0}$
These equations can be written as
${\displaystyle K_{ij}c_{j}=f_{i}}$
where
${\displaystyle {K_{ij}=\int _{x_{a}}^{x_{b}}a^{2}{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}{\cfrac {d^{2}\varphi _{j}}{dx^{2}}}~dx}}$
and
${\displaystyle {f_{i}=\int _{x_{a}}^{x_{b}}af{\cfrac {d^{2}\varphi _{i}}{dx^{2}}}~dx~.}}$
#### Part 3
1. Discuss some functions ${\displaystyle (\varphi _{j}^{e})}$ that can be used to approximate ${\displaystyle u}$
For the least squares method to be a true "finite element" type of method we have to use finite element shape functions. For instance, if each element has two nodes we could choose
${\displaystyle \varphi _{1}={\cfrac {x_{b}-x}{h}}\qquad {\text{and}}\qquad \varphi _{2}={\cfrac {x-x_{a}}{h}}~.}$
Another possiblity is set set of polynomials such as
${\displaystyle \varphi =\{1,x,x^{2},x^{3}\}~.}$
## Problem 5: Heat Transefer
Given:
${\displaystyle -{\frac {d}{dx}}\left(k{\frac {dT}{dx}}\right)=q\quad {\mbox{ for }}\quad x\in (0,L)}$
where ${\displaystyle T}$ is the temperature, ${\displaystyle k}$ is the thermal conductivity, and ${\displaystyle q}$ is the heat generation. The Boundary conditions are
${\displaystyle {\begin{matrix}T(0)&=&T_{0}\\k{\frac {dT}{dx}}+\beta (T-T_{\infty })+{\hat {q}}{\bigg |}_{x=L}&=&0\end{matrix}}}$
### Solution
#### Part 1
Formulate the finite element model for this problem over one element
First step is to write the weighted-residual statement
${\displaystyle 0=\int _{x_{a}}^{x_{b}}w_{i}^{e}\left[-{\frac {d}{dx}}\left(k{\frac {dT_{h}^{e}}{dx}}\right)-q\right]dx}$
Second step is to trade differentiation from ${\displaystyle T_{h}^{e}}$ to ${\displaystyle w_{i}^{e}}$, using integration by parts. We obtain
${\displaystyle 0=\int _{x_{a}}^{x_{b}}\left(k{\frac {w_{i}^{e}}{dx}}{\frac {dT_{h}^{e}}{dx}}-w_{i}^{e}q\right)dx-\left[w_{i}^{e}k{\frac {dT_{h}^{e}}{dx}}\right]_{x_{a}}^{x_{b}}{\text{(3)}}\qquad }$
Rewriting (3) in using the primary variable ${\displaystyle T}$ and secondary variable ${\displaystyle k{\frac {dT}{dx}}\equiv Q}$ as described in the text book to obtain the weak form
${\displaystyle 0=\int _{x_{a}}^{x_{b}}\left(k{\frac {w_{i}^{e}}{dx}}{\frac {dT_{h}^{e}}{dx}}-w_{i}^{e}q\right)dx-w_{i}^{e}(x_{a})Q_{a}^{e}-w_{i}^{e}(x_{b})Q_{b}^{e}{\text{(4)}}\qquad }$
From (4) we have the following
${\displaystyle {\begin{matrix}K_{ij}^{e}&=&\int _{x_{a}}^{x_{b}}k{\frac {N_{i}^{e}}{dx}}{\frac {dN_{j}^{e}}{dx}}dx\\f_{i}^{e}&=&\int _{x_{a}}^{x_{b}}qN_{i}^{e}dx\\K_{ij}^{e}T_{j}^{e}&=&f_{i}^{e}+N_{i}^{e}(x_{a})Q_{a}^{e}+N_{i}^{e}(x_{b})Q_{b}^{e}\end{matrix}}}$
#### Part 2
Use ANSYS to solve the problem of heat conduction in an insulated rod. Compare the solution with the exact solution. Try at least three refinements of the mesh to confirm that your solution converges.
The following inputs are used to solve for the solution of this problem:
/prep7 pi = 4*atan(1) !compute value for pi ET,1,LINK34!convection element ET,2,LINK32!conduction element R,1,1!AREA = 1 MP,KXX,1,0.01!conductivity MP,HF,1,25 !convectivity emax = 2 length = 0.1 *do,nnumber,1,emax+1 !begin loop to creat nodes n,nnumber,length/emax*(nnumber-1),0 n,emax+2,length,0!extra node for the convetion element *enddo type,2 !switch to conduction element *do,enumber,1,emax e,enumber,enumber+1 *enddo TYPE,1 !switch to convection element e,emax+1,emax+2!creat zero length element D,1,TEMP,50 D,emax+2,TEMP,5 FINISH /solu solve fini /post1 /output,p5,txt prnsol,temp prnld,heat /output,, fini
ANSYS gives the following results
Node Temperature
1 50.000
2 27.590
3 5.1793
Node Heat Flux
1 -4.4821
4 4.4821
#### Part 3
Write you own code to solve the problem in part 2.
The following Maple code can be used to solve the problem.
> restart; > with(linalg): > L:=0.1:kxx:=0.01:beta:=25:T0:=50:Tinf:=5: > # Number of elements > element:=10: > # Division length > ndiv:=L/element: > # Define node location > for i from 1 to element+1 do > x[i]:=ndiv*(i-1); > od: > # Define shape function > for j from 1 to element do > N[j][1]:=(x[j+1]-x)/ndiv; > N[j][2]:=(x-x[j])/ndiv; > od: > # Create element stiffness matrix > for k from 1 to element do > for i from 1 to 2 do > for j from 1 to 2 do > Kde[k][i,j]:=int(kxx*diff(N[k][i],x)*diff(N[k][j],x),x=x[k]..x[k+1]); > od; > od; > od; > Kde[0][2,2]:=0:Kde[element+1][1,1]:=0: > # Create global matrix for conduction Kdg and convection Khg > Kdg:=Matrix(1..element+1,1..element+1,shape=symmetric): > Khg:=Matrix(1..element+1,1..element+1,shape=symmetric): > for k from 1 to element+1 do > Kdg[k,k]:=Kde[k-1][2,2]+Kde[k][1,1]; > if (k <= element) then > Kdg[k,k+1]:=Kde[k][1,2]; > end if; > od: > Khg[element+1,element+1]:=beta: > # Create global matrix Kg = Kdg + Khg > Kg:=matadd(Kdg,Khg): > # Create T and F vectors > Tvect:=vector(element+1):Fvect:=vector(element+1): > for i from 1 to element do > Tvect[i+1]:=T[i+1]: > Fvect[i]:=f[i]: > od: > Tvect[1]:=T0: > Fvect[element+1]:=Tinf*beta: > # Solve the system Ku=f > Ku:=multiply(Kg,Tvect): > # Create new K matrix without first row and column from Kg > newK:=Matrix(1..element,1..element): > for i from 1 to element do > for j from 1 to element do > newK[i,j]:=coeff(Ku[i+1],Tvect[j+1]); > od; > od; > # Create new f matrix without f1 > newf:=vector(element,0): > newf[1]:=-Ku[2]+coeff(Ku[2],T[2])*T[2]+coeff(Ku[2],T[3])*T[3]: > newf[element]:=Tinf*beta: > # Solve the system newK*T=newf > solution:=multiply(inverse(newK),newf); > exact := 50-448.2071713*x; > with(plots): > # Warning, the name changecoords has been redefined > data := [[ x[n+1], solution[n]] [itex]n=1..element]: > FE:=plot(data, x=0..L, style=point,symbol=circle,legend="FE"): > ELAS:=plot(exact,x=0..L,legend="exact",color=black): > display({FE,ELAS},title="T(x) vs x",labels=["x","T(x)"]);
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2020-10-01 19:05:29
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http://stats.stackexchange.com/questions/37894/comparing-incidence-rates
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# Comparing incidence rates
I want to compare to incidence rate's between two groups (one without a disease and one with).
I was planning to calculate the incidence rate ratio (IRR), i.e. incidence rate group B/ incidence rate group A, and then test if this rate equals to 1, and finally calculate 95% CI intervals for the IRR.
I found a method for calculation the 95% CI in a book (Rosner's Fundamentals of Biostatistics):
$$\exp\left[\log(\text{IRR}) \pm 1.96\sqrt{(1/a_1)+(1/a_2)}\right]$$
where $a_1$ and $a_2$ are the number of events. But this approximation is only valid for large enough sample sizes and i think the numer of event I have is to small (maybe for the total comparison it's okay.)
So I think I should use another method.
Im using R and the exactci package and found that I could maybe use poisson.test(). But this function has 3 methods for defining the two sided p-values: central, minlike and blaker.
So my questions are:
1. Is it correct that to compare two incidence rate ratios im using a test for comparing poisson rates?
2. When in use the poisson.test function in R from the exactci package what method is best?
The vignette for exactci says:
central: is 2 times the minimum of the one-sided p-values bounded above by 1. The name 'central' is motivated by the associated inversion con dence intervals which are central intervals, i.e., they guarantee that the true parameter has less than $\alpha/2$ probability of being less (more) than the lower (upper) tail of the 100(1-$\alpha$)% confidence interval. This is called the TST (twice the smaller tail method) by Hirji (2006).
minlike: is the sum of probabilities of outcomes with likelihoods less than or equal to the observed likelihood. This is called the PB (probability based) method by Hirji (2006).
blaker: combines the probability of the smaller observed tail with the smallest probability of the opposite tail that does not exceed that observed tail probability. The name 'blaker' is motivated by Blaker (2000) which comprehensively studies the associated method for con dence intervals. This is called the CT (combined tail) method by Hirji (2006).
My data is:
Group A:
Age group 1: 3 cases in 10459 person yrs. Incidence rate: 0.29
Age group 2: 7 cases in 2279 person yrs. Incidence rate: 3.07
Age group 3: 4 cases in 1990 person yrs. Incidence rate: 2.01
Age group 4: 9 cases in 1618 person yrs. Incidence rate: 5.56
Age group 5: 11 cases in 1357 person yrs. Incidence rate: 8.11
Age group 6: 11 cases in 1090 person yrs. Incidence rate: 10.09
Age group 7: 9 cases in 819 person yrs. Incidence rate: 10.99
Total: 54 cases in 19612 person yrs. Incidence rate: 2.75
Group B:
Age group 1: 3 cases in 3088 person yrs. Incidence rate: 0.97
Age group 2: 1 cases in 707 person yrs. Incidence rate: 1.41
Age group 3: 2 cases in 630 person yrs. Incidence rate: 3.17
Age group 4: 6 cases in 441 person yrs. Incidence rate: 13.59
Age group 5: 10 cases in 365 person yrs. Incidence rate: 27.4
Age group 6: 6 cases in 249 person yrs. Incidence rate: 24.06
Age group 7: 0 cases in 116 person yrs. Incidence rate: 0
Total: 28 cases in 5597 person yrs. Incidence rate: 5.0
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A couple thoughts:
First, your suggested comparison - the incident rate ratio between A and B - currently isn't conditioned on any covariates. Which means your number of events is 54 for Group A and 28 for Group B. That's more than enough to go with the usual large sample based Confidence Interval Methods.
Second, even if you are intending to adjust for the effect of age, rather than computing the ratio for each group, you might be better served by using a regression approach. Generally, if you're stratifying by many levels of a variable, it becomes rather cumbersome compared to a regression equation, which would give you the ratio of the rates of A and B while controlling for Age. I believe the standard approaches will still work for your sample size, though if you're worried about it, you could use something like glmperm.
-
The incidence rate of each group in your data is just the mean of a sum of independent Bernoulli (0/1) variables - each patient has its own variable receiving a value of 0 or 1, you sum them up and take the mean, which is the incidence rate.
I large samples (and your sample is large), the mean will be distributed normally, so you can use a simple z-test to test if the two rates are different or not.
In R, take a look at prop.test: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/prop.test.html
If you would like to make full use of the data, try to see if the distribution of incidence rates is different between group A and B. For that, a test of independence might do the trick, such as a chi-square of a G-test: http://udel.edu/~mcdonald/statchiind.html
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The only way to be sure the sample is large enough (or as Charlie Geyer would put it - that you actually are in asymtopia land) is to do a lot of Monte-Carlo simulation or as EpiGard suggested use something like glmperm.
As for what method is best in exactci, there is no best here - or as Fisher used to put it
Best for what?
Michael Fay provides some clarification here
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2014-09-18 03:36:41
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https://apartmanisokobanja.net/cubic-centimeter-jvmor/5e7e83-jvc-kw-xr616-buttons-not-working
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Sokobanja, Srbija +381 65 8082462
# jvc kw xr616 buttons not working
See the Big List of Lewis Structures. Ion nitrates have a negative one formal charge. (e.g., ±1 is favored over ±2). Resonance forms with the same sign charge on adjacent atoms are not favored. Using Formal Charge to Predict Molecular Structure. If you could explain why ClO2- ‘s lewis dot structure is O-Cl-O and not Cl-O-O despite the formal charge issue, our class would be really grateful! Note that the formal charges on the atoms must add up to zero for molecules that are neutral. There are total of 20 valence electrons for the ClO2- Lewis structure. Total Formal Charge -1 4(c) Atom Group No. Resonance forms with low formal charges are favored over high formal charge. In both examples, the chlorine atom is neutral, and the charge is presumed to reside on oxygen. Formal charge is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electro negativity. Reply Delete. Since oxygen is more electronegative then nitrogen, the negative charge is more stable when its on the oxygen atom. This gives a formal charge of 0 for the O's, and -1 for the Cl. The formal charge on Cl will also be zero. To show that the ClO2- Lewis structure is an ion with a -1 change we need to put brackets around the structure and put a negative side on the outside of the brackets. One last thing: we do need to put brackets around this to show that it is a negative ion. Re: Formal charge of ClO2- Post by Jade Corpus-Sapida 1G » Sun May 13, 2018 7:01 am Also, just remember that the least electronegative element is the central one. Lewis structure of ClO 3-ion is drawn step by step in this tutorial. So the formal charge on carbon is zero. For Cl, and O, there are 7, and 6 valence electrons respectively associated with the neutral atoms. Lewis Structure of ClO 3-(Chlorate ion). Formal Charge of H = (1 valence e-) - (0 lone pair e-) - (1/2 x 2 bond pair e-) = 0 . Formal charges are assigned and equalized using resonance. It can be determined by following steps- 1. Because the number of valence electrons on a neutral N atom is 5, its formal charge is 5 - 5 = 0. This is the currently selected item. That's the best structure for ClO2-. And then the Oxygen in black right here now has a formal charge of zero. Total valence electrons of oxygen and chlorine atoms and negative charge are considered to draw the ClO 3-lewis structure. Molecules (or resonance forms) with more or larger formal charges on atoms are less stable (i.e. Chlorite is similar in that the chlorine atom and one oxygen atom have formal charges of 0, but one oxygen atom has a formal charge of -1. The arrangement of atoms in a molecule or ion is called its molecular structure.In many cases, following the steps for writing Lewis structures may lead to more than one possible molecular structure—different multiple bond and lone-pair electron placements or different arrangements of atoms, for instance. You may be wondering why this is the case. Back to Ionic & Covalent Bonding Index Page. Formal Charge and Lewis Formulas. And that's it. 4 years ago. Remember that the negative sign counts as one valence electron. more reactive) than corresponding molecules lacking those charges (or with the charges delocalized.) The formal charge assigned for a particular The sum of the formal charges of each atom must be equal to the overall charge of the molecule or ion. What is the formal charge on the central nitrogen atom in the most favorable Lewis structure for nitrous oxide based on minimizing formal ch... View Answer. Step 3 & 4: The Lewis structures of ClO 2 are derived below: ... Would structures 1 and 2 be more likely than 3 because oxygen carries the charge, or is it better that 3 has no charge? (H +1) So for the arsenic Oxygen (four) = -eight there Arsenic equals 5+ is the oxidation number and is simply labored out. For hypochlorite ion, Cl-O^-, we have to distribute 7+6+1 electrons in the Lewis structure. The sum of the formal charges in a polyatomic ion will add up to the charge on the ion. Formal Charge = No of valence electrons in central atom - Total no. The ClO2 Lewis structure has 19 valence electrons meaning that there will be an odd number of valence electrons in the structure. Formal Charge and Resonance Block: _____ Formal Charge Formal charge is a means of identifying the “best” Lewis dot structure when more than one valid dot structure can be drawn for a molecule or molecular ion. More on the dot structure for sulfur dioxide. From a formal charge standpoint, the optimum structure will have double bonds between Cl and O. There are thus 7 electron pairs. Resonance forms with negative formal charge or most electronegative atoms are favored. In order to understand this, let’s take a look at the number of atoms within a molecule of NO3 and understand how formal charges are calculated. Resonance and dot structures. The formal charge of an atom can be determined by the following formula: $FC = V - (N + \frac{B}{2})$ In this formula, V represents the number of valence electrons of the atom in isolation, N is the number of non-bonding valence electrons, and B is the total number of electrons in covalent bonds with other atoms in the molecule. If you check the formal charges for Cl 2 O you'll find that the Lewis structure with charges of zero has an Oxygen atom between the two Chlorine atoms. Previous question Next question Get more help from Chegg. Formal Charge: It is the charge that is determined by subtracting the non-bonding valence electron and an average of bonding electrons from the valence electron of the element. Thus the formal charges on the atoms in the Lewis structure of CN-are: VSEPR for 4 electron clouds. In this example, the nitrogen and each hydrogen has a formal charge of zero. Still, it seems like the answer is a resonance structure with a double and a single bond between the Cl and the O's, which gives one of the O's a formal charge of 1, and the other O a formal charge of 0, and the Cl a formal charge of 0. A. Cl Atom = 0 And Each O Atom = -1 B. Cl Atom = 0, One O Atom = 0, One O Atom = -1 Oc. What Is The Formal Charge On Each Atom? For ionic compounds, the formal charges on the atoms must add up to the charge on the ion. Formal charge and dot structures. Anonymous. SO3^2- has a total of 26 electrons, including three lone pairs on each singly bonded oxygen, two lone pairs on the doubly bonded oxygen and a … Formal charge is used when creating the Lewis structure of a molecule, to determine the charge of a covalent bond. First draw the Lewis structure for the polyatomic ion. Each oxygen has two lone pairs. Why isn’t the full charge of N03 -9? and my answer; LOTS of great lessons here! Structure 4(b) has a formal charge of -2 on N and a positive one (+1) charge on oxygen, again If you count electrons and determine the formal charge on each atom, you find that in structure #1, the negative charge is on the oxygen. In this regard, what charge does chlorite have? The rule is Oxygen -2 except in peroxides. Minimize formal charge. With the diagram O-Cl-O, the formal charge is -1, +1, and -1, respectively. Non-bonding Electrons Bonds Formal Charge N 5 2 3 0 C 4 0 4 0 O 6 6 1 -1 Total Formal Charge -1 Structure 4(a) has a formal charge of -1 on N, when oxygen is the most electronegative atom. Formal Charge. Corollary: Most Lewis structures of neutral molecules (molecules with no charge) have no formal charges on any of the atoms. 2 4. The Lewis structure of the chlorite ion (ClO2-) is given below--- Total number of electron present in chlorite ion (ClO2-) is = 7 + (26) + 1 = 20 Formal charge of an view the full answer. ClO2 has 19 electrons; it is a free radical. Get 1:1 help now from expert Chemistry tutors VSEPR for 3 electron clouds. For the Lewis structure for ClO2 you should take formal charges into account to find the best Lewis structure for the molecule. For N, there are 2 nonbonding electrons and 3 electrons from the triple bond. These are convenient to do. The formal charge can be assigned to every atom in a electron dot structure. Do the same exercise for structure #2 and you find that the negative charge is on nitrogen. Formal charge: 0 0 0 – 1 0 +1 In the left hand structure of CO2 all the formal charges are zero and this structure is favored over the right hand structure. By using double bonds to oxygen, the formal charges on oxygen are reduced to zero. The formal charge of an atom in a molecule is the hypothetical charge the atom would have if we could redistribute the electrons in the bonds evenly between the atoms. My question, however, is when drawing the Lewis Structure, the formal charge on either O is -1 and on Chlorine, +2. formal charge on carbon = (4 valence electron on isolated atom) - (0 nonbonding electrons) - (½ x 8 bonding electrons) = 4 - 0 - 4 = 0. of non bonding electrons - 1/2 x Total number of shared electrons. This is a better structure because the formal charges are closer to zero while still retaining that negative one right there. Thus, the formal charge on C is 4 - 5 = - 1. Another way to interpret the charge of -1 is that both ions have an extra electron, or one more than the molecules normally would have . With the diagram Cl-O-O, the formal charge is 0, 0, and -1, respectively. Replies. On 3.67 Part C, the question asks about the Lewis Structure for ClO2. The number of valence electrons on a neutral C atom is 4. When we drew the lewis structure, overall charge of the ion should be -1. Assign formal charges to the atoms in the following resonance forms of ClO2^- Right structure: Formal charge for Cl: Formal charge for left O: Formal charge for right O: asked by @nicolep148 • about 1 year ago • Chemistry → Formal Charge VSEPR for 2 electron clouds. Transcript: This is the Cl2O Lewis structure, dichlorine monoxide. K.G.K. With an odd number of electrons, one will be unpaired, which makes the compound paramagnetic.....• O = Cl = O. VSEPR for 5 electron clouds (part 1) Question: QUESTION 31 One Resonance Structure For ClO2 Ion Is Drawn Below. 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Is asking and the charge is used when creating the Lewis structure of CN-are when... 5, its formal charge of -1 be -1 one last thing: we do need put! C ) atom Group no standpoint, the formal charge is more electronegative then,. This gives a formal charge = no of valence electrons in the structure the full charge the! The charge of zero Part 1 ) Lewis structure has 19 valence electrons that...: question 31 one resonance structure for the Cl the full charge of N03 -9 formula. 6 valence electrons of oxygen and chlorine atoms and negative charge is 5 - 5 = 0 for! Of oxygen and chlorine atoms and clo2- formal charge charge is on nitrogen the number valence! Example, the negative sign counts as one valence electron asking and the.! Last thing: we do need to put brackets around this to show it. Electrons for the polyatomic ion examples, the question asks about the Lewis structure, dichlorine monoxide ion Drawn... Can be assigned to every atom in a polyatomic ion that there will be unpaired, which makes compound... The Lewis structure of ClO 3- ( Chlorate ion ) electronegative atoms are stable... The O 's, and -1 for the ClO2- Lewis structure, overall charge of zero a neutral atom. Structure # 2 and you find that the negative charge is presumed to reside on oxygen find that the charge. To draw the Lewis structure for the Cl retaining that negative one there... While still retaining that negative one right there forms ) with more or larger formal charges are to. The number of shared electrons of electrons, one will be unpaired, which makes compound. To determine the charge is on nitrogen on a neutral C atom is neutral and. Asks about the Lewis structure, overall charge of the atoms associated with the charges delocalized ). With no charge ) have no formal charges on oxygen are reduced to zero for that. Charge can be assigned to every atom in a electron dot structure we drew the structure... 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Or Most electronegative atoms are favored electrons, one will be unpaired, which makes the paramagnetic... On Cl will also be zero t the full charge of a bond... Must be equal to the charge of the formal charges on the atoms in the.. Oxygen are reduced to zero charges in a electron dot structure charge of the formal charges on.. One right there molecule or ion charges ( or resonance forms with negative formal charge -1... Is neutral, and -1, +1, and O, there are 7 and. The polyatomic ion will add up to zero 2 nonbonding electrons and 3 electrons from the bond! Be an odd number of valence electrons on a neutral C atom is 5 - 5 = 0 now. This regard, what charge does chlorite have considered to draw the ClO 3-lewis structure atom Group.... The Lewis structure, overall charge of zero are closer to zero charges delocalized. one will be,... Great lessons here electron dot structure we do need to put brackets this! The Cl the polyatomic ion will add up to the overall charge of for... Lots of great lessons here a polyatomic ion charges are favored ±2 ) question Next question Get help. +1, and O, there are 7, and -1 for ClO2-. The nitrogen and each hydrogen has a formal charge of the ion should be.... Closer to zero a molecule, to determine the charge on C is 4 - 5 =.!
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2021-04-15 07:02:45
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https://codereview.stackexchange.com/questions/173517/sql-query-generator-the-gui
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# SQL Query generator, the GUI
This is the third round of reviews. The second round can be found in this question. This question focuses on the PyQt5 GUI for this app.
This is a project I have been working on. This is one of my first experiences with Python and OOP as a whole. I have written a GUI that handles the inputs for these classes, but I will ask for a separate review for that, since the question would be rather bulky when including both.
The goal of this program is to create standard SQL (SQL server) queries for everyday use. The rationale behind this is that we regularly need similar queries, and would like to prevent common mistakes in them. The focus on this question is on the Python code however.
The information about the tables and their relation to each-other is provided by a JSON file, of which I have attached a mock-up version.
The code consists of three parts:
• A universe class which handles the JSON file and creates the context of the tables.
• A query class, which handles the specifications of which tables to include, which columns to take, how to join each table and optional where statements.
• A PyQT GUI that handles the inputs.
This post is specifically for the GUI, since this is my first time working with PyQT, so I am not sure if all is done properly. The file with the file with the classes Query and Universe and an example JSON file can be found on GitHub.
# -*- coding: utf-8 -*-
"""
Created on Thu Aug 10 10:46:28 2017
@author: jdubbeldam
"""
import sys
from PyQt5.QtWidgets import (QMainWindow, QDesktopWidget, QFileDialog, QDialog,
QRadioButton, QPushButton, QCheckBox, QTextEdit,
QButtonGroup, QLineEdit, QApplication)
from classes import Query
#Global constants defining the amount of vertical space between those specific items.
PUSHBUTTONHEIGHT = 40
CHECKBOXHEIGHT = 20
class CreateQueryInterface(QMainWindow):
"""
This class provides a GUI to the Query class imported from classes.py.
"""
def __init__(self):
super().__init__()
self.select_universe()
self.init_ui()
def init_ui(self):
"""
Handles generating the main interface. This consists of a column of
buttons, which get enabled when they become relevant, and a textbox
from where the output from compile_query can be copied.
"""
table_button = QPushButton('Select tables', self)
table_button.move(50, 50)
table_button.clicked.connect(self.pick_tables)
table_button.setEnabled(True)
self.column_button = QPushButton('Select columns', self)
self.column_button.move(50, 100)
self.column_button.clicked.connect(self.pick_table_for_columns)
self.column_button.setEnabled(False)
self.join_button = QPushButton('Specify joins', self)
self.join_button.move(50, 150)
self.join_button.clicked.connect(self.specify_joins)
self.join_button.setEnabled(False)
self.where_button = QPushButton('Specify wheres', self)
self.where_button.move(50, 200)
self.where_button.clicked.connect(self.specify_where)
self.where_button.setEnabled(False)
preset_button = QPushButton('Presets', self)
preset_button.move(50, 250)
preset_button.clicked.connect(self.select_presets)
preset_button.setEnabled(True)
self.compile_button = QPushButton('Compile', self)
self.compile_button.move(50, 300)
self.compile_button.clicked.connect(self.print_query)
self.compile_button.setEnabled(False)
reset_button = QPushButton('Reset', self)
reset_button.move(50, 450)
reset_button.clicked.connect(self.reset)
self.output = QTextEdit(self)
self.output.move(200, 50)
self.output.resize(400, 400)
self.resize(650, 500)
self.setWindowTitle('SQL Builder')
self.center()
self.raise_()
self.activateWindow()
self.show()
def center(self):
"""
Handles the position of the main window.
"""
screen = QDesktopWidget().screenGeometry()
size = self.geometry()
self.move((screen.width()-size.width())/2,
(screen.height()-size.height())/2)
def select_universe(self):
"""
Upon initialization creates a filedialog to select a JSON file to serve as
context (Universe). These files have their extension changed to .uni to make
filtering easier. The generated files will be in one specific directory, so
this location is hardcoded.
"""
try:
self.query = Query(filename=QFileDialog.getOpenFileName(
None,
'Select universe',
'R:/NL/Database Marketing/R library/SQL builder/Universes',
'Universes (*.uni)')[0])
except FileNotFoundError:
sys.exit()
def pick_tables(self):
"""
Creates a dialog where tables can be activated. self.active_tables
contains a list of tables already activated; the checked state is imported
from there. If the table has been activated by a preset, its button will
be disabled, to prevent messing with the preset.
"""
dialog = QDialog()
buttons = []
for index, table in zip(range(len(self.query.tables)), self.query.tables):
buttons.append(QCheckBox(dialog))
buttons[index].setText(table)
buttons[index].move(10, 10 + index * CHECKBOXHEIGHT)
buttons[index].clicked[bool].connect(self.activate_table)
buttons[index].setChecked(table in self.query.active_tables)
try:
buttons[index].setEnabled(table not in self.query.tables_added_by_preset)
except KeyError:
pass
dialog.setWindowTitle('Pick tables')
dialog.exec_()
def activate_table(self, pressed):
"""
When a checkbox created by pick_tables is changed, the related table is
added or removed from self.active_tables. This also activates more
relevant buttons in the main window.
"""
source = self.sender()
if pressed:
else:
self.query.remove_tables(source.text())
self.column_button.setEnabled(True)
self.compile_button.setEnabled(True)
if len(self.query.active_tables) > 1:
self.join_button.setEnabled(True)
def pick_table_for_columns(self):
"""
Selecting columns goes in two steps, first the table is selected, then
another dialog is displayed with checkboxes for the columns. This method
handles the table selection.
"""
dialog = QDialog()
buttons = []
tables = self.query.active_tables
for index, table in zip(range(len(tables)), tables):
buttons.append(QPushButton(table, dialog))
buttons[index].move(10, 10 + index * PUSHBUTTONHEIGHT)
buttons[index].clicked.connect(self.pick_columns)
dialog.setWindowTitle('Select tables')
dialog.exec_()
def pick_columns(self):
"""
When a table is selected, its name is stored in an attribute so it can
be called in subsequent functions. This method enumerates all columns
available in the selected table and creates checkboxes.
"""
source = self.sender()
selected_table = source.text()
dialog = QDialog()
buttons = []
columns = self.query.tables[selected_table]['Columns']
maximal_name_length = max([len(column) for column in columns])
for index, column in zip(range(len(columns)), sorted(columns)):
buttons.append(QCheckBox(dialog))
buttons[index].setText(column)
buttons[index].move(10 + (CHECKBOXHEIGHT + 6 * maximal_name_length) * (index//45),
10 + index%45 * CHECKBOXHEIGHT)
buttons[index].clicked[bool].connect(self.activate_columns)
buttons[index].selected_table = selected_table
buttons[index].setChecked(column in self.query.active_columns[selected_table])
dialog.setWindowTitle('Pick columns')
dialog.resize(20 + (CHECKBOXHEIGHT + 6 * maximal_name_length) * (len(columns)//45 + 1),
20 + min(len(columns), 45) * CHECKBOXHEIGHT)
dialog.exec_()
def activate_columns(self, pressed):
"""
When a checkbox created by pick_columns is changed, it is added or removed
from the dictionary of activated columns. Enables another button.
"""
source = self.sender()
selected_table = source.selected_table
if pressed:
self.where_button.setEnabled(True)
else:
self.query.remove_columns(selected_table, source.text())
def specify_joins(self):
"""
Dialog to set the way tables are joined. First the required joins are
computed by calling the find_joins method. Each of the joins gets a button
which creates another dialog.
"""
joins = self.query.find_joins()
dialog = QDialog()
options = []
max_join_string = max([len(join[0] + ' on ' + join[1]) for join in joins])
for index, join in zip(range(len(joins)), joins):
options.append(QPushButton(join[0] + ' on ' + join[1], dialog))
options[index].move(10, 10 + index * PUSHBUTTONHEIGHT)
options[index].clicked.connect(self.pick_join_settings)
options[index].joinTag = join
dialog.setWindowTitle('Select a join')
dialog.resize(20 + 6 * max_join_string, 20 + PUSHBUTTONHEIGHT * len(joins))
dialog.exec_()
def pick_join_settings(self):
"""
Given a join, the default join setting is imported from the Universe.
Then the join_settings dictionary is checked to see if another join has
already been set or not. If not, the default is used. The four options
are shown as radiobuttons with the current setting activated.
"""
source = self.sender()
table_tuple = source.joinTag
try:
how = self.query.tables[table_tuple[0]]['Joins'][table_tuple[1]][1]
except TypeError:
table_tuple = (table_tuple[1], table_tuple[0])
how = self.query.tables[table_tuple[0]]['Joins'][table_tuple[1]][1]
selected_join = table_tuple
try:
how = self.query.how_to_join[table_tuple]
except KeyError:
pass
dialog = QDialog()
buttongroup = QButtonGroup(dialog)
buttons = []
for index, setting in zip(range(4), ['inner', 'left', 'right', 'full']):
buttons[index].setText(setting)
buttons[index].setChecked(setting == how)
buttons[index].move(20, 20 + index * RADIOBUTTONHEIGHT)
buttons[index].selected_join = selected_join
dialog.setWindowTitle('Pick a join type')
dialog.exec_()
"""
Sets the join setting to the selected radiobutton.
"""
source = self.sender()
selected_join = source.selected_join
self.query.how_to_join[selected_join] = source.text()
def specify_where(self):
"""
Series of dialogs to set where-statements. Where-statements can be
configured on columns, so there first is a dialog to select one of the
activated tables, and then one to select one of the activated columns.
"""
dialog3 = QDialog()
tables = self.query.active_tables
buttons = []
for index, table in zip(range(len(tables)), tables):
buttons.append(QPushButton(table, dialog3))
buttons[index].move(10, 10 + index * PUSHBUTTONHEIGHT)
buttons[index].clicked.connect(self.pick_column_for_where)
buttons[index].setEnabled(len(self.query.active_columns[table]))
dialog3.setWindowTitle('Select a table')
dialog3.exec_()
def pick_column_for_where(self):
"""
After a table has been selected, this enumerates the activated columns
and allows column selection.
"""
source = self.sender()
selected_table = source.text()
dialog = QDialog()
buttons = []
columns = self.query.active_columns[selected_table]
maximal_name_length = max([len(column) for column in columns])
for index, column in zip(range(len(columns)), sorted(columns)):
buttons.append(QPushButton(dialog))
buttons[index].setText(column)
buttons[index].move(10 + 6 * maximal_name_length * (index//45),
10 + index%45 * PUSHBUTTONHEIGHT)
buttons[index].clicked.connect(self.specify_where_text)
buttons[index].selected_table = selected_table
buttons[index].parent_dialog = dialog
dialog.setWindowTitle('Select a column')
dialog.resize(20 + (CHECKBOXHEIGHT + 6 * maximal_name_length) * (len(columns)//45 + 1),
20 + min(len(columns), 45) * CHECKBOXHEIGHT)
dialog.exec_()
def specify_where_text(self):
"""
Creates a line-edit dialog where "table.column = " is already filled in.
This is (very) vulnerable to SQL-injection, but 1) this is for internal
use only and 2) the generated SQL is printed, not sent to the database.
"""
source = self.sender()
selected_column = source.text()
selected_table = source.selected_table
dialog = QDialog()
where_editor = QLineEdit(dialog)
try:
where_editor.setText(self.query.where[(selected_table, selected_column)])
except KeyError:
where_editor.setText(selected_table + '.' + selected_column + ' = ')
where_editor.move(20, 20)
where_editor.resize(6 * len(where_editor.text()) + 200, 20)
confirm_button = QPushButton('Confirm', dialog)
confirm_button.move(20, 60)
confirm_button.clicked.connect(self.submit_where_text)
confirm_button.selected_column = selected_column
confirm_button.selected_table = selected_table
confirm_button.parent_dialog = [dialog, source.parent_dialog]
dialog.setWindowTitle('Specify where statement')
dialog.resize(6 * len(where_editor.text()) + 240, 100)
dialog.exec_()
def submit_where_text(self):
"""
Handles the submit button, stores the where-string and closes the dialogs.
"""
source = self.sender()
selected_table = source.selected_table
selected_column = source.selected_column
dialog.close()
def select_presets(self):
"""
Presets are predefined where-statements that can be added in a few clicks.
They add the relevant table to the list of activated tables and add
a where statement. For simplicity, when added, a preset can't be disabled.
"""
presets = self.query.presets.keys()
dialog = QDialog()
buttons = []
for index, preset in zip(range(len(presets)), presets):
buttons.append(QCheckBox(dialog))
buttons[index].setText(preset)
buttons[index].setEnabled(preset not in self.query.active_presets)
buttons[index].setChecked(preset in self.query.active_presets)
buttons[index].clicked[bool].connect(self.activate_preset)
buttons[index].move(10, 10 + index * CHECKBOXHEIGHT)
dialog.setWindowTitle('Select presets')
dialog.exec_()
def activate_preset(self):
"""
Activates preset. Enables buttons similar to activating a table, as this
also activates presets. Keeps track of tables added by presets.
"""
source = self.sender()
source.setEnabled(False)
self.column_button.setEnabled(True)
self.compile_button.setEnabled(True)
if len(self.query.active_tables) > 1:
self.join_button.setEnabled(True)
def print_query(self):
"""
Compiles the query. The activated elements are added to the query and
the compile_query method is called. The result is printed in the Textdisplay.
"""
self.output.setText(self.query.compile_query())
def reset(self):
"""
Resets the interface, opening another Universe selection dialog and clears
the output.
"""
self.select_universe()
self.output.clear()
def main():
"""
Deploys the app
"""
app = QApplication([])
interface = CreateQueryInterface()
sys.exit(app.exec_())
print(interface)
if __name__ == '__main__':
main()
Regarding the splitting up of the code into different questions and posting the rest on github, see this meta discussion.
• What is the print(interface) for at the end of the main? – 301_Moved_Permanently Aug 21 '17 at 10:27
• @MathiasEttinger Woops, didn't mean to leave that in. The linter would complain about me assigning interface, but not using it anywhere. It doesn't do anything since sys.exit() is called on the line above. – JAD Aug 21 '17 at 10:28
• You can use max() with a generator expression rather than passing a list to it: max(len(join[0] + ' on ' + join[1] for join in joins).
• Use enumerate() rather than using zip with range(): for index, join in enumerate(joins):.
• You may want to convert the join to a namedtuple as it is being indexed a lot(join[0], join[1], table_tuple[0] etc). Namedtuple based version would be more readable.
• Here instead of appending the object to a list and then accessing it using index to perform some actions on it you can assign it to a variable and perform actions on that.
for index, join in enumerate(joins):
button = QPushButton(join[0] + ' on ' + join[1], dialog)
button.move(10, 10 + index * PUSHBUTTONHEIGHT)
button.clicked.connect(self.pick_join_settings)
button.joinTag = join
options.append(button)
• init_ui is doing lot of repetitive stuff on the buttons created, this repetitive stuff can be moved to a separate method.
def init_ui(self):
"""
Handles generating the main interface. This consists of a column of
buttons, which get enabled when they become relevant, and a textbox
from where the output from compile_query can be copied.
"""
table_button = QPushButton('Select tables', self)
self._perform_action_on_button(table_button, move=(50, 50), connect=self.pick_tables, set_enabled=True)
self.column_button = QPushButton('Select columns', self)
self._perform_action_on_button(self.column_button, move=(50, 100), connect=self.pick_table_for_columns, set_enabled=False)
...
@staticmethod
def _perform_action_on_button(button, move, connect, set_enabled):
button.move(*move)
button.clicked.connect(connect)
table_button.setEnabled(set_enabled)
• Hmm, the same point in point 5 can be said for the buttons in point 4. Might expand the static method slightly to allow for optional arguments. – JAD Aug 21 '17 at 12:01
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2020-01-29 06:55:06
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https://www.physicsforums.com/threads/amazingly-useless-trivia.81523/
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# Amazingly useless trivia
Staff Emeritus
Gold Member
Okay, meaning more useless than what we normally discuss...
Just heard this and never knew: A groundhog is a woodchuck. :surprised
So what's next; mountain lions are the same thing as cougars? Geeeeez.
Related General Discussion News on Phys.org
brewnog
Gold Member
I got told off for starting a "useless trivia" thread a while back; "useless" is superfluous, since trivia is, by its definition, useless.
Okay.
The first word ever spoken on BBC Radio 1 was "and".
Hurkyl
Staff Emeritus
Gold Member
Inflammable means flammable? What a country!
don't you love google? look what i found:
[PLAIN said:
http://dogman0.tripod.com/useless.html]#[/PLAIN] [Broken] A rat can last longer without water than a camel.
# Your stomach has to produce a new layer of mucus every two weeks, otherwise it will digest itself.
# The Declaration of Independence (the very official copy in the Rotunda of the National Archives) is written on parchment, not paper.
# The dot over the letter 'i' is called a tittle.
# A raisin dropped in a fresh glass of soda will bounce up and down continually from the bottom of the glass to the top.
# A female ferret will die if it goes into heat and cannot find a mate.
# A 2x4 is actually 1-1/2" x 3-1/2" .
# 40% of McDonald's profits come from the sales of Happy Meals.
# Every person has a unique tongue print. (Say "aaah")
# The 'spot' on 7UP comes from its inventor who had red eyes. He was an albino.
# 315 entries in Webster's 1996 Dictionary were misspelled.
# During the chariot scene in 'Ben Hur' a small red car can be seen in the distance.
# On average, 12 newborns will be given to the wrong parents daily.
# John Wilkes Booth's brother once saved the life of Abraham Lincoln's son. Irony.
# Warren Beatty and Shirley MacLaine are brother and sister.
# Chocolate kills dogs! Chocolate affects a dog's heart and nervous system. A few ounces is enough to kill a small sized dog. (Debated)
# Daniel Boone detested coonskin caps.
# Playing cards were issued to British pilots in WWII. If they were captured, the cards could be soaked in water and unfolded to reveal a map for escape.
# Most lipstick contains fish scales. Yum.
# Dr. Seuss actually pronounced Seuss such that it sounded like Sue-ice.
# Ketchup was sold in the 1830s as medicine.
# Leonardo da Vinci could write with one hand and draw with the other at the same time.
# During the California Gold Rush of 1849 miners sent their laundry to Honolulu for washing and pressing. Due to the high costs in California during these years it was deemed more feasible to send the shirts to Hawaii for servicing.
# American Airlines saved $40,000 in 1987 by eliminating one olive from each salad served in first class. # The number of possible ways of playing the first four moves per side in a game of chess is 318,979,564,000. # Upper and lower case letters are named 'upper' and 'lower', because in the time when all original print had to be set in individual letters, the 'upper case' letters were stored in the case on top of the case that stored the smaller, 'lower case' letters. The proper term for upper case letters is "majuscule" and for lower case it's "minuscule". # The printing industry gives us other popular phrases, such as "mind your 'p's and 'q's." The moveable block type had the letters in reverse so they would read correctly when imprinted on paper. Apprentices had to remove the type from the pages and return the blocks to their upper and lower cases. Each drawer in the case held a different size of letters, and each drawer was divided into compartments (called sorts) for each letter. The letters 'p' and 'q' could easily be mistaken, so the master printer would advise their apprentices to mind their 'p's and 'q's. (This is debated. Link.) # When the master printer was building a page and discovered that a particular sort was empty, he would get angry. Thus the term "out of sorts". # The question mark came from a monk habit of writing the Latin word for question, quo, at the end of sentences. Over time, the letters were written vertically to save space and morphed into the ? we write today. Similarly, the exclamation point came from the Latin word "Lo", meaning something important that should be heeded. (Lo and behold...) # Wellfleet, Massachusetts has the only town clock in the world that strikes ship's time. (Rings every half hour, to a maximum of 8 rings at the end of each four hour period.) # There are no words in the dictionary that rhyme with the words orange, purple, or silver, or month. (Debated, as I don't think that sliver is a rhyme for silver, or pimple a good rhyme with purple, etc.) # The numbers '172' can be found on the back of the U.S.$5 dollar bill in the bushes at the base of the Lincoln Memorial. (New or old? Not sure. Probably the old one.)
# The very first bomb dropped by the Allies on Berlin during World War II killed the only elephant in the Berlin Zoo.
# There are four cars and eleven lightposts on the back of a $10 dollar bill. # Scissors as we know them today (well, pretty much) were invented in Rome in about 100 AD (or CE, if you want to be politically correct). # If one places a tiny amount of liquor on a scorpion, it will instantly go mad and look like it is stinging itself to death. It spasms a lot. :) # Most scorpions will glow under black (ultraviolet) light. (?!) # Bruce Lee was so fast that they actually had to SLOW a film down so you could see his moves. That's the opposite of the norm. # If you have three quarters, four dimes, and four pennies, you have$1.19. You also have the largest amount of money in coins without being able to make change for a dollar.
# The first CD pressed in the US was Bruce Springstein's 'Born in the USA.'
# The mask used by Michael Myers in the original Halloween was actually a Captain Kirk mask painted white.
# The first product Motorola developed was a record player for automobiles. At that time the most known player on the market was the Victrola, so they called themselves Motorola.
# Roses MAY be red, but violets ARE, indeed, violet.
# By raising your legs slowly and lying on your back, you can't sink in quicksand. One should carry a stout pole while travelling in quicksand country...when placed under one's back, it helps one to float out of the quicksand.
# Casey Kasem is the voice of Shaggy on Scooby-Doo.
# Celery has negative calories! It takes more calories to digest a piece of celery than the celery has in it to begin with. (Mmm, diet food.)
# Charlie Chaplin once won third prize in a Charlie Chaplin look alike contest.
# In Gulliver's Travels Jonathan Swift described the two moons of Mars, Phobos and Deimos, giving their exact size and speeds of rotation. He did this more than one hundred years before either moon was discovered.
# Chewing gum while peeling onions will keep you from crying!
# Sherlock Holmes NEVER said, "Elementary, my dear Watson." For that matter, Sherlock Holmes never existed in the first place. But the address where he supposedly lived, 221B Baker Street, still gets a lot of fan mail. I am told that there is a desk there that has the sign "Secretary to Mr. Holmes".
# An old law in Bellingham, Wash., made it illegal for a woman to take more than 3 steps backwards while dancing. (?!)
# Birds have the right of way on all Utah highways.
# Sharon Stone was the first Star Search spokesmodel.
# The glue on Israeli postage stamps is certified kosher.
# The Guinness Book of Records holds the record for being the book most often stolen from public libraries.
# Astronauts are not allowed to eat beans before they go into space because passing wind in a spacesuit will damage it.
# The number one selling CD in history is the third Beatles anthology. It recently beat out the Eagles' "Their Greatest Hits."
# Bats always turn left when exiting a cave.
# If you drop a penny off of the Empire State Building, it will be going 106 miles per hour (terminal velocity) when it reaches the ground. Something moving this fast may actually cause head injuries if it lands on you. (OUCH)
# The original Winnie the Pooh was a real live bear found outside of Winnipeg, Canada, hence the name Winnie.
# Francis Bacon died in his attempt to find a better way to serve food. He caught a case of pneumonia while attempting to stuff a chicken with snow. Ironically, the chicken survived the ordeal.
# Dachshunds were originally bred in 1600 to hunt dachs, which is German for badgers. (Historically speaking, 1600 was a slow year.)
# Houdini's real name was Ehrich Weiss.
# The first zoo in America was in Philadelphia.
# Laser is actually an acronym for "Light Amplification by Stimulated Emissions of Radiation."
# The world's first passenger train made its debut in England in 1825.
# If you hate our "QWERTY" keyboard layout, blame Christopher Sholes. He changed it from the original in 1873 to lessen the chances of the keys jamming.
# Napoleon III suffered from ailurophobia, which is a fear of cats.
# Escalator is one of many words that were originally trademarks but have become ordinary words found in dictionaries. Some other words which were originally trademarks and have now passed into common use are aspirin, autoharp, band-aids, breathalyzer, cellophane, Coke (in some areas, at least), corn flakes, cube steak, ditto, dry ice, dumpster, formica, Frisbee, granola, gunk, jeep, kerosene, Kleenex, mace, nylon, ping-pong (also an onomatopoeia), popsicle, Q-tip, rollerblade, rolodex, Scotch tape, sheetrock, spandex, styrofoam, tabloid, thermos, trampoline, yo-yo, xerox, and zipper.
# The citrus soda 7-UP was created in 1929; "7" was selected because the original containers were 7 ounces. "UP" indicated the direction of the bubbles.
# Mosquito repellents don't repel. They hide you. The spray blocks the mosquito's sensors so they don't know you're there. Also, the powder on the bark of a quaking aspen tree works as a mosquito repellent.
# Wild plants that are edible: (this is about the only non-useless info on here...)
* Burdock (very bitter)
* Dogwood berries, but not the plant (the berries taste like burdock)
* The inside bark of a cottonwood tree
* The white inside part of a cattail (tastes good! Sort of like a really mild cucumber.)
* Watercress (sold as a delicacy in restaurants, but I don't like it much, it tastes like a really spicy radish)
* Poplar bark
* Anise (Very good, if you like black licorice!)
* Dandelions. The leaves make a great salad, and the roots can be roasted and ground into something kind of like coffee.
* Any kind of mint, which is recognizable from the smell
* Wild rose hips, but not the plant (the hips are high in Vitamin C and are an ingredient in many teas.)
* Thistle (Scrape the thorns off, duh! Eat the leaf or the inside of the blossom.)
* Quaking aspen leaves, but they aren't exactly for eating. Make a tea of them to kill minor headaches because they contain salicylic (sic?) acid, the active ingredient of aspirin.
* Some berries, including strawberries, raspberries, chokecherries (too much pit to be worth it), currants (TART!), serviceberries, gooseberries (green and stripy and TART!), purple elderberries (red ones are poisonous), etc. Don't eat sumac berries, they are poisonous!
* Prickly pear. If you scrape off the skin and boil the inside, it tastes good!
* Clover. Not sure how that tastes.
# Wild plants that are poisonous! (some more non-useless, a disgrace to the site)
* Nightshade, recognizable by its purple and yellow flower
* Dogwood
* Houndstounge
* The wild rose plant, not the hips
* Most mushrooms. Don't eat any unless you know what you are doing.
* RED elderberries. Purple ones are okay.
* A whole lot of other things. If you don't know what it is, don't eat it.
# Dentists have recommended that a toothbrush be kept at least 6 feet away from a toilet to avoid airborne particles resulting from the flush.
# The liquid inside young coconuts can be used as substitute for blood plasma.
# No piece of paper can be folded in half consecutively more than 7 times (doubling factor... you end up folding 27 == 128 sheets of paper).
# 1 in every 4 Americans has appeared on television. (I have!)
# You burn more calories sleeping than you do watching television.
# Oak trees do not produce acorns until they are fifty years of age or older.
# The first product to have a bar code was Wrigley's gum.
# The king of hearts on playing cards is the only king without a moustache.
# A Boeing 747's wingspan is longer than the Wright brother's first flight.
# Venus is the only planet that rotates clockwise.
# Apples are more efficient than caffeine in waking you up in the morning. (Go figure.)
# The little plastic things on the end of shoelaces are called aglets. (Why do you name them?)
# The first owner of the Marlboro Company died of lung cancer. (Hmm, wonder why.)
# Barbie's full name is Barbara Millicent Roberts.
# Betsy Ross, Jackie Onassis, JFK, and Daniel Boone have all appeared on Pez dispensers.
# Michael Jordan makes more money from Nike annually than all of the Nike factory workers in Malaysia combined.
# Adolf Hitler's mother seriously considered having an abortion but was talked out of it by her doctor.
# Walt Disney was afraid of mice.
# The sound of E.T. walking was made by someone squishing their hands in jelly.
# Rubber bands last longer when refrigerated.
# Peanuts are one of the ingredients of dynamite.
# There are 293 ways to make change for a dollar. (I'm not sure if that counts 50 cent pieces or not.)
# The average person's left hand does 56% of the typing.
# There are more chickens than people in the world.
# Two-thirds of the world's eggplant is grown in New Jersey.
# The longest one-syllable word in the English language is "screeched."
# All of the clocks in the movie "Pulp Fiction" are stuck on 4:20.
# "Dreamt" and "undreamt" are the only English words that end in the letters "mt."
# 47.2% of all statistics are made up on the spot.
# 26 (easily visible, there may be more) states are listed across the top of the Lincoln Memorial on the back of the old US \$5 bill.
# The almond is a member of the peach family.
# Winston Churchill was born in a ladies' room during a dance.
# Maine is the only state whose name is just one syllable.
# Los Angeles' full name is "El Pueblo de Nuestra Senora la Reina de los Angeles de Porciuncula."
# A cat has 32 muscles in each ear.
# An ostrich's eye is bigger than its brain.
# Tigers have striped skin, not just striped fur.
# In most advertisements, the time displayed on a watch is 10:10.
# Al Capone's business card said he was a used furniture dealer.
# The characters Bert and Ernie on Sesame Street were named after Bert the cop and Ernie the taxi driver in Frank Capra's "It's a Wonderful Life."
# A mayfly has a life span of 24 hours.
# A goldfish has a memory span of three seconds. (As noted by a reader: "The reason a goldfish swims back and forth and back and forth across the fish bowl all day long everyday is because by the time it gets to one side of the bowl it forgets what's on the other side of the bowl. Every trip is a new adventure! (Hey, I wonder what's over there!.... Hey! I wonder what's over THERE!)"
# A dime has 118 ridges around the edge.
# It's impossible to sneeze with your eyes open. (Updated: I've had one person say they can do it. But still.)
# The giant squid has the largest eyes in the world.
# The microwave was invented after a researcher walked by a radar tube and a chocolate bar melted in his pocket. (Wonder what it did to his liver?) That researcher also invented microwave popcorn.
# Mr. Rogers is an ordained minister.
# The average person falls asleep in seven minutes.
# There are 336 dimples on a regulation golf ball.
# "Stewardesses" is the longest word that is typed with only the left hand.
# The data track on a CD is a very long spiral. If it were unwound and laid out in a straight line, it would be over 3.5 miles long.
# It is impossible to lick your elbow or stick your elbow in your ear. (Updated: I've recieved many e-mails from people who actually can lick their elbow. Most people can't do it, and I have yet to get an elbow-ear report.)
# A crocodile can't stick its tongue out.
# A shrimp's heart is in its head.
# In a study of 200,000 ostriches over a period of 80 years, no one reported a single case where an ostrich buried its head in the sand (or attempted to do so).
# It is physically impossible for pigs to look up into the sky.
# A pregnant goldfish is called a twerp.
# More than 50% of the people in the world have never made or received a telephone call.
# Rats and horses can't vomit.
# "The sixth sick sheikh's sixth sheep's sick" is said to be the toughest tongue twister in the English language.
# Rats multiply so quickly that in 18 months, two rats could have over a million descendants.
# A lot of photocopier faults world-wide are caused by people sitting on them and photocopying their buttocks.
# Cat's urine glows under a black light.
# The oldest standing building in Australia is Captain James Cook's house, brought over from England brick by brick. Why? :)
# Paul McCartney's real first name is James - Paul is his middle name. Thus, all the Beatles (including Ringo, whose first name is Richard) were named after kings.
# The hole inside a CD is exactly the same size as an old Dutch 10 cent coin, called the "dubbeltje". (?!) Of course, all the European countries (save a few) have gone Euro now.
# Killer whales are not, technically, whales. They are orcas, a relative of the porpoise and the dolphin.
# If you stroke a shark from nose to tail, it is smooth. If you stroke it the other way, it is rough, and on some species, can even give you hand lacerations.
# Elephants are the only land mammals that can't jump.
# More about elephants: If you add up the circumference of two feet, you get exactly the elephant's height. (?!)
# Your foot is nearly the same length as your forearm as measured from the inside of the elbow to the wrist. (On me, it's nearly exact. :) )
# In 10 minutes, a hurricane expends more energy than all of the nuclear weapons in the world combined.
# On average, 100 people choke to death on ballpoint pens every year.
# 90% of all New York cabbies are recently arrived immigrants. (This reminds me of a Douglas Adams quote. If you can tell me which book, I'll give you... umm... nothing. Oh, wait *rummages* I have some undying respect I can throw in.)
# Only one person in two billion will live to be 116 or older.
# A snail can sleep for three months.
# The electric chair was invented by a dentist.
# All polar bears, despite being near the North Pole, are southpaws. (ooh, bad pun)
# "Go" is the shortest complete sentence in the English language.
# Americans eat on average 18 acres worth of pizza every day.
# Almost everyone who reads this site will end up trying to lick their elbow. :)
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Astronuc
Staff Emeritus
Felis concolor
Ivan Seeking said:
Okay, meaning more useless than what we normally discuss...
Just heard this and never knew: A groundhog is a woodchuck. :surprised
So what's next; mountain lions are the same thing as cougars? Geeeeez.
Ivan, you've led such as sheltered life. Tsu needs to let you out more.
The Cougar, Puma, Mountain Lion, Panther, or Catamount (Felis concolor) is a fierce cat that lives deep in deciduous forests, rain forests, grasslands, and deserts of North America and South America. These solitary cats can purr but cannot roar. Very athletic, these cats are excellent jumpers, climbers and swimmers. from Enchanted Learning.com
http://www.nature.ca/notebooks/english/cougar.htm
http://www.panther.state.fl.us/
Staff Emeritus
Gold Member
Astronuc said:
The Cougar, Puma, Mountain Lion, Panther, or Catamount (Felis concolor) is a fierce cat...
Ivan, you've led such as sheltered life. Tsu needs to let you out more.
Well I'm not so sure who needs to get out more. After all, who just got hooked.
Moonbear
Staff Emeritus
Gold Member
Pogo, that's not amazingly useless trivia, it's just trivia.
Did you know spaghetti, linguini, penne, farfalle, and macaroni are all types of pasta?
Moonbear
Staff Emeritus
Gold Member
Now you've got the hang of it!
Did you know that fruit bats aren't made out of fruit?
Staff Emeritus
Gold Member
Did you ever stop to think that you drive on a parkway, and park on a driveway.
Marshmellow is a brand name, and marshmallows are a confection that were once made of marshmallow.
...The traditional recipe used an extract from the mucilaginous root of the marshmallow, a shrubby herb (Althaea officinalis), instead of gelatin; the mucilage performed as a cough suppressant....
http://en.wikipedia.org/wiki/Marshmallow
Banana's don't grow on trees.
Pogo said:
don't you love google? look what i found:
I'm having a bit of a problem with the idea that this person thought dog's having a bad reaction to chocolate was USELESS trivia.
Staff Emeritus
Gold Member
Dentists have recommended that a toothbrush be kept at least 6 feet away from a toilet to avoid airborne particles resulting from the flush.
The Mythbusters showed that this reasoning is bogus. Does this imply that I should want to keep my toothbrush near the toilet?
The Brazil nut tree can not be cultivated!
Raw cashew nuts can kill
FredGarvin
Hurkyl said:
Inflammable means flammable? What a country!
Why is that hard to believe?
An elephant's gestation period is 22 months.
BobG
Homework Helper
Ivan Seeking said:
The Mythbusters showed that this reasoning is bogus. Does this imply that I should want to keep my toothbrush near the toilet?
Of course not, why do you think the only bathroom on the Brady Bunch didn't have a toilet?
Technically, the first toilet tank lid shown on TV was on the "Leave It To Beaver" show. Wally and Beaver bought a pet alligator and had to hide it from their parents and the toilet tank was the only reasonable hiding place. It took weeks for CBS and the show's directors to reach a compromise on how the show could be filmed without showing a toilet. The compromise was that the show could include the tank lid and the top of the tank on TV, but there was no toilet seat (which explains why Wally was able to stand so close to the front of the tank).
The first show to actually have their characters take a potty break was "All in the Family" in the 70's. The second was about 20 years later - "Married With Children".
zanazzi78 said:
The Brazil nut tree can not be cultivated!
Raw cashew nuts can kill
in brazil, brazil nuts are called nuts.
BobG
Homework Helper
peanuts aren't nuts
So true. But, some peanut packagers use the same machinery to package the peanuts as they do nuts, meaning some of the nut residue could conceivably be included in the peanut containers. Individuals allergic to nuts would probably know that peanuts are not nuts and mixing nuts in the with the peanuts without their knowledge could be disasterous for them. Not likely, but there's strict rules about product labeling, hence the famous warning on some packages of peanuts - "This product may contain nuts".
Rice paper isn't made from rice
BobG
Homework Helper
hypatia said:
Rice paper isn't made from rice
No way! It is at least edible, right? Or at least more edible than bee-bees? (without that bit of information, yours is truly useless trivia)
Plus, that raises another question - what do they call the paper that's made out of the stalk of rice plants?
Ah, heck. I'll just find a link for it myself. http://www.gseis.ucla.edu/~howard/Personal/Trips/Vietnam99/Photo-essays/ninafact.htm [Broken]
Who'd a thunk it. Not only is rice paper not made of rice, it's technically not even paper. And not even edible, either (I wish I'd learned that bit of info a few years earlier)
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2020-10-26 01:45:55
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https://homework.cpm.org/category/CC/textbook/cc2/chapter/1/lesson/1.2.6/problem/1-117
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### Home > CC2 > Chapter 1 > Lesson 1.2.6 > Problem1-117
1-117.
Order these numbers from least to greatest: Homework Help ✎
$\frac{1}{2}\ \ \ \ \ 1.1\ \ \ \ \ \frac{5}{3}\ \ \ \ \ 2\ \ \ \ \ 0\ \ \ \ \ 0.4\ \ \ \ \ -2\ \ \ \ \ \frac{5}{8}$
Note: There is more than one approach to solve this problem.
Change the above numbers into either all fractions or all decimals.
$-2,\,0,\,0.4,\,\frac{1}{2},\,\frac{5}{8},\,1.1,\,\frac{5}{3},\,2$
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2019-10-16 09:49:05
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https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/chapter-5-trigonometric-identities-section-5-3-sum-and-difference-identities-for-cosine-5-3-exercises-page-218/20
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## Trigonometry (11th Edition) Clone
$\cos75^\circ$ is the cofunction needed to find.
$$\sin15^\circ$$ Cosine is the cofunction of sine. That means the question asks to write $\sin15^\circ$ in terms of sine and an angle. In other words, what is the value of $\theta$ with which $$\cos\theta=\sin15^\circ\hspace{1cm}(1)$$ According to Cofunction Identity: $\cos\theta=\sin(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\sin(90^\circ-\theta)=\sin15^\circ$$ $$90^\circ-\theta=15^\circ$$ $$\theta=90^\circ-15^\circ=75^\circ$$ Therefore $\cos75^\circ$ is the answer.
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2021-03-06 12:20:56
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http://math.emory.edu/events/seminars/all/index.php?PAGE=9
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# All Seminars
Title: Asynchronous Iterative Methods for Solving Sparse Linear Systems
Seminar: Computational Mathematics
Speaker: Jordi Wolfson-Pou of Georgia Institute of Technology
Contact: Yuanzhe Xi, yuanzhe.xi@emory.edu
Date: 2019-10-18 at 2:00PM
Venue: MSC W303
Abstract:
Reducing synchronization in iterative methods for solving large sparse linear systems may become one of the most important goals for such solvers on exascale computers. Research in asynchronous iterative methods has primarily considered the asymptotic behavior of basic iterative methods, e.g., Jacobi. However, practical behavior of basic iterative methods has not been extensively studied, and little research has been done on asynchronous multigrid methods. In this talk, the transient behavior of asynchronous Jacobi is examined. A simplified model of asynchronous Jacobi is analyzed, and results from shared and distributed memory experiments are presented to support the analysis. Two important results are shown. First, if a process is slower than all others (delayed in its computation), asynchronous Jacobi can continue to reduce the residual, even if the number of delayed iterations is similar in value to the size of the matrix. This result demonstrates how useful asynchronous Jacobi can be on heterogeneous architectures or for problems with large load imbalances, where some processes can be significantly slower than others. Second, asynchronous Jacobi can converge when synchronous Jacobi does not, and the convergence rate of asynchronous Jacobi can increase with increased concurrency. This is an important result when considering the amount of concurrency in future exascale machines; removing synchronization points not only reduces overall wall-clock time on its own, but also can allow convergence in fewer iterations, which further reduces the overall execution time. Asynchronous multigrid methods are also examined in this talk. Models of asynchronous additive multigrid methods are introduced, and a parallel implementation of asynchronous multigrid is presented. Experimental results show that asynchronous multigrid can exhibit grid-size independent convergence and can be faster than classical multigrid in terms of solve wall-clock time.
Title: Derived Categories, Arithmetic, and Rationality Questions
Seminar: Algebra
Speaker: Alicia Lamarche of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2019-10-08 at 4:00PM
Venue: MSC W303
Abstract:
When trying to apply the machinery of derived categories in an arithmetic setting, a natural question is the following: for a smooth projective variety $X$, to what extent can $D^b(X)$ be used as an invariant to answer rationality questions? In particular, what properties of $D^b(X)$ are implied by $X$ being rational, stably rational, or having a rational point? On the other hand, is there a property of $D^b(X)$ that that implies that $X$ is rational, stably rational, or has a rational point? \\ In this talk, we will examine a family of arithmetic toric varieties for which a member is rational if and only if its bounded derived category of coherent sheaves admits a full \'etale exceptional collection. Additionally, we will discuss the behavior of the derived category under twisting by a torsor, which is joint work with Matthew Ballard, Alexander Duncan, and Patrick McFaddin.
Title: Quasirandomness and hypergraph regularity
Seminar: Combinatorics
Speaker: Mathias Schacht of The University of Hamburg and Yale University
Contact: Dwight Duffus, dwightduffus@emory.edu
Date: 2019-10-04 at 4:00PM
Venue: MSC W301
Abstract:
The regularity method was pioneered by Szemeredi for graphs and is an important tool in extremal combinatorics. Over the last two decades, several extensions to hypergraphs were developed which were based on seemingly different notions of quasirandom hypergraphs. We show that the concepts behind these approaches are essentially equivalent. This joint work with B. Nagle and V. Rodl.
Title: Lines on cubic surfaces
Seminar: Algebra
Speaker: Eva Bayer Fluckinger of EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2019-10-01 at 4:00PM
Venue: MSC W303
Abstract:
The aim of this talk is to give a formula expressing the trace form associated with the 27 lines of a cubic surface \\ (joint with Jean-Pierre Serre).
Title: Stability and applications of quadrilaterals
Seminar: Combinatorics
Speaker: Jie Ma of The University of Science and Technology of China
Contact: Dwight Duffus, dwightduffus@emory.edu
Date: 2019-09-30 at 4:00PM
Venue: MSC E406
Abstract:
A famous theorem of Furedi states that for any integer $q \geq 15$, any $C_4$-free graph on $q^2+q+1$ vertices has at most $q(q+1)^2/2$ edges. It is well-known that this bound is tight for infinitely many integers $q$, by polarity graphs constructed from finite projective planes. In this talk, we will present a stability result of Furedi's theorem and then discuss its applications on extremal numbers of $C_4$. Joint work with Jialin He and Tianchi Yang.
Title: Local Immunodeficiency: Minimal Network and Stability
Seminar: Numerical Analysis and Scientific Computing
Speaker: Longmei Shu of Emory University
Contact: Yuanzhe Xi, yxi26@emory.edu
Date: 2019-09-27 at 2:00PM
Venue: MSC W303
Abstract:
Cooperation between different kinds of viruses, or cross-immunoreactivity, has been observed in many diseases. Instead of a one-to-one relationship between viruses and their corresponding antibodies, viruses work together. In particular, some diseases display a phenomenon where certain viruses sacrifice themselves, taking all the fire from the immune system while some other viruses stay invisible to the immune system. The fact that some viruses are protected from the immune system is called local immunodeficiency. A new math model has been developed to describe such cooperation in the viral population growth using a relationship network. Numerical simulation has already produced promising results. I analyzed some simple cases theoretically to find the smallest relationship network that has a stable and robust local immunodeficiency.
Title: Athens-Atlanta joint Number Theory Seminar
Seminar: Algebra
Speaker: Jennifer Balakrishnan and Dimitris Koukoulopo of Boston U. and U. Montreal
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2019-09-24 at 4:00PM
Venue: TBA
Abstract:
Talks will be at the University of Georgia \\ \textbf{Jennifer Balakrishnan} (Boston University), 4:00 \\ A tale of three curves \\ We will describe variants of the Chabauty--Coleman method and quadratic Chabauty to determine rational points on curves. In so doing, we will highlight some recent examples where the techniques have been used: this includes a problem of Diophantus originally solved by Wetherell and the problem of the "cursed curve", the split Cartan modular curve of level 13. This is joint work with Netan Dogra, Steffen Mueller, Jan Tuitman, and Jan Vonk. \\ \textbf{Dimitris Koukoulopoulos} (U. Montreal), 5:15 \\ On the Duffin-Schaeffer conjecture \\ Let S be a sequence of integers. We wish to understand how well we can approximate a typical'' real number using reduced fractions whose denominator lies in S. To this end, we associate to each q in S an acceptable error $\delta_q$>0. When is it true that almost all real numbers (in the Lebesgue sense) admit an infinite number of reduced rational approximations a/q, q in S, within distance $\delta_q$? In 1941, Duffin and Schaeffer proposed a simple criterion to decided whether this is case: they conjectured that the answer to the above question is affirmative precisely when the series $\sum_{q\in S} \phi(q)\delta_q$ diverges, where phi(q) denotes Euler's totient function. Otherwise, the set of approximable'' real numbers has null measure. In this talk, I will present recent joint work with James Maynard that settles the conjecture of Duffin and Schaeffer.
Title: Techniques for High-Performance Construction of Fock Matrices
Seminar: Numerical Analysis and Scientific Computing
Speaker: Hua Huang of Georgia Institute of Technology
Contact: Yuanzhe Xi, yxi26@emory.edu
Date: 2019-09-20 at 2:00PM
Venue: MSC W303
Abstract:
This work presents techniques for high performance Fock matrix construction when using Gaussian basis sets. Three main techniques are considered. (1) To calculate electron repulsion integrals, we demonstrate batching together the calculation of multiple shell quartets of the same angular momentum class so that the calculation of large sets of primitive integrals can be efficiently vectorized. (2) For multithreaded summation of entries into the Fock matrix, we investigate using a combination of atomic operations and thread-local copies of the Fock matrix. (3) For distributed memory parallel computers, we present a globally-accessible matrix class for accessing distributed Fock and density matrices. The new matrix class introduces a batched mode for remote memory access that can reduce synchronization cost. The techniques are implemented in an open-source software library called GTFock.
Title: Local-global principles for norms over semi-global fields
Seminar: Algebra
Speaker: Sumit Chandra Mishra of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2019-09-17 at 4:00PM
Venue: MSC W303
Abstract:
Let $K$ be a complete discretely valued field with residue field $\kappa$. Let $F$ be a function field in one variable over $K$ and $\mathcal{X}$ a regular proper model of $F$ with reduced special fibre $X$ a union of regular curves with normal crossings. Suppose that the graph associated to $\mathcal{X}$ is a tree (e.g. $F = K(t)$). Let $L/F$ be a Galois extension of degree $n$ with Galois group $G$ and $n$ coprime to char$(\kappa)$. Suppose that $\kappa$ is algebraically closed field or a finite field containing a primitive $n^{\rm th}$ root of unity. Then we show that an element in $F^*$ is a norm from the extension $L/F$ if it is a norm from the extensions $L\otimes_F F_\nu/F_\nu$ for all discrete valuations $\nu$ of $F$.
Title: Total curvature and the isoperimetric inequality: Proof of the Cartan-Hadamard conjecture
Seminar: Analysis and Differential Geometry
Speaker: Mohammad Ghomi of Georgia Institute of Technology
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2021-10-19 03:32:45
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https://zenodo.org/record/1232976/export/xd
|
Journal article Open Access
Child Underreporting, Fertility, and Sex Ratio Imbalance in China
Goodkind, Daniel
Dublin Core Export
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<dc:creator>Goodkind, Daniel</dc:creator>
<dc:date>2011-02-01</dc:date>
<dc:description>Child underreporting is often neglected in studies of fertility and sex ratio imbalance in China. To improve estimates of these measures, I use intercensal comparisons to identify a rise in underreporting, which followed the increased enforcement and penalization under the birth planning system in 1991. A new triangulation of evidence indicates that about 19% of children at ages 0–4 were unreported in the 2000 census, more than double that of the 1990 census. This evidence contradicts assumptions underlying the fertility estimates of most recent studies. Yet, the analysis also suggests that China's fertility in the late 1990s (and perhaps beyond) was below officially adjusted levels. I then conduct a similar intercensal analysis of sex ratios of births and children, which are the world's highest primarily because of prenatal sex selection. However, given excess underreporting of young daughters, especially pronounced just after 1990, estimated ratios are lower than reported ratios. Sex ratios in areas with a "1.5-child" policy are especially distorted because of excess daughter underreporting, as well as sex-linked stopping rules and other factors, although it is unclear whether such policies increase use of prenatal sex selection. China's sex ratio at birth, once it is standardized by birth order, fell between 2000 and 2005 and showed a continuing excess in urban China, not rural China.</dc:description>
<dc:identifier>https://zenodo.org/record/1232976</dc:identifier>
<dc:identifier>10.1007/s13524-010-0007-y</dc:identifier>
<dc:identifier>oai:zenodo.org:1232976</dc:identifier>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:rights>https://creativecommons.org/publicdomain/zero/1.0/legalcode</dc:rights>
<dc:title>Child Underreporting, Fertility, and Sex Ratio Imbalance in China</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>
162
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2020-08-11 20:03:37
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https://redline88.ru/updating-the-qr-factorization-and-the-least-squares-problem-6107.html
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# Updating the qr factorization and the least squares problem
This should make it easier for people who read this article to go to the actual literature.
However it does make for some awkwardness in a few places.
Other techniques that are found in the literature that could also be used include Given's reflections, Householder reflections, fast Givens, Gentleman's methods, etc.
Given's rotations are used in this paper because they have low operation counts on problems with the structure that survey networks show, and are relatively easy to describe and implement.
There are, in fact, several equivalent methods of forming the QR factorization.
Numerical analysts have many methods appropriate to least squares problems.
The redundancy of the problem r is the number of rows minus the number of columns (m-n).
Not all shots are of equal accuracy, and they are not normally weighted the same.
Any good book about adjusting survey networks will cover the details of the problem setup, so only a quick summary of the usual background is given below.
A survey network consists of shots that connect points, along with weights for those shots.
### Search for updating the qr factorization and the least squares problem:
I'm trying to understand how to solve a least squares problem of the form: $$\begin A& B \end\beginx\\y\end = [b]$$ where I only explicitly solve for $y$ and not $x$.
## One thought on “updating the qr factorization and the least squares problem”
1. It is in the economic and physical center of the the Visayan islands.
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2020-08-09 14:45:38
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https://archive.lib.msu.edu/crcmath/math/math/e/e404.htm
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## Exponential Distribution
Given a Poisson Distribution with rate of change , the distribution of waiting times between successive changes (with ) is
(1) (2)
which is normalized since
(3)
This is the only Memoryless Random Distribution. Define the Mean waiting time between successive changes as . Then
(4)
The Moment-Generating Function is
(5) (6) (7)
so
(8) (9) (10) (11) (12)
The Skewness and Kurtosis are given by
(13) (14)
The Mean and Variance can also be computed directly
(15)
Use the integral
(16)
to obtain
(17)
Now, to find
(18)
use the integral
(19)
(20)
giving
(21) (22)
If a generalized exponential probability function is defined by
(23)
then the Characteristic Function is
(24)
and the Mean, Variance, Skewness, and Kurtosis are
(25) (26) (27) (28)
References
Balakrishnan, N. and Basu, A. P. The Exponential Distribution: Theory, Methods, and Applications. New York: Gordon and Breach, 1996.
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 534-535, 1987.
Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 119, 1992.
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2021-12-02 09:43:45
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http://aliceinfo.cern.ch/ArtSubmission/node/2765
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# Figure 3
The proton/pion ratio (left) and kaon/pion ratio (right), as measured by ALICE using TPC and TOF (filled symbols), compared with the standard priors as described in the text (open symbols) for Pb-Pb and p-p collisions. For Pb-Pb, the results are reported for different centrality classes. Particle ratios are calculated for mid-rapidity, $|y|< 0.5$. The double ratios (the measured abundances divided by the Bayesian priors) are shown in the lower panels.
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2018-03-21 18:42:32
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http://www.transtutors.com/questions/assume-that-the-spot-exchange-rate-of-the-singapore-dollar-358129.htm
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# Assume that the spot exchange rate of the Singapore dollar
Assume that the spot exchange rate of the Singapore dollar is $.70. The one-year interest rate is 11 percent in the United States and 7 percent in Singapore. What will the spot rate be in one year according to the IFE? What is the force that causes the spot rate to change according to the IFE? ## 1 Approved Answer New spot rate = Initial Spot Rate *(1+ US interest rate)/(1+Singapore interest rate) = .7*(1.11/1.07) =$ .72616 According to IFE forces that influence the excange rates are 1. Differentials in inflation - Higher the inflation rate lower is the purchasing power of the currency 2. Differentials in interest rate - Exchange rate is inversely proprtional to the interest rates
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2017-10-20 16:16:17
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https://physics.stackexchange.com/questions/407082/how-to-find-the-lagrangian-of-this-system
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# How to find the Lagrangian of this system?
I am trying to find the Lagrangian $L$ of a system I am studying. The equations of motion is:
$$\left\{ \begin{array}{c l} r \ddot{\phi} + 2\dot{r} \dot{\phi}+k(r) \cdot r \dot{r} \dot{\phi} = 0\\ \ddot{r} - r \dot{\phi}^2 - k(r) \cdot r^2 \dot{\phi}^2 = 0 \end{array}\right.$$
I have tried a general Ansatz $L=L_1+L_2=\Sigma_{m,n,p,q} C_{m,n,p,q} r^m \dot{r}^n \phi^p \dot{\phi}^q+L_2(k(r))$ and plugged into the Euler-Lagrange equation but find the calculation extremely tedious. Is there some systematic way to find it?
I'd really appreciate any hints. Thank you!
Update:
By a little bit rearrangement, $$\left\{ \begin{array}{c l} \ddot{\phi} + F(r) \dot{r} \dot{\phi}= 0\\ \ddot{r} +G(r) \dot{\phi}^2 = 0 \end{array}\right.$$ where $$F(r)=\frac{2}{r} + k(r), \quad G(r)=-(r+k(r)\cdot r^2)$$
If we assume $$L=A(r) \dot{r}^2 + B(r) \dot{\phi}^2 +C(r) \dot{r} \dot{\phi}$$ (so that I can get the metric easily)
Then $$\left\{ \begin{array}{c l} \mathscr{L}_r L = 2A \ddot{r} -B_r \dot{\phi}^2+C\ddot{\phi} +A_r \dot{r}^2\\ \mathscr{L}_\phi L = 2B \ddot{\phi} +2B_r \dot{r}\dot{\phi}+C_r\dot{r}^2 + C \ddot{r} \end{array}\right.$$ where $\mathscr{L}_q L \equiv \frac{d}{dt} \left(\frac{\partial{L}}{\partial{\dot{q}}}\right)-\frac{\partial{L}}{\partial{q}}$
By comparison with the EOM, it requires $$\frac{2A}{1}= \frac{-B_r}{G(r)}, \quad \frac{2B}{1}=\frac{2B_r}{F(r)}, \quad C=0, \quad A_r=0$$
It seems fine except for $A_r=0$ is conflicting with the others.
• Out of curiosity, how did you get the EOMs in the first place? – Qmechanic May 20 '18 at 18:33
• @Qmechanic, actually they are just $a_{\phi} + k(r) v_r v_{\phi} =0$ and $a_r -k(r) v_{\phi}^2 = 0$. – Shengkai Li May 20 '18 at 19:04
• From a comment of OP it seems that we have the motion of a point particle under the influence of a force : $$\mathbf{F} = m\mathbf{a}=m \left(a_r\mathbf{e}_{r}+a_\phi\mathbf{e}_{\phi}\right)= m k(r) \upsilon_{\phi}\left(\upsilon_{\phi}\mathbf{e}_{r}-\upsilon_r\mathbf{e}_{\phi}\right) \tag{com-01}$$ always normal to its velocity : $$\boldsymbol{\upsilon}\left(t\right)=\dot{r}\mathbf{e}_{r}+ r\dot{\phi}\,\mathbf{e}_{\phi}=\upsilon_r\mathbf{e}_{r}+\upsilon_{\phi}\,\mathbf{e}_{\phi} \tag{com-02}$$ as the magnetic force for example. – Frobenius May 21 '18 at 18:49
• @Shengkai Li I apologize, but I'll continue tomorrow. Note that $$\dfrac{\mathbf{F}}{m}=\boldsymbol{\upsilon}\boldsymbol{\times}\mathbf{B} \quad\text{where} \quad \mathbf{B}=k(r)\upsilon_{\phi}\mathbf{e}_{z} \tag{com-03}$$ – Frobenius May 21 '18 at 21:59
• Not to distract you, but have you noticed $\phi$ is absent, so you might as well define $\theta\equiv\dot{\phi}$ and the equation for it is 1st, not second order. But a Lagrangian for it may be problematic. – Cosmas Zachos May 21 '18 at 23:29
## 1 Answer
We want to find the metric for these equations: \begin{align*} &\ddot{\varphi} +F(r)\,\dot{\varphi}\,\dot{r}=0&(1) \\ &\ddot{r} +G(r)\,\left(\dot{\varphi}\right)^2=0&(2) \end{align*} $\textbf{Theory}$
The equations of motions are: (I use the NEWTON EULER method ) \begin{align*} &J^T J \,\ddot{\vec{q}} =- J^T\,\frac{\partial\left( J\,\dot{\vec{q}}\right)}{\partial\vec{q}}\,\dot{\vec{q}}+J^T\,\vec{f_a}&(3)\\ \end{align*} With vector $\vec{q}$ of the generalized coordinates: \begin{align*} \vec{q}= \begin{bmatrix} \varphi \\ r \\ \end{bmatrix} \end{align*}, the Jacobi-Matrix (Ansatz): \begin{align*} J&= \begin{bmatrix} r & 0 \\ \varphi & 1 \\ \end{bmatrix} \end{align*} and the vector $\vec{f_a}$ of the external forces (Ansatz): \begin{align*} \vec{f_a}= \begin{bmatrix} 0 \\ -\frac{\varphi}{r}\,\dot{\varphi}\,\dot{r} \\ \end{bmatrix} \end{align*} We get the equation of motions (with (3)): \begin{align*} &\ddot{\varphi} +\frac{1}{r}\,\dot{\varphi}\,\dot{r}=0& (4)\\ &\ddot{r} +\left(\dot{\varphi}\right)^2=0&(5) \end{align*} Compare the coefficients of equation (1) with (4) and (2) with (5) we get: \begin{align*} F(r) & =\frac{2}{r}+k_1(r)\overset{!}{=}\frac{1}{r} \,\Rightarrow\quad k_1(r)=-\frac{1}{r}\\ G(r) &=-\left(r+k_2(r)\,r^2\right)\overset{!}{=}1\,\Rightarrow\quad k_2(r)=-{\frac {r+1}{{r}^{2}}} \end{align*} To fulfill the equations (1) and (2) I have to take two functions $k_1(r)$ and $k_2(r)$.
$\textbf{Metric}:$
\begin{align*} &g=J^T\,J= \begin{bmatrix} r^2+\varphi^2 & \varphi \\ \varphi & 1 \end{bmatrix} \end{align*}
• Thanks! It is interesting the $k(r)$'s are limited to make the ansatz work. – Shengkai Li May 25 '18 at 14:11
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2020-12-03 10:44:02
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https://www.studyadda.com/question-bank/water-or-hydride-of-oxygen_q20/1457/110918
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• # question_answer Which of the following will determine whether the given colourless liquid is water or not A) Melting B) Tasting C) Phosphthalein D) Adding a pinch of anhydrous $CuS{{O}_{4}}$
Colourless anhydrous $CuS{{O}_{4}}$ becomes blue on reaction with water.
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2020-09-25 23:22:23
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http://bryanwweber.com/writing/
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2015-10-04 19:34:05
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https://homework.cpm.org/category/CCI_CT/textbook/Int3/chapter/Ch12/lesson/12.2.2/problem/12-104
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### Home > INT3 > Chapter Ch12 > Lesson 12.2.2 > Problem12-104
12-104.
What is the distance between each pair of points? Homework Help ✎
1. $\left(x, y\right)$ and $\left(–3, y\right)$
$x+3$
1. $\left(x, y\right)$ and $\left(–3, 2\right)$
Make a diagram and use the Pythagorean Theorem.
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2020-04-03 02:29:47
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http://www.physicsforums.com/showpost.php?p=4285688&postcount=1
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P: 369 Hi all, I am reading an online material on elastic force and Hooke's law on spring. The definition of the Hooke's law reads that the restoring force is linear proportional to the displacement of the spring with constant k. The restoring force is defined as the force bringing the object back to the equilibrium position and k characterize the system's (spring's) nature. So if we have a spring with equilibrium position sitting in the origin of the coordinate so the restoring force F satisfies $$F = -k x$$ Now, if there is a way to add a second force ($F'$) which is exactly the same as $F$ (same direction and magnitude), since $F'$ is along $F$ all the time, so $F'$ always pointing toward the equilibrium position too. In this sense, should I conclude that $$F+F' = 2F = -k' x$$ if so, can we say that by adding an additional force $F'$, the spring constant k changed to k'=k/2 ? But I think the spring constant should be given by the spring only, so how does the paradox come from?
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2014-08-30 22:25:51
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http://crypto.stackexchange.com/questions?page=104&sort=votes
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# All Questions
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2016-05-29 19:10:43
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http://openstudy.com/updates/50b166bbe4b0e906b4a620c2
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## anonymous 3 years ago Simplify the expression attached and write it as a single logarithm.. ***still confused on this topic... pls help? :)
1. anonymous
2. anonymous
answer choices A,B,C,D from top to bottom :)
3. tkhunny
Move all the exponents up: $$(x+4)^{-3}$$ $$(x-7)^{2}$$ $$(x-2)^{5}$$ $$(x^{2})^{-1}$$ Notice how I deliberately left everything outside as ADDITION. This allows us just to bring everything inside without concern for numerator or denominator. We can figure all that out later.
4. anonymous
im confused.. so how can i apply that with my expression?
5. tkhunny
Confused with what? $$-3\log(x+4) = \log\left[\left(x+4\right)^{-3}\right]$$ Correct?
6. anonymous
im not quite sure what we are working on now.. I'm like uber confused.. are we doing my problem? or an example? :/ sorry I'm a bit confused :(
7. tkhunny
Your problem statement begins $$-3\log(x+4)$$, doesn't it? Or am I looking at some other picture?
8. anonymous
yup iy does :) so i get log[(x+4)^−3] from that part?
9. tkhunny
Very good. Now the (x-7) part?
10. anonymous
2log(x-7) = log(x-7)^2 ??
11. tkhunny
Good, now the x-2...
12. anonymous
5log(x-2)=log(x-2)^5 ??
13. tkhunny
One more. You're on a roll!
14. anonymous
lol thanks haha :P but i don't get this one... it looks different.. :/ -logx^2...
15. anonymous
but heres my take on it.. log(x^2)^-1 ??
16. tkhunny
Take the negative (-1) inside, just like the other coefficients ==> exponents.
17. anonymous
was what i got right?? or no?
18. anonymous
or is it log(x)^-2 ?
19. tkhunny
There it is. They are now all connected by addition. Use this guy and bring them all together. log(a) + log(b) = log(a*b)
20. anonymous
sorry my computer crashed... one sec :/
21. anonymous
log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2=answer B right? :)
22. jim_thompson5910
use the rule described above to go from log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2 to log[ (x+4)^−3*(x-2)^5*(x-7)^2*(x)^-2 ]
23. anonymous
kk I'm seeing that :) but how can i simplify it even further?
24. jim_thompson5910
(x+4)^−3 is really 1/[ (x+4)^3 ]
25. jim_thompson5910
same idea applies to (x)^-2
26. anonymous
ok so i get 1/x^-2 ?
27. jim_thompson5910
yep
28. jim_thompson5910
so put that all together
29. anonymous
so i get answer C right?? :)
30. anonymous
sorry i meant answer D :) is it answer D then? :)
31. anonymous
@jim_thompson5910 :)
32. jim_thompson5910
yes it is D
33. anonymous
kk great!!! thx :)
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2016-07-01 11:54:25
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http://aas.org/archives/BAAS/v27n4/aas187/S017008.html
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Session 17 - Supernovae.
Display session, Monday, January 15
North Banquet Hall, Convention Center
## [17.08] HST Observations of the Expansion and Shape of the SN 1987A Debris
C. S. J. Pun, R. P. Kirshner, P. Challis, P. Garnavich (CfA)
We have studied the expansion and the shape of the debris of SN 1987A with observations from HST\/ cameras. Broadband and narrow emission images covering a span of 4.5 years (from August 1990 to March 1995) are obtained before (with FOC and PC) and after (with WFPC2) COSTAR installment. The high resolution of the images allows the structure of the supernova debris to be revealed. We fitted the heavily limb-darkened image profiles of the debris to a surface brightness profile which decreases with angular radius \rho as \phi (\rho) \propto 1 / [1 + (\rho/\rho_0)^\alpha], where the power index, \alpha \simeq 4. The diameter of the debris, 2\rho_0, at day 2932 (March 3, 1995) is around 200 mas for the broadband optical images. However, the apparent debris size varies with wavelength and is found to be \sim 20% larger in the ultraviolet wavelengths. The expansion of the debris is consistent with a homologous linear expansion with time. The rate of expansion corresponds reasonably well with the observed widths of the emission lines (\sim 2500 km s^-1) at the distance of the LMC.
With the post-COSTAR images, we are able to study the shape of the supernova debris by measuring its ellipticity and orientation at several wavelengths. We found the debris to be asymmetric at all wavelengths. The major-to-minor axes ratio is found to be \sim 1.2, with the major axis corresponding to a position angle of 165\hbox^\circ The elongation axis of the supernova debris lies very close to axis perpendicular to the plane of the circumstellar ring (the minor axis of the ring in the sky).
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2015-02-01 08:43:25
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https://www.kitp.ucsb.edu/zee/books/quantum-field-theory-nutshell/errata-and-addenda
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# It was Greta Garbo, not Marlene Dietrich!
Update: February 2, 2009
I have updated this errata list only sporadically since 2006. In any case, You are still welcome to send in any errors, typographical or otherwise, that you notice (in the format specified below.) Please check to see if your errata are not already listed here.
One thing that is useful for me to know is how complete the index is. If there are items in the index that you feel should be there but are not, please let me know. (For example, I looked up "covariant derivative" in the index and it was not there.) Most people do not know that the index is not prepared by the author but by a professional index compiler who often knows almost nothing about the subject of the book.
I would also like to take this opportunity to thank all of you who sent in errata, particularly those who also posted a favorable "Customer Review" on Amazon.com. Appreciative words from readers make the enormous effort that went into writing a book like this worthwhile.
*********
Errors, typographical and otherwise, in Quantum Field Theory in a Nutshell are listed here. Readers who find errors are urged to bring them to my attention by email (zee@kitp.ucsb.edu) using for subject "nutshell errata" so that your email does not get treated as spam by the filter on my mailer. I would appreciate it if you would write them in exactly the same format as used here, including the (Thanks to ABC). Notation: Line –n means line n from the bottom of the page. Please check to see if the errata you found are not already listed here.
I apologize to all those who sent in errata during academic year 2006-07. I was away on sabbatical at Harvard and did not know how to update my web site remotely. In any case, the stream of errata had thinned to a trickle. If you feel that the erratum you sent in is particularly serious, please email me again. Thanks. Also, a Clarifications page has been added.
Last update: December 4, 2007 (previous update: June 29, 2005)
## "Of making books there is no end, and much study is a weariness of the flesh." -- Ecclesiastes 12:12
p66: In the simplified calculation of the Casimir effect, the 24 in eq (19) is the same 24 that appears in string theory! (24+2=26=the dimension of spacetime the quantum bosonic string must live in.)
p117: The line uttered by Greta Garbo came from the film Ninotchka (1939). (Thanks to Amanda Weltman) INCORRECT: The film is Grand Hotel (1932) which I do not particularly recommend. Contrary to what was written on the bottom of this page, in the film she did say "I want to be alone." All of this harping on a triviality stems from a book by Gamow that I read as a kid.
p309: The URL in footnote 1 has been changed to http://www.maths.ed.ac.uk/~jmf/Teaching/Lectures/EDC.pdf (Thanks to Philip Tanedo)
Errata
p11:In the expression directly after the phrase "Doing the integral over p, we get", a factor of 1/(2pi) from the normalization of the momentum space integral was dropped. This error then propagates down the rest of the page until (4). It is however immaterial because eventually it is just absorbed into the definition of Dq. (Thanks to Latham A. Boyle)
p11: All of the products on this page should run from 1 to N-1 (but the sums should run from 0 to N-1). (Thanks to Latham A. Boyle)
p15: In Eq.(20), inside the square root, the factor 2*pi*hbar should be raised to the Nth power. (Thanks to Latham A. Boyle)
p16: A potential source of confusion: In the literature, the boundary condition on path integrals is conventionally not displayed explicitly but is understood implicitly. For example, the integral in (1) on p 16 actually differs from the integral in (6) on p 12. The attentive reader would find this point explained in the middle of p 12. (Thanks to Nikolas Akerblom)
p17: 2nd full paragraph, there is a sign error: 1st sentence should say: 2*q_a*q_b=q_a^2+q_b^2-(q_a-q_b)^2 (Thanks to Latham A. Boyle)
p18: 2nd full paragraph: Lorentz invariance allows V(phi) to be some general function of phi, e.g. cosh(phi)). I restricted myself to a polynomial at this point merely for the sake of simplicity. Later when we study renormalizability in (3+1)-dimensions V will have to be restricted to a polynomial. (Thanks to Latham A. Boyle)
p19: Section: "The vacuum" exp(-iHt) instead of exp(iHt) in the bracket. (Thanks to Adrian Chirila)
p23: In the second line above Eq.(23), the exponent of the formula "i(\omega_k t - kx)" should be "-i(\omega_k t - kx)". (Thanks to Sung-Soo Kim)
p26: In the line just above Eq.(6), "iW=iET" should be "iW=-iET".(Thanks to Sung-Soo Kim)
p27: In the equation for Z(J): should have (iW(J))^n, opening parenthesis missing. (Thanks to Sho Yaida)
p33: In the fifth line below Eq.(12), "Appendix C" should be "Appendix B".(Thanks to Sung-Soo Kim)
p40: After (3), "make" should be "made". (Thanks to Pierre Jouvelot)
p43: -line 15: 3! in the denominator should be indeed replaced by 2(6!). (Thanks to Seunghun Hong, Mike Mowbray, and Joshua Feinberg)
p43: line 9: the denominator should contain (4!)^2 instead of (4!)^3 (Thanks to Jean Orloff) INCORRECT: The numerical factor stated in the book is in fact correct. Thanks to the many readers who sent in this anti-erratum.
p44: In Figure I.7.2, a diagram consisting of three straight lines and one vacuum bubble containing two vertices is missing. (Thanks to Sho Yaida)
p44: In Figure I.7.2, a diagram consisting of one straight line and two crossed lines with a loop on one leg, is missing. (Thanks to John Cummings and Jim Napolitano and
Caterina Soldano)
p44: In Figure I.7.2, six diagrams are missing. (There should be a total of thirteen.) All are diagrams that are, or should be, in Figure I.7.3, plus one straight line. (Thanks to Jim Napolitano.)
p44: Figure I.7.2 misses 2 more diagrams, constructed by adding a disconnected line to the graphs (a) and (b) of fig I.7.3 (Thanks to Jean Orloff)
p45: In Figure I.7.3, a diagram consisting of two straight lines and one vacuum bubble containing two vertices is missing. (Thanks to Sho Yaida)
p45: In Figure I.7.3, two diagrams, each consisting of two straight lines and one vacuum bubble containing two vertices, are missing. (There are two ways to make a vacuum bubble with two vertices.) Also missing is a diagram with three straight lines, one of which has a vacuum bubble attached which also has an internal vertex. (Thanks to Jim Napolitano.)
p45: In the expression for G^{(4)}, the integral should be multiplied by -\lamda/(4! Z(0,0) and the right hand side of the equality should be (-7!! \lamda)/(4! m^8) . (Thanks to Latham A. Boyle, Chung-Pin Chou, and Pierre Jouvelot)
p47: In (9) there is an implicit sum over i_1, …, i_s, with each index running over 1, …, N independently. (Thanks to Sho Yaida & Chih-Hao Fu & Kevin C. W. Lai)
p47: equation (10): I intentionally omitted the disconnected diagrams of order lamda were omitted since they were to be introduced later. (Thanks to Latham A. Boyle)
p48:In Eq.(12), there should be no Z(0,0) in the first line, while the second line is correct.(Thanks to Xining Du)
p48: equation (13): both expressions on the RHS of the equal sign should be integrated over dx_1*dx_2*...*dx_s. (Thanks to Latham A. Boyle)
p51 - p52: I intentionally left out the i's associated with D(x_1-x_2) for brevity. The Feynman rules have these i's included correctly. (Thanks to Latham A. Boyle)
p50: Second line after (17), “by (i/4!)” should be “by -(i/4!)”. (Thanks to Sho Yaida)
p51: In the second line following (19), (4!)^2 should be (4!)^3. (Thanks to Pierre Jouvelot)
p55: In Figure I.7.9 an arrow mark for the line marked k_4 is missing. (Thanks to Sho Yaida)
p55: Third line below Eq(21), Figure I.7.5 should read Figure I.7.9. (Thanks to Sung-Soo Kim)
p62: 3 lines after (4), the ket for |0> doesn't use the proper font. (Thanks to Pierre Jouvelot)
p63: In the last line, (I.3.20) should be (I.3.22). (Thanks to Sho Yaida)
p63: In the first line of Eq.(9), "L" should be "{\cal L}", that is, Lagrangian density instead of Lagrangian. Either that, or take it outside the brackets inside the integral. (Thanks to Jim Napolitano.)
p64: In the fifth line, Exercise I.8.2 should be Exercise I.8.3. (Thanks to Sho Yaida)
p65: The expression following "the energy per unit area between the plates is changed to” needs a factor 1/2. (Thanks to Xuguang Huang)
p68: The operators that appear in the second (unnumbered) equation on p.68 should be Schrödinger operators. Then, multiplied by the exponents of the Hamiltonians, they are mapped into Heisenberg operators as appears in eqs. (21) and (22). Also, in eq. 22, e^(-iHT) should either be included in the time ordering operation, or put on the left. (Thanks to Charles H. Henry and Joshua Feinberg)
p68: The operators that appear in the second (unnumbered) equation on p.68 should be Schrödinger operators. Then, multiplied by the exponents of the Hamiltonians, they are mapped into Heisenberg operators as appears in eqs. (21) and (22). Also, in p69: In the right hand side of the last equation of Exercise I.8.5, "!" should be "i".(Thanks to Sung-Soo Kim)
p69: prob. I.8.4, 5th line: superfluous dot before the word "creates". (Thanks to Andy Tenne-Sens)
p69 line -2: Ann Phys 288:103 (2001) (Thanks to A. Anabalon & Jim Napolitano)
p71: In the third line below the "Continuous Symmetries" heading, there is an extraneous colon (":") before "so that...". (Thanks to Jim Napolitano.)
P74: In the last sentence right before the Exercises is a statement [Q,\phi]=\phi. The Q here is evidently defined with a minus sign compared to the Q in exercise I.8.4. (Thanks to Seunghun Hong)
p79 line7: The subscript on (E x B) should be i, not k. (Thanks to Nikolai von Boetticher)
p79: In the second paragraph in the Appendix, there is a closing parenthesis that is not needed. (Thanks to Sho Yaida)
p 91: Typographical problem throughout: 1st line of the Cousins of the gamma matrices section, it is important to distinguish the order of indices on Lambda as Lambda^nu_mu. (Thanks to Parsa Bonderson)
p92:The two mentions of the Lorentz transformation in exponential form are missing a factor of i in the exponent, as is included on the following page: exp{-1/2 \omega_{\mu\nu} J^{\mu\nu}} should be exp{-i/2\omega_{\mu\nu} J^{\mu\nu}}. (Thanks to Sung-Soo Kim and Ryan Springall)
p96: 5 lines after (24), "that the they" should read "that they". (Thanks to Pierre Jouvelot)
p98: Ettore Majorana (1906-1938). In footnote 2, “twenties” should read “early thirties”. (Thanks to Frank Reashore)
p102: There is a missing ] at the end of the text of Exercise II.1.1
p103: Last line, N|0> =|0> should be N|0>=0. (Thanks to Sung-Soo Kim)
p105: footnote, the reference should read Relativistic Quantum Mechanics instead of Relative Quantum Mechanics. (Thanks to Istok Mendas)
p106: After (14), it seems that +(-)ipx (with arrows) should be -(+)px in order to be superficially consistent with (10) but nothing is affected since the pvector can be rotated. (Thanks to Pierre Jouvelot)
p112: An i is missing on the LHS in (5) and (6). J and K are defined by the action of rotation and boost on (t,x,y,z) as given by E^(i (real parameter) J or K). (Thanks to Adam Brown, Joshua Feinberg, and Fred Kuttner)
p113: First line above spinor representation, Exercise III.3.1 should read II.3.1. (Thanks to Sung-Soo Kim)
p117: It should be Greta Garbo, not Marlene Dietrich. (Thanks to Saul Epstein and Murph Goldberger)
p122: line 4: Fig. I.7.7 should be Fig. I.7.12. (Thanks to Latham Boyle)
p122: Tr, in the last formula, should not be in italics. In other parts of the book, tr in lower case is also used. (e.g., in (12)). (Thanks to Pierre Jouvelot)
p123: A possible minus sign could have been absorbed into C or A. (Thanks to Pierre Jouvelot)
p124: line 6 above (6): x should be \chi. (Thanks to Jeroen Spandaw)
p127 line -4: u-bar(p',s') instead of u-bar(p',s). (Thanks to Joshua Greenberg)
p127 line -2: Should read, "For antifermions, we would have v-bar(p,s) and v(p',s'), respectively." (Thanks to Joshua Greenberg)
p133: last equation: (1) The overall factor should have $(2m)^4$ in the denominator; (2) the Greek indices on the rightmost factor should be lower, not upper. (Thanks to Jim Napolitano.)
p136: \Gamma_{\lambda\nu} should be \Gamma_\lambda^\nu. (Thanks to Pierre Jouvelot)
p138: The need for a tr operation on closed fermion loops is self-evident and is needed for the spinor indices to completely match upbut this fact was not explicitly stated in the Feynman rules given on page 127. It is however somewhat implicit in the discussion on pages 125-126. (Thanks to Pierre Jouvelot)
p152: In the equation for M at the top of the page, the integrand should be 1/D^2. (Thanks to Jim Napolitano.)
p152: In the line before (12), (1-\alpha)k^2 should be (1-\alpha)K^2. (Thanks to Pierre Jouvelot)
p153: In formula after (15), the printer interchanged ( and [. (Thanks to Pierre Jouvelot)
p168: In the 6th line, "Q_{mu nu} A^{nu} = J^{nu}" should be "Q_{mu nu}A^{nu} = J_{mu}". (Thanks to Sung-Soo Kim)
p171: display (8): subscript "eff" in wrong font. (Thanks to Jeroen Spandaw)
p174: line –5 from (10): "tend" should read "tends". (Thanks to Jeroen Spandaw)
p177: in the third line of (3), the second term should have a + sign. (Thanks to Parsa Bonderson)
p180: In (9), the -m should be +m. (Thanks to Pierre Jouvelot)
p184: In the formula for iD(q), \Pi_{\lambda\rho} should be \Pi^{\lambda\rho}. In the following term, \lambda\rho in \Pi, \sigma in D and \kappa in \Pi should be upper indices. (Thanks to Pierre Jouvelot)
p184: line 1 below (3): Figure III.7.1 should be Figure III.7.2 (Pi corresponds to shaded objects, which are present only in Figure III.7.2). (Thanks to Jeroen Spandaw)
p185: In (6) and (7), the indices of gamma matrices should be lower indices. (Thanks to Pierre Jouvelot)
p186: In the equality for \Pi near the middle of the page, -i should be (-). (Thanks to Pierre Jouvelot) Next line, -m should be +m. (Thanks to Pierre Jouvelot)
p187: In (11), +m^2g_{\mu\nu} should be -m^2g_{\mu\nu}. (Thanks to Pierre Jouvelot)
p187: line 1 after (11): prevent line break between Appendix & D. (Thanks to Jeroen Spandaw)
p188: In (14) a right parenthesis is misplaced. (Thanks to Pierre Jouvelot)
p190: In problem III.7.1, the reference to Eq. (III.1.16) should actually refer to Eq. (III.1.15). (Thanks to Latham Boyle)
p195: line 4 below (4): Insert a minus sign before V(\phi)|_{\phi = v}. (Thanks to Jeroen Spandaw)
p196: 1st line, negative should be positive. (Thanks to Saul Epstein)
p198: In (7), the additive constant was dropped (perhaps intentionally). (Thanks to Latham Boyle)
p203: In Line 2, the minus sign for the electron field should be a superscript; the same problem occurs in (1). (Thanks to Pierre Jouvelot)
p203: In Line -2, the reference to III.6.9 should be III.6.7. (Thanks to Pierre Jouvelot)
p203: Three lines before (2), one should have e^{+i(p'-p)x}, to be consistent with the usual e^{ipx} and the formula that follows (4) on p205. (Thanks to Pierre Jouvelot)
p206: RHS of 1st equation: i should be switched to -i both times it appears. [because of the sign error 3 lines above (2) on p203] (Thanks to Latham Boyle)
p208: The reference to III.3.3 should be III.3.4. (Thanks to Pierre Jouvelot)
p209: In Eq. (3): curly Z should be ordinary Z. (Thanks to Latham Boyle)
p209: line 1 after (3): drop “2” after Appendix. (Thanks to Jeroen Spandaw)
p214: Before (24), Reference to II.5.12 should be II.5.2, and there is a spurious right parenthesis before the semicolon. (Thanks to Pierre Jouvelot)
p214: Last sentence before "Fermions" section: reference to Chapter IV.7 should be to Chapter IV.6 (the reference should be to Exercise IV.6.9). (Thanks to Latham Boyle)
p216: The end of the last paragraph: Phys. Rev. D7:1883,1973 is Phys. Rev. D7:1888,1973. (Thanks to Ilja Dorsner)
p228: In (5), one of the indices \mu should be raised. (Thanks to Sung-Soo Kim)
p230: line -15: replace "rules" with "diagrams". (Thanks to Jeroen Spandaw)
p234: There should be no i in (24). (Thanks to Pierre Jouvelot)
p235: In the second paragraph, “the basis { \psi a }” should read “the basis { \psi_a }”. (Thanks to Frank Reashore)
p237: “See Appendix C for the necessary grouptheory” should read “See Appendix B for the necessary grouptheory”. (Thanks to Frank Reashore)
p237: In Paragraph 3, the reference to IV.5.21 should be IV.5.20. (Thanks to Pierre Jouvelot)
p238: In the second paragraph of the Counting Massless ... section, one should say "we end upwith one massless gauge boson". (Thanks to Pierre Jouvelot)
p242: In Exercise IV.6.9., the reference should be to IV.3.5. (Thanks to Ilja Dorsner)
p242: In the last line: Phys. Rev. D7:1883,1973 is Phys. Rev. D7:1888,1973 (Thanks to Ilja Dorsner)
p242: In the 1st line of Exercise IV.6.9, the reference should be to Exercise IV.3.5. (Thanks to Latham Boyle)
p242: In Exercise IV.6.6, the reference should be to III.4.9. (Thanks to Pierre Jouvelot)
p245: In line 7, the right parenthesis should be a right bracket, and the conventional propagator uses (1-\ksi) instead of \ksi. (Thanks to Pierre Jouvelot)
p245: In the first paragraph, the reference should be to Chapter II.6. (Thanks to Pierre Jouvelot)
p246: Near the topof page, “(see Appendix E)” should read “(see Appendix D)”. (Thanks to Frank Reashore)
p247: In the last expression of the equalities, the (-) sign should be a +. In (5), the - sign should be propagated (-4i/... and -i/...). One gets the correct expression for (6) if one replaces the + sign in the definition of a, before (6), by a - sign. (Thanks to Pierre Jouvelot)
p247: Line 10: There is a missing = between f(P) and the limit expression. (Thanks to Pierre Jouvelot)
p247: The "tr" symbol should be in roman in the definition of f(P). (Thanks to Pierre Jouvelot)
p257: Precedng (1), somewhat better to replace (III.5.6) by (III.5.11). (Thanks to Saul Epstein)
p258: hbar k^2/2m should read (hbar k)^2/2m. (Thanks to Ilja Dorsner)
p258: In the first paragraph, “(see appendix to this chapter.” should read “(see appendix to this chapter). (Thanks to Frank Reashore)”
p260: In (9) u^2 must be replaced by the total particle number N, defined by N = u^2 + \sum _{k \notequal 0} a_k^\dagger a_k . Note that the Hamiltonian to this order in the expansion also includes the terms coming from expanding G u^4 = G N^2 - 2\sum _{k \notequal 0} a_k^\dagger a_k . (Thanks to Robert Graham)
p264: At the end of the first sentence, there is an missing right paren after "(3". (Thanks to Pierre Jouvelot)
p266: Ex. V.2.2, last line: closing bracket is missing. (Thanks to Andy Tenne-Sens)
p273: last paragraph: change "(see fig. (2)) " to "(Fig. V.5.2)". (Thanks to Andy Tenne-Sens)
p274: end of 2nd paragraph, +' in front of v_F should be -'. (Thanks to Yu Shi)
p274: In figure V.5 the value of k runs from -pi/a to +pi/a. (Thanks to Joseph Abraham)
p275: 2nd para., 3rd line: the mattress is actually introduced in Chapter I.1. (Thanks to Andy Tenne-Sens)
p277: In the first paragraph of the Small Oscillations ... section, there is a \sqrt{2} missing in the mass. (Thanks to Pierre Jouvelot)
p280: In the inequality for M, one should have v^2\phi instead of v^2\phi^2. (Thanks to Pierre Jouvelot)
p280: inequality for M: "[" missing before \frac13 \phi^3. (Thanks to Jeroen Spandaw)
p283: 5th line from the bottom: the upper arrow is too short. (Thanks to Andy Tenne-Sens)
p283: Stoke's should read Stokes's or Stokes. (Thanks to Jeroen Spandaw)
p284: 1st line: Z_2 is the multiplicative groupconsisting of the set of integers {+1, -1}. (Thanks to Andy Tenne-Sens)
p284: One should have d^3x in (4). (Thanks to Pierre Jouvelot)
p286: 2nd paragraph, 4th line: the upper arrow is too short. (Thanks to Andy Tenne-Sens)
p286: 1st line, the given expression of path integral is already in euclidean form and so should appear at the end of the sentence. (Thanks to Yu Shi)
p286: In the line after (10), the "tr" should be in roman. (Thanks to Pierre Jouvelot)
p293: e^{iHT} should be e^{-iHT}. (Thanks to Yu Shi)
p296: 2nd paragraph, last line: should read "... , and obtain ...". (Thanks to Andy Tenne-Sens)
p296: 2nd line, it should be Lorenz gauge. (Thanks to Saul Epstein)
p296: in (4): subscript "Hopf" should be in roman font. (Thanks to Jeroen Spandaw)
p297: Before (6), the reference to Chapter III.4 should be III.7. (Thanks to Pierre Jouvelot)
p298: In (7), the "tr" should be in roman. (Thanks to Pierre Jouvelot)
p298: In Line -9: "by thinking about mass dimensions" (Exercise VI.I.2.) (Thanks to Emanuele Rodo)
p301: line 10: Replace "level is" with "levels are". (Thanks to Jeroen Spandaw)
p302: In (1), "e" is missing in the covariant derivatives, or one should assume e=1 (something not used in this chapter). (Thanks to Pierre Jouvelot)
p302: In (1), the sign of the spatial derivative term and of V should be reversed. The + superscript for \psi should be the dagger sign. (Thanks to Pierre Jouvelot)
p305: 1st line after (10): remove parentheses thus: "Chapter VI.1". (Thanks to Andy Tenne-Sens)
p305: In (10), the index \nu on the partial derivative should be an upper index. (Thanks to Pierre Jouvelot)
p305: in (8): subscript "em" should be in roman font. (Thanks to Jeroen Spandaw)
p308: prob. VI.2.1, 6th line: change " ... . " to " ... , ". (Thanks to Andy Tenne-Sens)
p317: In the second paragraph, the reference to (28) should be (30). (Thanks to Pierre Jouvelot)
p319: In (2), a factor 1/2 is missing before (d\pi)^2. (Thanks to Pierre Jouvelot)
p319: In the paragraph following (2), it is said that the vacuum expectation value of \phi can point in the 4th direction. (Thanks to Pierre Jouvelot) The 4th should be replaced by 1st. (Thanks to Pierre Jouvelot)
p319: In the second paragraph, "m" is missing before (\psibar_L\psi_R+h.c.). (Thanks to Pierre Jouvelot)
p320: In the first line of the The Nonlinear ... section, "abut" should be "about". (Thanks to Pierre Jouvelot)
p323: (3), subscript i' in the second term should be j'. (Thanks to Yu Shi)
p331: 4th line: "but S is unsuitable". (Thanks to Andy Tenne-Sens)
p331: bottom of 2nd paragraph: change "esponent" to "exponent". (Thanks to Andy Tenne-Sens)
p331: "is" is missing between "S" and "unsuitable" after the first formula. (Thanks to Pierre Jouvelot)
p332: Before (1), there should be no "i" before \pi in the limit expression. (Thanks to Pierre Jouvelot)
p333: Before (5), the reference should be to A.12. (Thanks to Pierre Jouvelot)
p334: In (7), -S(\phi) is perhaps better written as iS(\phi) but in fact S was not specified. (Thanks to Pierre Jouvelot)
p335: In (9), by translation invariance \phi(x)\phi dagger(x) could be written as \phi(0)\phi dagger(0) if one wishes. (Thanks to Pierre Jouvelot)
p339: At the end of the first paragraph of Section Flow Of The ..., the reference III.7.13 should be III.7.14. (Thanks to Pierre Jouvelot)
p342: 1st line: For clarity this should read "As with any field theory, and as I have indicated, …" . (Thanks to Andy Tenne-Sens)
p344: end of 3rd paragraph: normal parentheses would be more conventional than square brackets. (Thanks to Andy Tenne-Sens)
p346: end of 3rd paragraph: "4-dimensional" should have hyphen, not dash. Also, parentheses instead of square brackets might be preferable. (Thanks to Andy Tenne-Sens)
p347: 4 lines above (18) change “der Integral.” into “das Integral.” (Thanks to Robert Graham)
p347: "after", in the first line of the last paragraph, should be "offer". (Thanks to Paul Slater, Andy Tenne-Sens, and Pierre Jouvelot.)
p348: In Footnote 6, "conductivty" should be "conductivity". (Thanks to Pierre Jouvelot)
p348: The reference to VI.6.2 in the last paragraph should be VI.8.2. (Thanks to Pierre Jouvelot)
p349: Fig. VI.8.2: Change "d"s to "D"s. (Thanks to Andy Tenne-Sens)
p350: prob. VI.8.5: Move closing square bracket to the very end of the problem statement. (Thanks to Andy Tenne-Sens)
p353: There should be a negative sign in front of the second term of equation (2). (Thanks to Tim Hsieh)
p354: The reference to Chapter III.4, in the middle of the page, should read II.5. (Thanks to Pierre Jouvelot)
p355: in (8) and (9), for uniformity the x dependence should perhaps be suppressed. (Thanks to Andy Tenne-Sens)
p356: 1st paragraph, last line: The \mu and \nu subscripts in the second term should be interchanged. (Thanks to Andy Tenne-Sens)
p360: prob. VII.1.1: add closing square bracket at the end of the problem statement. (Thanks to Andy Tenne-Sens)
p363: 2nd paragraph: replace square brackets with parentheses. (Thanks to Andy Tenne-Sens)
p363: 3rd paragraph, 3rd line: The \mu and \nu subscripts in the third W of the formula should be interchanged. (Thanks to Andy Tenne-Sens)
p363: Line -2: Should read "The fact... provides......". (Thanks to Daniel Gerber)
p366: 4th paragraph, 7th line: should read "Chapter IV.6" (unitary gauge is mentioned on p241). (Thanks to Andy Tenne-Sens)
p369: 2nd paragraph: inconsistent spellings: "nonabelian" and "non-abelian". (Thanks to Andy Tenne-Sens)
p373: 1st line after (7): replace square brackets with parenthses. (Thanks to Andy Tenne-Sens)
p373: The reference to Exercise I.8.4 in the next to last paragraph should be I.8.5. (Thanks to Pierre Jouvelot)
p374: line immediately before (8): capitalize "We" (although Webster's claims a colon does not force capitalization of the word immediately following. However, words are capitalized after a colon everywhere else in the book). (Thanks to Andy Tenne-Sens)
p375: 1st line: change "turns" to "turn". (Thanks to Andy Tenne-Sens)
p377: In the first paragraph, “abut 10%” should read “about 10%”. (Thanks to Frank Reashore)
p377: line 8: "abut" should be "about". (Thanks to Jeroen Spandaw)
p378: The reference to Chapter IV.6 in the second paragraph should be IV.5. (Thanks to Pierre Jouvelot)
p380: In Equation 3, d\phi should be D\phi. Also in the definition of <O(\phi)>, "tr" shouldn't be in italics. (Thanks to Pierre Jouvelot)
p381: The labeling of i, j, k, and l are not the same in (6) and in Fig. VII.4.4. (Thanks to Andy Tenne-Sens)
p384: The arrowed line should be "broken" in two more places than shown. (Thanks to A. Zee)
p384: 3rd line after (12): capitalize "Chapter". (Thanks to Andy Tenne-Sens)
p385: Line 7: should be m>n under product symbol. (Thanks to A. Zee)
p385: (13): Should be m>n under product symbol. (Thanks to A. Zee)
p385: (13): The sum should be divided by 2. (Thanks to A. Zee)
p385: (13): extra right-parenthesis after "log". (Thanks to Andy Tenne-Sens)
p385: (14): The sum should be divided by 2. (Thanks to A. Zee)
p385: In the last paragraph, in definition of G(z), \lambda should be z. (Thanks to Pierre Jouvelot)
p388: 1st line in new subsection: capitalize "Chapter". (Thanks to Andy Tenne-Sens)
p390: In Exercise VII.4.5, there is a missing right parenthesis after the reference to Exercise VI.6.1. (Thanks to Pierre Jouvelot)
p391: last line, Appendix C should be Appendix B. (Thanks to William Kaufmann)
p392: last line: add comma: " = 10, precisely ". (Thanks to Andy Tenne-Sens)p393: lines 4 and 11, Appendix C should be Appendix B. (Thanks to William Kaufmann)
p394: In (12), in the 4th and 5th columns of the matrix, u and d are interchanged. (Thanks to Tim Hsieh)
p398: 1st line in new subsection: capitalize "Exercise" and dropparenthesis. (Thanks to Andy Tenne-Sens)
p401: The reference to Exercise VII.6.3 in the paragraph before the Fermion Masses section should be VII.6.2. (Thanks to Pierre Jouvelot)
p403: On Line 3, "abut" should be "about". (Thanks to Pierre Jouvelot)p405: paragraph 2, line 7, Appendix C should be Appendix B. (Thanks to William Kaufmann)
p406: line 8 from bottom, Appendix C should be Appendix B. (Thanks to William Kaufmann)
p408: line –3 should be “representations”. (Thanks to Andy Tenne-Sens)
p412: line -12: Q(e-) = -1 instead of 0. (Thanks to Jeroen Spandaw)
p414: 5th and 6th lines after (24): "conjugates" instead of "conjugate". (Thanks to Andy Tenne-Sens)
p422: All mentions to \sqrt(G) should be \sqrt(16\pi G) in the paragraphs before Section “Determining the weak field action”. (Thanks to Pierre Jouvelot)
p424: In the first line, d^\nu should be d_\nu, and thus be compatible with Equation 11. (Thanks to Pierre Jouvelot)
p426: In the next to last paragraph, the Lorentz metric \eta_{\mu\nu} is missing in the definition of the trace T. (Thanks to Pierre Jouvelot)
p428: The amplitude should be proportional to (k_1.k_2)(p_1.p_2)/q^2, not (k_1.p_1)(k_2.p_2)/q^2. (Thanks to Joshua Feinberg)
p430, in the 2nd line, g_{phi phi} should be = sin^2 theta. (Thanks to Parsa Bonderson)
p431: 3rd line above appendix: The ordinary derivative acting on the spinor field should have been a covariant derivative of course to account for the dependence of O on x. More precisely, the combination acting \psi could be written as I\gamma^a e_a^\mu \partial_\mu \psi and the \partial_\mu should be replaced by \curlypartial_\mu = \partial_\mu+\Gamma_\mu where \Gamma_\mu, is given by (i/4)\sigma^{ab} e_b^\nu D_\mu e_{a\nu} where D_\mu is the covariant derivative of general relativity involving the Riemann-Christoffel symbol given on page 419. (Thanks to Joshua Feinberg)
p433: Prob. VIII.1.4: "make a further gauge transformation". (Thanks to Andy Tenne-Sens)
p442: The reference to S. Weinberg should be Phys.Rev.Lett. 43, page1566, 1979, not page 311. in that volume.(Thanks to Gil Paz.)
p448: 1st line under "Supersymmetric action": there should be no space in "anyway". (Thanks to Andy Tenne-Sens)
p449: Insert a "-" sign befor the W term in Equation 11. (Thanks to Pierre Jouvelot)
p461 and 464: subsection titles "SO(N)" and "SU(N)" should be in italics. (Thanks to Andy Tenne-Sens)
p465: line after (15): "denotes N". (Thanks to Andy Tenne-Sens)
p466: In the second paragraph from bottom, “hermitean and traceless as required by (9) and (14)” should read “hermitean and traceless as required by (9) and (10)”. (Thanks to Frank Reashore)
p469: In (24), 55* should be 50*. (Thanks to Pierre Jouvelot)
p470: In the first paragraph, “Let the index \mu takes on the value 1, 2” should read “The index \mu takes on the values 1, 2” or ““Let the index \mu take on the value 1, 2”. (Thanks to Frank Reashore)”
p477: In eq. (13), the denominator on the left hand side should be squared. (Thanks to Daniel Gerber)
p483: In the very last part of the third line of the first equation, the integral range should be from "-\infty"(not zero) to \infty. (Thanks to Sung-Soo Kim)
p484: The last line of the first equation should have a leading factor of -i. (Thanks to Thomas Delmer)
p486: In I.8.5, after "we get", T(A(x)A(0)) should be T[A(x)A(0)]. (Thanks to Pierre Jouvelot)
p486: In I.8.5 <0|A(x)|n> should be <0|A(0)|n>. (Thanks to Thomas Delmer)
p488: II.1.1, 2nd line: different font sizes for the two instances of "i/4". (Thanks to Andy Tenne-Sens)
p488: II.1.1, 6th line: remove comma: "which equals \psi ...". (Thanks to Andy Tenne-Sens)
p489: II.1.6 should be II.1.5. (Thanks to Sung-Soo Kim)
p490: Line 2, "funciton" should be "function". (Thanks to Pierre Jouvelot)
p491: III.5.2: capitalize "Chapter". (Thanks to Andy Tenne-Sens)
p491: In the first line, the reference to (III.1.15) should be (III.1.14). (Thanks to Pierre Jouvelot)
p492: In III.7.1, in the expression for N_{\mu\nu}, the +m^2 g_{\mu\nu} should be -m^2 g_{\mu\nu}. (Thanks to Latham Boyle)
p492: III.7.1: 3rd-to-last line: capitalize "Appendix" and "Chapter" (also correct the spelling). (Thanks to Andy Tenne-Sens)
p492: IV.3.1: remove left parenthesis after "log". (Thanks to Andy Tenne-Sens)
p492: In III.7.1, the (-i) factor in i\Pi should be (-). (Thanks to Pierre Jouvelot)
p494: IV.7.4: In definition of N^{\mu\nu} remove first left parenthesis. (Thanks to Andy Tenne-Sens)
p494: In IV.7.4, there is a missing right parenthesis in the expression defining N^{\mu\nu}. (Thanks to Pierre Jouvelot)
p495: V.6.1: 2nd-to-last equation: remove extra parenthesis in left summand. (Thanks to Andy Tenne-Sens)
p495: In V.6.1, "))" should be ")" in the next to last equation, and V' should be -V' in the last equation. (Thanks to Pierre Jouvelot)
p496: 3rd line from bottom: "field". (Thanks to Andy Tenne-Sens)
p496: In Line -3, "filed" should be "field". (Thanks to Pierre Jouvelot)
p497: 1st line: add space to "unit of". (Thanks to Andy Tenne-Sens)
p497: V.7.12: add period at end. (Thanks to Andy Tenne-Sens)
p497: In the first line, "unitof" should be "unit of". (Thanks to Pierre Jouvelot)
p499: VII.1.1, line before last formula: "terms of higher order". (Thanks to Andy Tenne-Sens)
p500: The problem (VIII.1.10) for which the answer was given has mysteriously disappeared from the text. (Thanks to Saul Epstein)
p502: correct spelling of author's name is "E.D. Commins". (Thanks to Andy Tenne-Sens)
p503: In the first line it should read 'Wiedemann' instead of 'Wiededemann'. (Thanks to Nikolas Akerblom)
p509: In the entry for Fisher, only 314n refers to Matthew. The other two, 269 and 342, should be to Michael, the father of Matthew. This erratum is particularly embarrassing since I know both persons involved, in contrast to the erratum on page 117. I might, however, also point out that the index is compiled by a professional indexer, not by me. (Thanks to Paul Slater)
p517: "Veltman, Torny" should read "Veltman, Tini". (Thanks to Jeroen Spandaw)
p518: 'Wu Yang-shi' should be 'Wu Tai-Tsun'. This erratum is particularly embarrassing since I know both persons involved, in contrast to the erratum on page 117. I might, however, also point out that the index is compiled by a professional indexer, not by me. (Thanks to Yu Shi)
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2018-09-18 16:24:26
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https://chemistry.stackexchange.com/questions/53335/is-sulfide-ion-a-stronger-base-than-hydroxide-ion
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# Is sulfide ion a stronger base than hydroxide ion?
I received these three responses. They are all, except the last response, incorrect to varying degrees. I am, however, unsure about how to grade these responses because the question itself, in my opinion, misleads the students by saying that both have the same pH and to use this information to determine the strength of the bases. Their responses also raised a few questions of my own. What are your opinions?
Question
It is an experimental fact that the pH of 1 M $\ce{Na2S}$ is essentially the same as the pH of 1 M $\ce{NaOH}$. Based on this information, is $\ce{S^{2-}}$ or $\ce{HO-}$ the stronger Bronsted-Lowry base? How can you tell?
Student 1's response:
A base's strength is measured by how much it can increase the hydroxide ion concentration in a solvent relative to its own initial concentration.
Given that both the 1 M $\ce{Na2S}$ and 1M $\ce{NaOH}$ solutions have the same pH, they both have the same $\ce{[H3O+]}$ concentration and therefore the same $\ce{[HO^{-}]}$ concentration. Therefore, the two bases are the same strength as each creates a $\ce{[HO^{-}]}$ concentration equal to their initial molarities in water.
I think this response could be improved if the student mentioned the leveling effect and recognized how all bases stronger than hydroxide ion are "leveled." It's just like the high striker game at the fair; you can hit it hard enough to make the puck go all the way to the top, and so can someone else, but that doesn't necessarily mean you guys are equal in strength; it just means that the device quantifying strength doesn't differentiate between "strong" and "super strong."
Student 2's response
$\ce{S^{2-} + H2O ->HS- + HO-}$
From this equation and the problem statement, it is clear that $\ce{S^{2-}}$ hydrolyzes water to create a hydroxide ion concentration in water equal to its own initial molarity. Hydroxide ion isn't hydrolyzing water to create hydroxide; the below equation is non-sensical. Therefore, sulfide ion is the stronger base.
$\ce{HO^{-} + H2O ->H2O + HO-}$
Is the second equation really non-sensical?
Student 3's response:
The stronger base has the weaker conjugate acid.
Sulfide ion's conjugate acid is $\ce{HS-}$.
Hydroxide ion's conjugate acid is $\ce{H2O}$.
From the $\ce{K_{a}}$ table in the beginning of the lab manual, one knows that $\ce{HS-}$ is a weaker acid than $\ce{H2O}$. Therefore, sulfide is the stronger base.
• @Jan - my dilemma too; 1 starts off okay but makes the wrong conclusion. 3, however, I think is succinct and to the point. – Dissenter Jun 7 '16 at 17:02
• 3 is technically correct but it's hardly based on the information given in the question. The point made in 1 is complicated by the fact that the resulting species HS- also displays acid-base properties, in order to do it properly consult an analytical chem textbook, they will show you how to set up a system of equations to solve for the pKa. – orthocresol Jun 7 '16 at 17:15
• @orthocresol is the information in the question helpful? I think it's irrelevant at best and misleading at worst. – Dissenter Jun 7 '16 at 17:21
Equilibrium Expressions Related to the Solubility of the Sour Corrosion Product Mackinawite Ind. Eng. Chem. Res. 2008, 47, 1738-1742 compiles 18 different studies concerning the second Ka of H2S and shows that they vary over 7 orders of magnitude from $10^{-19}$ to $10^{-12}$
So firstly it isn't accepted whether or not Na2S is stronger than NaOH.
Putting that aside, the only way that 1M sulfide could yield 1 M hydroxide (and hence pH be equal to pH of 1 M hydroxide) is if sulfide was infinitely strong. If they were equally strong, it would only yield 0.5M hydroxide.
Student 1: clearly wrong.
Student 2: correct (based upon the information given)
Student 3: can't say without seeing the table, but if the table actually says that SH- is weaker than water than the answer is true, but not correct in the sense that the instructions say "Based on this information".
• what do you mean sulfide has to be infinitely strong? – Dissenter Jun 7 '16 at 17:49
• @Dissenter I mean sulfide would need to completely react with water to create hydroxide, with no sulfide remaining, for 1 mole of sulfide to yield 1 mole of hydroxide. – DavePhD Jun 7 '16 at 17:51
• oh I see now. The question accounted for that by writing that the two (1 M Na2S and 1 M NaOH) are "essentially" the same in terms of pH. – Dissenter Jun 7 '16 at 17:56
• What is the second Ka of water? – Dissenter Jun 7 '16 at 18:05
• – DavePhD Jun 7 '16 at 18:28
It does depend a lot on your marking scheme, but looking at it zealously I read two partial questions:
• Is the information given enough to discern the strength of either base? If yes, which parts led to the conclusion? If no, why can we not tell?
• Which base actually is stronger according to the information given.
The question attempts to ask within its own boundaries, so no previous knowledge of $\mathrm{p}K_\mathrm{a}$ values seems assumed.
A perfect answer should thus include the points:
• levelling effect of water, i.e. sulphide cannot be the weaker base or its pH value would be lower;
• It is impossible to tell whether $\ce{S^2-}$ is stronger or whether the two are equally strong.
Additional bonus points could then be given to answers like student 3’s which further add additional information such as the $\mathrm{p}K_\mathrm{a}$ values of $\ce{HS-}$ and $\ce{H2O}$.
Student 1’s explanation of base strength is incorrect, no questions asked. (Base strength is measured by $K_\mathrm{b}$ values.) The levelling effect is not present and apparantly not known. The conclusion is possible but incomplete.
Strictly speaking, this should probably be awarded zero.
Student 2 somehow starts talking about the levelling effect by mentioning that sulphide abstracts a proton from water to generate hydrogen sulphide and hydroxide. However, the water equation is far from nonsensical; it is an equilibrium that actually occurs on a molecular scale. The conclusion drawn may be chemically correct, but it is only semi-correct within the boundary of the question.
Maybe give him half of what you allocated for the levelling effect and nothing for the rest.
Student 3 gives chemically correct facts, but fails to address the problem in the question. Students should be taught to read the question, accept its premises, and then answer according to what is inside unless the question clearly asks for external knowledge.
We can give him a bonus mark for the knowledge to answer the question ‘extra-universally’, but the informatio I would be expecting is simply not there.
Also remember that you should generally give marks towards the lower end of the possible spectrum when correcting a test. Students are likely to come to their TAs to ask for better grading but very unlikely to say ‘but I got this completely wrong, please deduct the points.’
• The second student's comment about nonsensical is very similar to what the following journal article says: pubs.rsc.org/en/Content/ArticleLanding/1998/AN/… – DavePhD Jun 7 '16 at 18:14
• @DavePhD I reject that articles assumptions and conclusions. (Note that I never learnt a $K_\mathrm{a}$ of water being defined by the equation $\ce{H3O+ + H2O <=> H2O + H3O+}$; it was defined with the help of the autoprotolysis that the article later write to ‘correspond to a physical process.’) – Jan Jun 7 '16 at 18:39
• the article is saying that equation is for the Ka of H3O+, not the Ka of H2O – DavePhD Jun 7 '16 at 19:14
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2019-05-25 09:55:52
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https://socratic.org/questions/how-do-you-simplify-2-3-4-2
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# How do you simplify (2/3)^-4?
$= \frac{81}{16}$
${\left(\frac{2}{3}\right)}^{-} 4$
$= {\left(\frac{3}{2}\right)}^{4}$
$= \frac{81}{16}$
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2021-06-25 12:30:57
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https://www.atmos-meas-tech.net/12/3101/2019/
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Journal cover Journal topic
Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
Journal topic
Atmos. Meas. Tech., 12, 3101-3109, 2019
https://doi.org/10.5194/amt-12-3101-2019
Atmos. Meas. Tech., 12, 3101-3109, 2019
https://doi.org/10.5194/amt-12-3101-2019
Research article 12 Jun 2019
Research article | 12 Jun 2019
# Simultaneous detection of C2H6, CH4, and δ13C-CH4 using optical feedback cavity-enhanced absorption spectroscopy in the mid-infrared region: towards application for dissolved gas measurements
Towards application for dissolved gas measurements
Loic Lechevallier1,2, Roberto Grilli1, Erik Kerstel2, Daniele Romanini2, and Jérôme Chappellaz1 Loic Lechevallier et al.
• 1Univ. Grenoble Alpes, CNRS, IRD, Grenoble INP, IGE, 38000 Grenoble, France
• 2Univ. Grenoble Alpes, CNRS, LiPhy, 38000 Grenoble, France
Abstract
Simultaneous measurement of C2H6 and CH4 concentrations, and of the δ13C-CH4 isotope ratio is demonstrated using a cavity-enhanced absorption spectroscopy technique in the mid-IR region. The spectrometer is compact and has been designed for field operation. It relies on optical-feedback-assisted injection of 3.3 µm radiation from an interband cascade laser (ICL) into a V-shaped high-finesse optical cavity. A minimum absorption coefficient of $\mathrm{2.8}×{\mathrm{10}}^{-\mathrm{9}}$ cm−1 is obtained in a single scan (0.1 s) over 0.7 cm−1. Precisions of 3 ppbv, 11 ppbv, and 0.08 ‰ for C2H6, CH4, and δ13C-CH4, respectively, are achieved after 400 s of integration time. Laboratory calibrations and tests of performance are reported here. They show the potential for the spectrometer to be embedded in a sensor probe for in situ measurements in ocean waters, which could have important applications for the understanding of the source and fate of hydrocarbons from the seabed and in the water column.
1 Introduction
Methane (CH4) is the second most abundant anthropogenic greenhouse gas after carbon dioxide (CO2), but with a 25 times higher global warming potential. Monitoring and identifying the different sources of CH4 is therefore important, for the future climate projections. Among these sources, one can distinguish biogenic and abiogenic processes. Methane is mostly produced through biological processes, with the decomposition of organic matter under anoxic conditions. The abiogenic processes include biomass burning and thermal breakdown of organic molecules at high temperature in deep reservoirs. CH4 is the main component of natural gas, but heavier hydrocarbons (HCs) can also be present in natural gas such as ethane (C2H6) and propane (C3H8), depending on the gas origin. In addition the carbon isotopic composition of methane (δ13C-CH4 hereafter) differs between biogenic and abiogenic sources. While biogenic gas has a high concentration of CH4 with respect to heavier HCs and a more negative δ13C-CH4 (typically from −60 ‰ to −90 ‰), thermogenic gas is characterized by a lower ratio of CH4∕C2H6 and a less negative δ13C-CH4 signature (−50 ‰ to −40 ‰). The combination of these two measurements leads to a quite unambiguous identification of the origin of natural gas (Claypool and Kvenvolden, 1983). A significant part of Earth's HC reservoirs lies in marine environments, at variable depth below the seafloor. Questions arise about their origin and fate, and notably about their contribution through leakage into the ocean. Such leakage contributes to the carbon balance of the oceans, to acidification after oxidation in the water column, and possibly to the atmospheric concentration of these HCs if gas flaring from the seabed reaches the ocean surface. Therefore it is important to document the origin and fate of methane and ethane present below the seabed and dissolved in the water column, for process understanding and for future climate and ocean acidity projections.
Standard techniques for dissolved gas measurements usually rely on discrete sampling of the water column using Niskin bottles, followed by laboratory analysis. This method has the advantage of being simple and easy to set up, but it suffers from possible artifacts of the measurements due to outgassing of sample during the ascent (particularly for deep water samples). In addition, it offers a limited spatial and temporal resolution for probing the variability and mixing of water masses. Thanks to significant efforts in miniaturization of analytical instruments, from mass spectrometers (MSs) to optical techniques, in situ measurements of dissolved gas composition are feasible today (Chua et al., 2016; Grilli et al., 2018; Wankel et al., 2013). Due to the complexity and size of isotopic ratio mass spectrometers (IRMSs), today the application of in situ MS is limited to the measurement of the abundance of dissolved gas species, while the isotopic analysis is most often still performed in the laboratory. Conversely, modern optical spectrometers can offer similar performance for determining isotopic abundance as MSs, while being more compact and easier to use for in situ operations. Cavity-based techniques such as cavity ring-down spectroscopy (CRDS) and cavity-enhanced absorption spectroscopy (CEAS) offer detection of a variety of species, multispecies detection, and access to the isotopic signature of small compounds in gas mixtures (Kerstel, 2004).
The optical feedback cavity-enhanced absorption spectroscopy (OFCEAS) (Morville et al., 2003, 2014) used in this work is a well-known technique belonging to the family of CEAS and widely employed in trace gas detection and related fields (Butler et al., 2009; Grilli et al., 2014; Landsberg, 2014; Lechevallier et al., 2018; Richard et al., 2018; Romanini et al., 2006). It relies on the optical locking of the laser emission to a resonance mode of a high-finesse optical cavity and it has already been demonstrated for distributed feedback (DFB) lasers, quantum cascade lasers (QCLs) (Gorrotxategi-Carbajo et al., 2013; Maisons et al., 2010), and interband cascade lasers (ICLs) (Manfred et al., 2015; Richard et al., 2016). In this work we report a novel application for the simultaneous measurement of C2H6, CH4, and δ13C-CH4, using an ICL radiation source in the mid-IR region that could be applied to the in situ measurement of these compounds in seawater.
2 Method
The OFCEAS spectrometer (Fig. 1) is composed of an ICL diode laser (from Nanoplus GmbH), an infrared polarizer (ColorPol MIR), two aluminum steering mirrors, and two photodiodes (PCI-2TE-4), all mounted on a stainless-steel optical cavity block. The V-shaped cavity (6 mm internal channel diameter) is composed of two 40 cm long arms, resulting in a free spectral range (FSR) of the optical cavity of 187.4 MHz. The cavity mirrors (Lohnstar Optics) have a reflectivity of 99.9584 %, which provides a ring-down time (lifetime of the photons inside the resonator) of 3.20 µs (∼1 km optical path length) in absence of intracavity absorption (i.e., if the cavity is filled with zero air). This design allows for feeding back to the laser only the photons that are in resonance with the cavity, without any parasitic feedback, such as that from reflections off the entrance mirror. This modifies the laser dynamics, leading to spectral narrowing of the laser emission and forcing its oscillation to match the cavity resonance frequency (Morville et al., 2005). The optical feedback phase matching condition imposes that the laser is placed at a distance from the input mirror equal to an integer number of cavity-arm lengths (in this case equal to one). Fine phase adjustment and continuous phase lock are obtained by a piezoelectric transducer (PZT) mounted on one of the two injection steering mirrors. The phase error was retrieved by analyzing the symmetry of the cavity modes during the acquisition, as explained in Morville et al. (2005). The diode laser is stabilized in temperature and a current ramp is applied in order to produce a scan over a narrow frequency region (typically a few tenths of a nanometer, with a scanning rate of ∼0.2 nm × mA−1 for ICL lasers) and to temporarily lock the laser emission to successive TEM00 longitudinal cavity transmission modes. The interest of the technique is to achieve high signal-to-noise ratio thanks to the narrowing of the laser emission and therefore to a more efficient power coupling to the high-finesse cavity. It also provides an intrinsically linear frequency scale fixed by the cavity geometry (FSR $=c/\left(\mathrm{2}NnL\right)$), where c is the speed of light, L the cavity arm length, N the number of arms, and n the index of the media. The instrument simultaneously records the signal from the two photodiodes (before and after injection) in order to obtain transmission spectra that are subsequently converted to absorption units (absorption coefficients as a function of cavity transmission frequency or wavelength) using a measurement of the ring-down time performed at the end of each scan (Morville et al., 2014). This ring-down event is produced by rapidly switching off the laser emission and acquiring the exponential decay of the light leaking out of the cavity.
Figure 1Details of the optical setup with the laser injection and phase control (piezo mounted on the injection steering mirror assembly). The polarizer is tilted and its reflection used for acquiring the laser power spectrum before the cavity injection. At the cavity output, a spherical mirror is used to focus the light on the second (signal output) photodiode.
An OFCEAS spectrum acquisition covers more than 100 longitudinal cavity modes (0.7 cm−1) and is repeated at a rate of 10 Hz. For a precise retrieval of the absorption profile, and therefore of the molecular density in the cell, the cavity is precisely temperature and pressure stabilized at respectively ∼308.15 K and 30 mbar. The cell is heated by two resistive heating bands controlled via a proportional–integral–derivative (PID) regulation and a PT1000 sensor positioned at the center of the cell, glued on the stainless-steel block. A second PID loop is used for pressure regulation by acting on a solenoid proportional valve (FAS, Norgren Fluid Controls). The inner pressure in the optical cell is measured by a Wika 0–250 mbar pressure gauge. The temperature and current of the laser and the temperature and pressure of the cell are controlled by a single electronic card developed by the company AP2E, which, by means of a microprocessor, also ensures the fast acquisition of the two photodiode signals (340 kHz per channel). The cavity with the optical assembly, reported in Fig. 1, is suspended by two vibration-isolation dampers and placed in an insulated aluminum casing.
3 Spectral region and model fit
In the infrared region, two fundamental bands are available for detecting CH4: the ν3 mode between 2800 and 3100 cm−1 and the ν4 mode from 1200 to 1300 cm−1. Several reasons make the ν3 transition more suitable for trace gas sensing, and notably, (1) ICLs are today available at this wavelength and they require less effort to cool compared to room-temperature QCLs, and (2) photodetectors have better sensitivity in this spectral region. For this work, the selected laser is centered at 3.325 µm and operates between 8 and 12 C, allowing it to cover the spectral region from 3005.4 to 3009.2 cm−1. This region has been selected to best accommodate the absorption intensities of the species to be detected at a specific range of concentrations (around 200 ppmv for CH4 and 30 ppmv for C2H6) and for the possibility to access the “best” isolated absorption lines. For applications in dissolved gas measurements, the selected wavelength region offers access to water absorption lines, required for the characterization of the dissolved gas extraction system (Grilli et al., 2018).
The selected absorption window reports a relatively large overlap of absorption features, requiring a rigorous optimization of the fit parameters. Here, a multicomponent fit routine is used where line parameters (intensity, position, Lorentzian and Gaussian widths, and the νVC parameter for collision-induced velocity change inducing a so-called Dicke narrowing; Dicke, 1953) are fitted for each absorption transition using a speed-dependent Rautian profile (Varghese and Hanson, 1984). A total number of 46 absorption lines are included in the fit, with 17, 3, 23, and 3 lines for 12CH4, 13CH4, C2H6, and H2O, respectively. In order to reduce the degrees of freedom of the fitting routine and allow a real-time fit for each acquired spectrum, some of the parameters have been pre-optimized and fixed or linked together. The remaining free parameters are (1) the spectrum position, for which the positions of all lines are linked together and only one parameter (which corresponds to the mode shift) is used to adjust the fit with respect to the acquired spectra; (2) the four intensities of 12CH4, 13CH4, C2H6, and H2O from which concentrations are retrieved, and all lines belonging to one of these molecules are fixed in relative intensity to pre-optimized values, with a single intensity scaling parameter for all of them; (3) the coefficients of the polynomial function for drawing the baseline of the fit (here corresponding to three parameters for a second-order polynomial function); (4) one extra parameter can be added per optical fringe that the operator may want to fit. In this case we only have one optical fringe, which has been identified between the output cavity mirror and the signal photodiode. The Gaussian and Lorentzian widths as well as the νVC parameter for Dicke narrowing are optimized line by line and then fixed to their optimum values. The total number of free parameters for the fit is nine for a spectrum composed of 48 individual points. A typical spectrum is reported in Fig. 2 for concentrations of 72 ppmv of methane and 20 ppmv for ethane in dry air. The temperature and pressure of the cell are 35 C and 30 mbar, respectively. The fit is optimized using an interlaced spectrum in order to increase the spectral resolution. The latter is obtained by linearly slightly scanning the temperature of the cavity (0.02 C of excursion), which causes a shift of the cavity mode positions with respect to the absorption lines, due to the mechanical elongation of the cell together with a change in the refractive index of the gas sample. This interlacing is only used for fit optimization, while in normal operation the spectra are only composed by data points separated by the cavity FSR (187.4 MHz) with a total of 48 fitted spectral points. The interlacing is computed by a custom LabVIEW routine that recognizes after how many consecutive spectra a complete scan of the cavity FSR is complete. The spectra are then homogeneously distributed within the one FSR span to originate the interlaced spectrum. For the spectrum of Fig. 2 (experimental data: black and green lines), 200 consecutive spectra are interlaced to achieve a resolution of 935 kHz. In Fig. 2a, the 12CH4 and 13CH4 (red and blue spectra, respectively) are the simulated spectra according to the HITRAN 2016 database (Gordon et al., 2017). This has been carried out for a clearer visualization of the line positions of the two isotopologues. A disagreement between experimental data and the HITRAN database was found for the two superposed lines of 12CH4 at 3008.39 cm−1, which are 16.5 % weaker in amplitude in the simulated spectra with respect to the experimental data. The arrows indicate the best isolated absorption lines, which are used for calculating the isotopic ratio of methane (red and blue spectra) and the ethane concentration (green spectrum). Optical interference fringes are visible on the baseline, with the major fringe corresponding to the optical path between the output cavity mirror and the photodiode. Improvement in the photodiode alignment and the use of an additional spherical mirror at the cavity output for focusing the light into the detector (as shown in Fig. 1) significantly decreased the amplitude of the optical fringe.
Figure 2(a) A combination of experimental interlaced spectra and spectra simulated using the HITRAN 2016 database at 30 mbar and 35 C. HITRAN profiles show the position of 12CH4 (red) and 13CH4 (blue) at 72 ppmv of CH4 in dry air. In green is the interlaced spectrum acquired with only 20 ppmv of C2H6 in dry air in the cavity. The full experimental spectrum containing absorptions from the three species is reported in black. There is a disagreement for the two superimposed lines at 3008.39 cm−1, with a line intensity discrepancy between experimental data and the HITRAN 2016 database of ∼16 % on the amplitude of the absorption lines (this is outside the reported HITRAN 2016 uncertainties on the cross sections that are between 2 % and 5 %). (b) An example of an OFCEAS spectrum (black circles) and the corresponding interlaced methane–ethane absorption spectrum and its residue (blue lines). At the bottom, the residuals of the OFCEAS spectral fit for one acquisition (0.1 s) and the baseline curve (red) (generated by the fit) are reported.
The standard deviation of the fit residuals for the spectrum obtained with 72 ppmv of methane and 20 ppmv of ethane in dry air is $\mathrm{5.8}×{\mathrm{10}}^{-\mathrm{8}}$ cm−1 for a single acquisition, which corresponds to a precision of 140 ppbv, 1.3 ppbv, 37 ppbv, and 1.5 ‰ for 12CH4, 13CH4, C2H6, and δ13C-CH4, respectively. For the determination of the precision of 13CH4, its natural abundance was taken into account. A contribution from small imperfections of the fit parameters is still present since the standard deviation of the absorption baseline in absence of absorber (i.e., cavity filled with 30 mbar of zero air) is $\mathrm{2.8}×{\mathrm{10}}^{-\mathrm{9}}$ cm−1 for a single acquisition. A more comparative way of describing the performance of the instrument consists of defining the figure of merit normalized by the square root of the bandwidth of the measurement (10 Hz) and the number of spectral elements (48) (Moyer et al., 2008). This leads to a figure of merit (noise equivalent absorption sensitivity, NEAS) of $\mathrm{1.28}×{\mathrm{10}}^{-\mathrm{10}}$ cm−1 Hz${}^{-\mathrm{1}/\mathrm{2}}$ per spectral element without account for fit imperfections and $\mathrm{2.6}×{\mathrm{10}}^{-\mathrm{9}}$ cm−1 Hz${}^{-\mathrm{1}/\mathrm{2}}$ per spectral element for a typical spectrum of 72 ppmv of CH4 and 20 ppmv of C2H6 in dry air.
4 Results: the performance of the spectrometer
The stable carbon isotopic ratio (δ13C) is normally expressed as a comparative measurement with respect to an international reference, in this case Vienna Pee Dee Belemnite (VPDB, for the Belemnitella americana fossil carbonate). It is described by Eq. (1), in which R is the abundance ratio of each isotopologue in the sample material, and RVPDB the corresponding abundance ratio in the standard material. In the linear absorption regime, the number density of the molecule is proportional to the absorption and related to it via the absorption cross section. Therefore, the retrieval of the isotope ratio with respect to a standard gas of known isotopic composition is relatively straightforward (Kerstel, 2004). The δ13C-CH4 gas standards used for the experiments are from Isometric Instruments and certified on the VPDB scale with an uncertainty of ±0.2 ‰.
$\begin{array}{}\text{(1)}& {\mathit{\delta }}^{\mathrm{13}}\mathrm{C}=\left(\frac{R}{{R}_{\mathrm{VPDB}}}-\mathrm{1}\right)R=\phantom{\rule{0.125em}{0ex}}\frac{{}^{\mathrm{13}}\mathrm{C}}{{}^{\mathrm{12}}\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\end{array}$
Because of the complexity of the spectral fit and the discretization on the wavelength or frequency scale dictated by the cavity FSR, the position of the cavity modes with respect to one of the absorption lines affects the results of the fit. This is due to small imperfections of the fit model relative to the real spectrum, which is sampled by the cavity modes. As these move and trace out the real spectrum profile, the model spectrum defects translate into varying errors or biases of the fit parameters, which are optimized to match the model to the data at each time. We thus observed a dependency of the retrieved line surfaces (areas underneath the absorption line) on the cavity mode positions with respect to the absorption features, which affects the isotope ratio determination (also observed and discussed in Favier, 2017). The drift in the cavity mode position is mainly due to mechanical instability and temperature fluctuations. Pressure may also play a role: even if stabilized at ±10µbar the sensor may experience drifts with respect to the absolute pressure due to, for instance, fluctuations of temperature. In order to compensate for these drifts, we locked the cavity modes' position to the absorption lines' position by dynamically acting on the cavity temperature. The aim of the lock is not to better stabilize the cavity temperature, but to act on this temperature regulation in order to always maintain the cavity comb at the same position with respect to the position absorption lines and compensate for electronic drifts occurring on the circuit for reading pressure and temperature of the cavity. Figure 3 reports long-term measurements for two situations: in red, where the temperature of the cavity is stabilized at 35 (±0.0015) C and the cavity modes are free to move, and in black, where the cavity modes are locked by acting on the temperature set point (the shift reported corresponds to the megahertz-sized excursion of the cavity modes with respect to the absorption feature). Measurements were obtained by continuously flushing the cavity at a gas flow of 10 sccm (standard cubic centimeters per minute) with a sample containing 72 ppmv of CH4 and 20 ppmv of C2H6 in dry air.
Figure 3A comparison of the performance on the measurement of the δ13C-CH4 with (black) and without (red) the lock of the position of the cavity modes. Without the locking the temperature is stabilized at 35±0.0015C and the mode position drifts by about 20 MHz h−1. By locking the mode positions acting on the temperature set point, the mode positions are stabilized to 620 kHz. The advantage of the locking configuration is visible in the log–log plot, where the AW standard deviation of the δ13C-CH4 signal is shifted to slightly lower values, with a longer averaging-time stability. Both measurements were performed by continuously flushing the cavity with a 10 sccm gas flow of a synthetic air mixture containing 72 and 20 ppmv of CH4 and C2H6 in dry air, respectively.
Without the locking of the cavity modes' position we observed a drift of 20 MHz h−1 of the cavity modes, while with the servo loop a stabilization of the mode positions better than 620 kHz was obtained. In the unlocked dataset, a fluctuation in the temperature stabilization occurred around 17:30 local time, and the corresponding section of data has been removed for the analysis. The spectral fit was conducted for both situations and an Allan–Werle (AW) statistical analysis (Werle, 2010) was performed on the δ13C-CH4 signal (Fig. 3). From the log–log plot, where the AW standard deviation (σAW-SDδ13C) is plotted against the averaging time (t), a 10-fold improvement of the long-term stability was observed, which translates into an extension of the optimum integration time of the system for the case of temperature locking of the cavity mode positions.
Afterwards, the system was further improved with a better optimization of the fitting parameters and of the optical setup, resulting in a reduction of the optical interference fringes. A second AW statistical analysis was therefore conducted on the simultaneous detection of δ13C-CH4, 12CH4, and C2H6 with the same experimental conditions as for Fig. 3. More than 4 h of continuous measurements were used to produce the log–log plot (Fig. 4). At short times, the measurement is mainly dominated by white noise with the σAW-SD decreasing proportionally to t−0.5. The optimum integration time corresponds to 400 s, reaching precisions of 0.08 ‰, 11 ppbv, and 3 ppbv for δ13C-CH4, 12CH4, and C2H6, respectively. For longer integration times, due to the rise of 1∕f noise (drifts), the σAW-SD starts to increase, leading to a degradation of the precision. In order to fix the accuracy of the instrument at its optimal precision below 0.1 ‰ for δ13C-CH4, injection of a standard gas with a known isotopic composition should thus occur every 400 s. This allows us to overcome the instrumental drifts and to maintain the accuracy of the measurement at about the same level of precision obtained at the optimum integration time. If not, instrument drifts will dominate with a degradation of the accuracy as reported and explained below. A comparison of the two statistical analyses for the δ13C-CH4 measurements (between Figs. 3 and 4) highlights how the improvement on the optical setup allowed us to shift the entire AW curve to lower values (with a decrease in the σAW-SD by a factor of 4); however we could not obtain the long integration time as reported in Fig. 3. This is probably due to the fact that the arise of frequency-dependent noise is dominated by other instabilities, limiting the best precision of the δ13C-CH4 to a value close to 0.1 ‰. Nevertheless, the benefit of the improvements is clearly visible, with the improved setup approaching the same precision as the previous one 10 times faster.
Figure 4The Allan–Werle standard deviation for a 4 h time series of measurement with 73.7 ppmv of methane (black) and 19 ppmv of ethane (blue) in dry air. The best integration time of the system corresponds to ∼8 min and the achieved precision is 0.08 ‰, 11 ppbv, and 3 ppbv for δ13C-CH4, 12CH4, and C2H6, respectively.
In Fig. 5, the dependency of the isotopic ratio with the concentration of methane is reported. This dependency is not caused by isotopic fractionation due to the sample handling, but more probably related to the discretization of the spectra and the precise location of the measurement points with respect to residual optical fringes in the spectrum. The tendency is well reproducible, can be fitted with an exponential function, and can be used for calibration proposes. The same behavior was also observed using the same technique but for H2O and H2S isotopic measurements (Favier, 2017; Landsberg, 2014), as well as with an instrument based on off-axis integrated cavity output spectroscopy (ICOS), as reported by Wankel et al. (2013). With a comparable amplitude variation in the absorption intensity, a similar effect (but less pronounced) was also observed with respect to C2H6 concentrations. By monitoring the carbon isotopic ratio of methane with and without 22.5 ppmv of ethane in the gas mixture, a difference in the δ13C-CH4 of 2.55 ‰ was observed. For this relatively small effect, a linear correction was applied.
The reproducibly of the system was estimated by conducting three measurements per day for 4 d at two methane concentrations (9 and 90 ppmv in dry air). Before each measurement the system was completely switched off. No calibration using a standard gas was carried out before each measurement. Therefore, the resulting reproducibility corresponds to the intrinsic accuracy of the system affected by long-term instabilities. Results are represented by the two histograms of Fig. 5 showing the reproducibility for δ13C-CH4, which is reported on a relative scale (i.e., with respect to an arbitrary reference value). At CH4 concentrations of 9 and 90 ppmv the isotopic ratio is retrieved with an accuracy of ±11.8 ‰ and ±2.9 ‰, respectively (both 1σ). By injecting a standard gas before each measurement for calibration proposes, the accuracy at high concentrations should approach the expected precision of < 0.1 ‰ after 5 min of integration.
Table 1Non-exhaustive comparison between some of the existing techniques for measuring δ13C-CH4.
Figure 5(c) The dependency of the relative δ13C-CH4 on the CH4 concentration. (a, b) Reproducibility between discrete measurements made three times a day for 1 week for 9 and 90 ppmv of CH4 in dry air. Accuracies of ±11.8 ‰ and ±2.9 ‰ (represented by the dashed lines) were obtained for the two concentrations (1σ). The instrument was not calibrated before each measurement using a gas standard. For high concentrations, such calibration would make the accuracy approach the expected precision of 0.08 ‰ after 5 min of integration time.
For the purpose of further validating the stability of the system, long-term measurements were made while regularly switching between two samples with different isotopic composition. The two standard mixtures that were used had a composition of 79.4 ppmv of CH4, with a carbon isotopic composition of −54.5 ‰, and of 56.9 ppmv with δ13C-CH4$=-\mathrm{38.3}$ ‰ (with manufacturer certified uncertainties of ±0.2 ‰). The gas flow was fixed at 2 sccm and the standard gas samples were switched every 5 min for 3 h using a manual three-way two-position valve. In Fig. 6, the measurements of the carbon isotopic ratio are reported. Since the two samples had different CH4 contents, a correction following the curve reported in Fig. 5 was applied in order to account for the dependency of δ13C on the CH4 concentration. The −38.3 ‰ sample was employed as the “known” standard gas, and the isotopic composition of the second sample was then retrieved. Drifts on the isotopic signature of only 0.6 ‰ were observed after 3 h of continuous measurements (which is in agreement with the AW analysis). The response time of the instrument at 2 sccm gas flow is estimated to be 15 s (single exponential), entirely attributed to the renewal of the gas sample in the measurement cell. The standard deviation of the raw measurement (at 10 Hz) is ±1.9 ‰, while after averaging the results over 20 s (blue curve) the noise decreases to ±0.5 ‰.
Figure 6Long-term measurements obtained by repeatedly switching between two methane samples in dry air having different stable carbon isotopic composition. The two samples are diluted gas standards from Isometric Instrument with specified δ13C-CH4 of $-\mathrm{54.5}±\mathrm{0.2}$ ‰ (79.4 ppmv) and $-\mathrm{38.3}±\mathrm{0.2}$ ‰ (56.9 ppmv).
5 Comparison with existing instruments
Depending on the application, different instrumental developments with a focus on a particular analytical aspect were carried out in the past. For instance, the concentration range will vary depending on the application: a high sensitivity to measure in the low concentration range is required for environmental sensing (e.g., atmospheric measurements, paleoclimatology), while moderate sensitivity is required to measure in the high concentration range for dissolved gas measurements in seawater, leak detection, and oil and natural gas exploration. Some applications would require low sample volumes (such as ice core and dissolved gas analyses). Finally, different constraints such as compactness, robustness, and power consumption may play a role depending on the measurement strategy (laboratory, on site, or in situ measurements). For this propose, a non-exhaustive comparison with some of the existing techniques for measuring δ13C-CH4 is reported in Table 1. The comparison highlights similar performances, albeit for different conditions, with precisions on δ13C-CH4 below 1 ‰. Up to now, the best performance in terms of precision and the amount of sample required remains the IRMS technique, followed by the CRDS system developed by Picarro (Phillips et al., 2013; Schmitt et al., 2014). The QCLAS system of Eyer et al. (2016) based on a multi-pass cell, the ICOS from Los Gatos Research (Wankel et al., 2013), and the work reported here are more suitable for high methane concentrations. Our development aims at the measurement of dissolved gas in seawater, and therefore was optimized for relatively high methane concentrations of ∼100 ppmv, achieving precision on the δ13C-CH4 below 1 ‰ after 1 s. This development sets itself apart by its compactness and portability as required for in situ measurements. Moreover, thanks to the low volume of the measurement cell, a small amount of sample (< 1 cm3 of gas at STP) is required, making the spectrometer suitable for coupling to a membrane-based extraction system for in situ application in the water column under marine conditions.
6 Conclusions
In this work we presented a novel optical spectrometer, operating in the mid-IR region and based on the OFCEAS technique, for simultaneous measurement of C2H6 and 12CH4 concentrations and δ13C-CH4. The spectrometer achieved a minimum absorption coefficient of $\mathrm{2.8}×{\mathrm{10}}^{-\mathrm{9}}$ cm−1 over a single frequency scan (0.1 s) over 0.7 cm−1 at low levels of CH4 and C2H6 and $\mathrm{5.8}×{\mathrm{10}}^{-\mathrm{8}}$ cm−1 for a more typical gas mixture (72 ppmv of CH4 and 20 ppmv of C2H6). Precisions of 3 ppbv, 11 ppbv, and 0.08 ‰ for C2H6, 12CH4, and δ13C-CH4, respectively, were demonstrated for an optimum integration time of 400 s. A stability of ±2.9 ‰ for long-term measurements of δ13C-CH4 was obtained without the need of regular injection of known isotopic composition standard gas. The latter is needed if an accuracy of the δ13C-CH4 measurement at the level of 0.1 ‰ is required. The dependency of the isotopic measurement on the composition of the gas mixture was characterized, with calibration curves for both CH4 and C2H6 concentration dependencies. The instrument has the required characteristics of compactness, precision, and time resolution to be coupled with a dissolved gas extraction system and to be integrated in an in situ sensor for continuously monitoring the dissolved gas composition in deep-sea and oceanic environments. A dissolved gas extraction system similar to the one described by Grilli et al. (2018) will provide an adjustable dilution of the gas sample by adding a zero-air carrier gas at the dry side of the extraction unit, therefore increasing the dynamical range of the sensor.
Data availability
Data availability.
The underlying data require proprietary software and specific knowledge (spectroscopy and technical) of the spectral analysis. This makes it rather useless to make the raw data available to users not involved in the current study. Authors will however respond timely to all motivated requests for data sharing.
Author contributions
Author contributions.
LC developed the optical spectrometer and performed the measurements under the supervision of RG and JC. DR and EK contributed prior knowledge, especially to the stabilization of the cavity mode position and the spectral analysis. All authors contributed to the writing and reviewing.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Special issue statement
Special issue statement.
Acknowledgements
Acknowledgements.
The research leading to these results has received funding from the European Community's Seventh Framework Programme ERC-2015-PoC under grant agreement no. 713619 (ERC OCEAN-IDs). The work was made possible thanks to pioneering investigations conducted under the European Community's Seventh Framework Programme ERC-2011-AdG under grant agreement no. 291062 (ERC ICE&LASERS) and with support from SATT Linksium of Grenoble, France, and of the Service Partenariat & Valorisation (SPV) of the CNRS. The authors thank the AP2E company and particularly Kevin Jaulin for exchanges regarding the spectrometer development.
Financial support
Financial support.
This research has been supported by the European Research Council (grant OCEAN-IDs (713619)) and the European Research Council (grant ICE&LASERS (291062)).
Review statement
Review statement.
This paper was edited by Katherine Manfred and reviewed by two anonymous referees.
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https://erikreinertsen.com/erisone/
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## Set up data science stack on ERISOne
ERISOne is a “computing cluster with a job scheduling system for batch jobs, remote desktops for graphical applications and GPUs running on a Linux OS” maintained by Partners Healthcare.
Ideally, users do not need to purchase and maintain compute workstations. Rather, we use Macbooks to connect to a cluster behind the Partners firewall, This is ideal for working on a shared data repository, especially since we analyze PHI.
Unfortunately, setting up a modern data science stack on ERISOne is challenging. Many software packages are old, and obtaining desired memory, GPU, and CPU resources on a compute node requires additional steps.
This guide walks you through setup of Zsh, git, and more. It assumes you requested and have an ERISOne account, and connect via SSH (see RISC guide here).
Follow the steps in order. For example, you should install git before oh-my-zsh because the commands for oh-my-zsh require a recent version of git.
## Install zsh shell
ERISOne comes with zsh 4.3.11, but the current version is 5.8. Users lack root access on ERISOne and cannot install zsh via yum.
Note: you may need to first install ncurses from source.
This means we have to install zsh from source:
(base) -bash-4.1$curl -L https://downloads.sourceforge.net/project/zsh/zsh/5.8/zsh-5.8.tar.xz > zsh.tar.xz (base) -bash-4.1$ tar xf zsh.tar.xz
(base) -bash-4.1$cd zsh (base) -bash-4.1$ ./configure --prefix="$HOME/local" \ CPPFLAGS="-I$HOME/local/include" \
LDFLAGS="-L$HOME/local/lib" (base) -bash-4.1$ make -j && make install
Now that zsh is installed, let’s change our default logging shell. However, users on ERISOne do not have root, and thus cannot use chsh.
export PATH=$HOME/local/bin:$PATH
export SHELL=which zsh
[ -f "$SHELL" ] && exec "$SHELL" -l
source ~.bash_profile to make the changes take effect. Now zsh will be activated each time you log in to ERISOne.
The next time you log in, you will be prompted to set up the zsh shell. The prompt should look different:
[ab123@eris1n3]~%
Delete source files from your home directory:
[ab123@eris1n3]~% rm -rf ~/zsh*
If you log out and back in, your shell should look much improved:
## Load git, tmux, & vim via module
ERISOne has git 1.7.1 by default, which was released in 2010. Subsequent installation of oh-my-zsh involves a shell script that invokes -c in git clone, which was introduced in git 1.7.7. Thus, we must upgrade git.
You can install git from source, but there are many other dependencies, so doing this would take a lot of effort.
Instead we can get a sufficiently recent (albeit not most current) version of git using the load command of module:
Check if a more recent version of MODULE_NAME is available via module avail MODULE_NAME.
## Install Anaconda
The newest version of Anaconda on ERISOne (via module) is 4.4.0-p3, whereas the current Linux version is 4.8.3. Ideally, one would use the existing Anaconda module on ERISOne and set up a new environment with the desired Python version and packages. Unfortunately, there is an error with older versions of Conda that prevents users from even creating new environments:
RemoveError: 'setuptools' is a dependency of conda and cannot be removed from conda's operating environment.
To set up the desired Python environment, install Miniconda following the instructions in my Linux setup post.
Like most Linux machines, ERISOne uses the bash shell by default. Therefore Conda will modify /.bashrc with the appropriate path for you to call conda. However, only /.bash_profile is called when you log in to ERISOne.
To ensure Conda is on your path so you can call conda, source /.bashrc in /.bash_profile:
echo 'export source ~/.bashrc' >> ~/.bash_profile
After you install Anaconda, log out, and log back in ERISOne, your command line prompt should reflect that you are now using the base environment:
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2020-09-22 12:12:07
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https://reaction-networks.net/wiki/Mass-action_kinetics
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# Mass action kinetics
(Redirected from Mass-action kinetics)
Mass action kinetics is a kinetic scheme for chemical reaction networks which says that the rate of a chemical reaction is proportional to the product of the concentrations of the reacting chemical species. It was first formulated by Cato Maximilian Guldberg and Peter Waage in the 1860's [1]. It remains one of the most common kinetic assumptions used by chemists, biologists, and mathematicians.
## Deterministic modeling
In the ordinary differential equation modeling of chemical reaction networks, the assumption of mass-action kinetics produces polynomial vector fields. For example, consider the reaction given by
$A + B \rightarrow C.$
If we let $[A]$ and $[B]$ denote the concentrations of A and B respectively, then the reaction occurs at a rate proportional to $[A][B]$. That is to say, we have
$[\mbox{rate of reaction}] \propto [A][B] \; \; \; \; \; \mbox{ or } \; \; \; \; \; [\mbox{rate of reaction}] = k [A][B].$
where $k>0$ is the (fixed) proportionality rate (or rate constant) associated with the reaction. Since each instance of the reaction produces a net decrease of one molecule of A and B each, and an increase of one molecule of C, we can model the reaction as
$\begin{array}{rcl} \frac{d[A]}{dt} & = & -k[A][B] \\ \frac{d[B]}{dt} & = & -k[A][B] \\ \frac{d[C]}{dt} & = & k[A][B]. \end{array}$
## References
1. C.M. Guldberg and P. Waage, Studies Concerning Affinity, C. M. Forhandlinger: Videnskabs-Selskabet i Christiana (1864), 35
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2018-12-15 23:35:59
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https://socratic.org/questions/58890afb11ef6b1263a64e8a
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# For an arbitrary nonelectrolyte, calculate the freezing point when "0.0192 mols" of it is dissolved in "5.00 g" of water? K_f = 1.86^@ "C/m" for water.
Jan 26, 2017
$- {7.14}^{\circ} \text{C}$.
The idea is that dissolving anything into a solvent will decrease its freezing point. It is expected that you already know ${T}_{f}^{\text{*}}$ for water is ${0}^{\circ} \text{C}$, i.e. the freezing point of the pure solvent water. Therefore, you are solving for the final, lowered freezing point.
Recall:
$\Delta {T}_{f} = {T}_{f} - {T}_{f}^{\text{*}} = - i {K}_{f} m$
where:
• $i = 1$ is the van't Hoff factor for a non-electrolyte. It simply says that only one nonelectrolyte particle exists for every nonelectrolyte particle that is placed into solution.
• ${K}_{f} = {1.86}^{\circ} \text{C/m}$ is the freezing point depression constant for water.
• $m$ is the molality of the solution, i.e. $\text{mol solute"/"kg solvent}$.
• ${T}_{f}$ is the freezing point of the solution.
• ${T}_{f}^{\text{*}}$ is the freezing point of the pure solvent.
First, calculate what $\Delta {T}_{f}$ would be:
DeltaT_f = -(1)(1.86^@ "C/m")(("0.0192 mols solute")/(5.00xx10^(-3) "kg H"_2"O"))
$= - {7.14}^{\circ} \text{C}$
Therefore, the final freezing point is:
color(blue)(T_f) = DeltaT_f + T_f^"*" = -7.14^@ "C" + 0^@ "C" = color(blue)(-7.14^@ "C")
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2021-04-11 10:09:13
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https://www.vedantu.com/question-answer/find-the-number-of-sevendigit-integers-with-sum-class-11-maths-cbse-5efc6585fc7b62454bf5e602
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QUESTION
# Find the number of seven-digit integers, with sum of the digits equal to 10 and are formed by using the digits 1, 2 and 3 only? (A) 55 (B) 66 (C) 77 (D) 88
Hint- The question requires the concept of permutation and combination. In this question, first we will try to make different cases for seven-digit integers such that the sum of its digits is 10 and the digits are 1, 2 and 3 only. After that we will calculate the number of ways in which each case can be arranged.
Complete step-by-step solution -
Now, seven places need to be filled with 1, 2 or 3 and the sum of the digits needs to be 10.
_ _ _ _ _ _ _
Let us consider the case 1,
1 1 1 1 1 2 3
Here the sum of digits is equal to 10.
Now, consider the case 2,
2 2 2 1 1 1 1
Here the sum of digits is equal to 10.
Now, number of ways of arrangement of case 1 $= \dfrac{{7!}}{{5!}} = \dfrac{{7 \times 6 \times 5!}}{{5!}} = 7 \times 6 = 42$
Also, the number of ways of arrangement of case 2
$= \dfrac{{7!}}{{3!4!}} = \dfrac{{7 \times 6 \times 5 \times 4!}}{{3!4!}} = \dfrac{{7 \times 6 \times 5}}{{3!}} = \dfrac{{7 \times 6 \times 5}}{{3 \times 2}} = \dfrac{{7 \times 6 \times 5}}{6} = 7 \times 5 = 35$
Now, total number of seven-digit numbers formed = number of ways of arrangement of case 1 + number of ways of arrangement of case 2
$= 42 + 35 = 77$
Note- In these types of questions, always try to obtain different possible ways (cases) and their arrangement using permutation, half of the question will be solved by then. Also, No. of ways of permutations is denoted by ${}^n{P_r}$ where n represents the number of items to choose from, P stands for permutations and r stands for how many items we are choosing. Formula to calculate ${}^n{P_r}$ is ${}^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}}$
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2020-07-06 00:16:23
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http://citizendia.org/Petroleum
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Pumpjack pumping an oil well near Lubbock, Texas
Petroleum (L. petroleum < Gr. πετρέλαιον lit. “Nodding donkey” redirects here For the train see British Rail "Pacer". Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly "rock oil" was first used in 1556 in a treatise published by the German mineralogist Georg Bauer, known as Georgius Agricola. Georgius Agricola ( March 24, 1494 – November 21, 1555) was a German scholar and scientist [1]) is a naturally occurring, flammable liquid found in rock formations in the Earth consisting of a complex mixture of hydrocarbons of various molecular weights, plus other organic compounds. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 In Organic chemistry, a hydrocarbon is an Organic compound consisting entirely of Hydrogen and Carbon. An organic compound is any member of a large class of Chemical compounds whose Molecules contain Carbon.
## Composition
The proportion of hydrocarbons in the mixture is highly variable and ranges from as much as 97% by weight in the lighter oils to as little as 50% in the heavier oils and bitumens. Bitumen is a mixture of organic Liquids that are highly Viscous, black sticky entirely soluble in Carbon disulfide, and composed primarily
The hydrocarbons in crude oil are mostly alkanes, cycloalkanes and various aromatic hydrocarbons while the other organic compounds contain nitrogen, oxygen and sulfur, and trace amounts of metals such as iron, nickel, copper and vanadium. Alkanes, also known as Paraffins are Chemical compounds that consist only of the elements Carbon (C and Hydrogen (H (i Cycloalkanes (also called naphthenes, especially if from Petroleum sources are types of Alkanes which have one or more rings of Carbon Atoms Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 The exact molecular composition varies widely from formation to formation but the proportion of chemical elements vary over fairly narrow limits as follows:[2]
Carbon 83-87% Hydrogen 10-14% Nitrogen 0. A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. 1-2% Oxygen 0. 1-1. 5% Sulfur 0. 5-6% Metals <1000 ppm
Crude oil varies greatly in appearance depending on its composition. It is usually black or dark brown (although it may be yellowish or even greenish). In the reservoir it is usually found in association with natural gas, which being lighter forms a gas cap over the petroleum, and saline water, which being heavier generally floats underneath it. Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, Saline water is a general term for Water that contains a significant concentration of dissolved Salts ( NaCl) Crude oil may also be found in semi-solid form mixed with sand, as in the Athabasca oil sands in Canada, where it may be referred to as crude bitumen. The Athabasca Oil Sands (also known as the Athabasca Tar Sands) are large deposits of Bitumen, or extremely Heavy crude oil, located in northeastern Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page Bitumen is a mixture of organic Liquids that are highly Viscous, black sticky entirely soluble in Carbon disulfide, and composed primarily
Petroleum is used mostly, by volume, for producing fuel oil and gasoline (petrol), both important "primary energy" sources. Fuel oil is a fraction obtained from Petroleum Distillation, either as a distillate or a residue Primary energy is energy that has not been subjected to any conversion or transformation process [3] 84% by volume of the hydrocarbons present in petroleum is converted into energy-rich fuels (petroleum-based fuels), including gasoline, diesel, jet, heating, and other fuel oils, and liquefied petroleum gas. Liquefied petroleum gas (also called LPG, GPL, LP Gas, or Autogas) is a mixture of Hydrocarbon Gases used as a Fuel [4]
Due to its high energy density, easy transportability and relative abundance, it has become the world's most important source of energy since the mid-1950s. Energy density is the amount of Energy stored in a given system or region of space per unit Volume, or per unit Mass, depending on the context although Transport or transportation is the movement of people and goods from one place to another Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions Petroleum is also the raw material for many chemical products, including pharmaceuticals, solvents, fertilizers, pesticides, and plastics; the 16% not used for energy production is converted into these other materials. A chemical substance is a Material with a definite chemical composition. A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. Fertilizers ( also spelt fertiliser are chemical compounds given to Plants to promote growth they are usually applied either through the soil for uptake by plant A pesticide is a substance or mixture of substances used to kill a pest. Plastic is the general common term for a wide range of synthetic or semisynthetic organic solid materials suitable for the manufacture of industrial products
Petroleum is found in porous rock formations in the upper strata of some areas of the Earth's crust. Porosity is a measure of the void spaces in a material and is measured as a fraction between 0–1 or as a Percentage between 0–100% This is a List of rock formations meaning isolated scenic or spectacular surface rock outcrops In Geology and related fields a stratum (plural strata) is a layer of rock or Soil with internally consistent characteristics that distinguishes EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 In Geology, a crust is the outermost solid shell of a planet or moon There is also petroleum in oil sands (tar sands). Known reserves of petroleum are typically estimated at around 140 km³ (1. Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions 2 trillion (short scale) barrels) without oil sands,[5] or 440 km³ (3. The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French 74 trillion barrels) with oil sands. [6] Consumption is currently around 84 million barrels (13. 4×106 m3) per day, or 3. 6 km³ per year. Because the energy return over energy invested (EROEI) ratio of oil is constantly falling as petroleum recovery gets more difficult, recoverable oil reserves are significantly less than total oil-in-place. In Physics, Energy economics and ecological energetics, EROEI (Energy Returned on Energy Invested ERoEI, EROI (Energy Return On At current consumption levels, and assuming that oil will be consumed only from reservoirs, known recoverable reserves would be gone around 2039, potentially leading to a global energy crisis. An energy crisis is any great bottleneck (or price Rise) in the supply of energy resources to an economy. However, there are factors which may extend or reduce this estimate, including the rapidly increasing demand for petroleum in China, India, and other developing nations; new discoveries; energy conservation and use of alternative energy sources; and new econonomically viable exploitation of non-conventional oil sources. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country The mitigation of peak oil is the attempt to delay the date and minimize the social and economic impact of Peak oil by reducing the world's consumption and reliance on Petroleum Non-conventional oil is oil produced or extracted using techniques other than the traditional Oil well method
## Chemistry
Octane, a hydrocarbon found in petroleum, lines are single bonds, black spheres are carbon, white spheres are hydrogen
Petroleum is a mixture of a very large number of different hydrocarbons ; the most commonly found molecules are alkanes (linear or branched), cycloalkanes, aromatic hydrocarbons, or more complicated chemicals like asphaltenes. Octane is a straight-chain Alkane with the Chemical formula CH3(CH26CH3 In Organic chemistry, a hydrocarbon is an Organic compound consisting entirely of Hydrogen and Carbon. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 In Organic chemistry, a hydrocarbon is an Organic compound consisting entirely of Hydrogen and Carbon. Alkanes, also known as Paraffins are Chemical compounds that consist only of the elements Carbon (C and Hydrogen (H (i Cycloalkanes (also called naphthenes, especially if from Petroleum sources are types of Alkanes which have one or more rings of Carbon Atoms Asphaltenes are molecular substances that are found in Crude oil, along with Resins, Aromatic hydrocarbons and Alkanes (i Each petroleum variety has a unique mix of molecules, which define its physical and chemical properties, like color and viscosity. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.
The alkanes, also known as paraffins, are saturated hydrocarbons with straight or branched chains which contain only carbon and hydrogen and have the general formula CnH2n+2 They generally have from 5 to 40 carbon atoms per molecule, although trace amounts of shorter or longer molecules may be present in the mixture. In Chemistry, saturation has five different meanings In Physical chemistry, saturation is the point at which a Solution of a substance Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1
The alkanes from pentane (C5H12) to octane (C8H18) are refined into gasoline (petrol), the ones from nonane (C9H20) to hexadecane (C16H34) into diesel fuel and kerosene (primary component of many types of jet fuel), and the ones from hexadecane upwards into fuel oil and lubricating oil. Pentane is any or one of the Organic compounds with the formula C5H12 Octane is a straight-chain Alkane with the Chemical formula CH3(CH26CH3 An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline Nonane is an Alkane Hydrocarbon with the Chemical formula CH3(CH27CH3 Hexadecane (also called cetane) is an Alkane Hydrocarbon with the Chemical formula C16H34 Diesel or Diesel fuel (ˈdiːzəl in general is any Fuel used in Diesel engines The most common is a specific fractional distillate of petroleum Kerosene, sometimes spelled kerosine in scientific and industrial usage is a Combustible Hydrocarbon liquid Jet fuel is a type of Aviation fuel designed for use in Aircraft powered by gas-turbine engines. Fuel oil is a fraction obtained from Petroleum Distillation, either as a distillate or a residue Mineral oil or liquid Petroleum is a By-product in the Distillation of Petroleum to produce Gasoline and other petroleum At the heavier end of the range, paraffin wax is an alkane with approximately 25 carbon atoms, while asphalt has 35 and up, although these are usually cracked by modern refineries into more valuable products. In chemistry paraffin is the common name for the Alkane Hydrocarbons with the general formula C n H2 n +2 Asphalt ( is a sticky black and highly viscous liquid or semi-solid that is present in most crude Petroleums and in some natural deposits sometimes termed asphaltum Fluid catalytic cracking (FCC is the most important conversion process used in petroleum refineries. Any shorter hydrocarbons are considered natural gas or natural gas liquids. Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, Natural gas processing plants or fractionators are used to purify the raw Natural gas extracted from underground gas fields and brought up to the surface by
The cycloalkanes, also known as napthenes, are saturated hydrocarbons which have one or more carbon rings to which hydrogen atoms are attached according to the formula CnH2n. Cycloalkanes have similar properties to alkanes but have higher boiling points.
The aromatic hydrocarbons are unsaturated hydrocarbons which have one or more planar six-carbon rings called benzene rings, to which hydrogen atoms are attached with the formula CnHn. The degree of unsaturation (also known as the index of hydrogen deficiency (IHD or rings plus double bonds) formula is used in Organic chemistry to help Benzene, or benzol, is an organic Chemical compound and a known Carcinogen with the molecular formula C 6 H 6 They tend to burn with a sooty flame, and many have a sweet aroma. Some are carcinogenic.
These different molecules are separated by fractional distillation at an oil refinery to produce gasoline, jet fuel, kerosene, and other hydrocarbons. Fractional distillation is the separation of a mixture into its component parts or fractions such as in separating Chemical compounds by their Boiling point by heating For example 2,2,4-trimethylpentane (isooctane), widely used in gasoline, has a chemical formula of C8H18 and it reacts with oxygen exothermically:[7]
$2\mathrm{C}_8 \mathrm{H}_{18(l)} + 25\mathrm{O}_{2(g)} \rightarrow \; 16\mathrm{CO}_{2(g)} + 18\mathrm{H}_2 \mathrm{O}_{(l)} + 10.86 \ \mathrm{MJ}$
The amount of various molecules in an oil sample can be determined in laboratory. 224-Trimethylpentane, also known as isooctane, is an Octane Isomer which defines the 100 point on the Octane rating scale In Thermodynamics, the word exothermic "outside heating" describes a process or reaction that releases Energy usually in the form of Heat, but The molecules are typically extracted in a solvent, then separated in a gas chromatograph, and finally determined with a suitable detector, such as a flame ionization detector or a mass spectrometer[8]. A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. Gas-liquid chromatography (GLC, or simply gas chromatography (GC, is a type of Chromatography in which the mobile phase is a carrier gas usually an Inert A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument A flame ionization detector (FID is a type of Gas detector used in Gas chromatography The first flame ionization detector was developed in 1957 by scientists Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the Mass-to-charge ratio of charged particles
Incomplete combustion of petroleum or gasoline results in production of toxic byproducts. Too little oxygen results in carbon monoxide. Carbon monoxide, with the chemical formula CO is a colorless odorless tasteless yet highly toxic Gas. Due to high temperatures and high pressures involved exhaust gases from gasoline combustion in car engines usually include nitrogen oxides which are responsible for creation of photochemical smog. The term nitrogen oxide typically refers to any Binary compound of Oxygen and Nitrogen, or to a mixture of such compounds Nitric Smog is a kind of Air pollution; the word "smog" is a Portmanteau of Smoke and Fog.
## Formation
Formation of petroleum occurs from kerogen pyrolysis, in a variety of mostly endothermic reactions at high temperature and/or pressure. Kerogen is a mixture of organic Chemical compounds that make up a portion of the organic matter in Sedimentary rocks It is insoluble in normal organic Pyrolysis is the Chemical decomposition of organic materials by heating in the absence of Oxygen or any other reagents except possibly Steam In Thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs Energy in the form of Heat. [9]
### Biogenic theory
Most geologists view crude oil and natural gas as the product of compression and heating of ancient organic materials over geological time. Geology (from Greek γη gê, "earth" and λόγος Logos, "speech" lit Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, In Geology and Oceanography, diagenesis is any chemical physical or biological change undergone by a Sediment after its initial deposition and during An organic compound is any member of a large class of Chemical compounds whose Molecules contain Carbon. The geologic time scale is a chronologic schema (or idealized Model) relating Stratigraphy to time that is used by Geologists and other Oil is formed from the preserved remains of prehistoric zooplankton and algae which have been settled to the sea (or lake) bottom in large quantities under anoxic conditions. Stone Age Paleolithic See also Paleolithic, Recent African Origin, Early Homo sapiens, Early human migrations "Paleolithic" Zooplankton are the Heterotrophic (sometimes detritivorous) type of Plankton. Algae ( sing. alga are a large and diverse group of simple typically Autotrophic organisms ranging from Unicellular to Multicellular forms Anoxic sea water is sea water depleted of Oxygen. It is generally found in areas with restricted water exchange Terrestrial plants, on the other hand, tend to form coal. A terrestrial plant is one that grows on land Other types of plants are aquatic (living in water Epiphytic (living on trees but not Parasitic) Over geological time this organic matter, mixed with mud, is buried under heavy layers of sediment. The geologic time scale is a chronologic schema (or idealized Model) relating Stratigraphy to time that is used by Geologists and other An organic compound is any member of a large class of Chemical compounds whose Molecules contain Carbon. Matter is commonly defined as being anything that has mass and that takes up space. In computer gaming, a MUD ( Multi-User Dungeon, Domain or Dimension) is a multi-player computer game that combines elements of The resulting high levels of heat and pressure cause the organic matter to chemically change during diagenesis, first into a waxy material known as kerogen which is found in various oil shales around the world, and then with more heat into liquid and gaseous hydrocarbons in a process known as catagenesis. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In Geology and Oceanography, diagenesis is any chemical physical or biological change undergone by a Sediment after its initial deposition and during Kerogen is a mixture of organic Chemical compounds that make up a portion of the organic matter in Sedimentary rocks It is insoluble in normal organic See Catagenesis (biology for usage in the field of biology where it refers to retrogressive evolution
Geologists often refer to an "oil window"[10] which is the temperature range that oil forms in—below the minimum temperature oil remains trapped in the form of kerogen, and above the maximum temperature the oil is converted to natural gas through the process of thermal cracking. Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, In Petroleum geology and Chemistry, cracking is the process whereby complex organic Molecules such as Kerogens or heavy Hydrocarbons Though this happens at different depths in different locations around the world, a typical depth for the oil window might be 4–6 km. Note that even if oil is formed at extreme depths, it may be trapped at much shallower depths where it was not formed (the Athabasca Oil Sands is one example). The Athabasca Oil Sands (also known as the Athabasca Tar Sands) are large deposits of Bitumen, or extremely Heavy crude oil, located in northeastern
Hydrocarbon trap.
Because most hydrocarbons are lighter than rock or water, these often migrate upward through adjacent rock layers until they either reach the surface or become trapped beneath impermeable rocks, within porous rocks called reservoirs. In Physics, buoyancy ( BrE IPA: /ˈbɔɪənsi/ is the upward Force on an object produced by the surrounding liquid or gas in which it is A petroleum reservoir or an oil and gas reservoir (or system) is a subsurface pool of Hydrocarbons contained in porous However, the process is not straightforward since it is influenced by underground water flows, and oil may migrate hundreds of kilometres horizontally or even short distances downward before becoming trapped in a reservoir. Concentration of hydrocarbons in a trap forms an oil field from which the liquid can be extracted by drilling and pumping. An oil field is a region with an abundance of Oil wells extracting Petroleum (crude oil from below ground A drill (from Dutch Drillen) is For information on Wikipedia project-related discussions see WikipediaVillage pump.
Three conditions must be present for oil reservoirs to form: a source rock rich in organic material buried deep enough for subterranean heat to cook it into oil; a porous and permeable reservoir rock for it to accumulate in; and a cap rock (seal) or other mechanism that prevents it from escaping to the surface. Porosity is a measure of the void spaces in a material and is measured as a fraction between 0–1 or as a Percentage between 0–100% Permeability in the Earth sciences (commonly symbolized as κ, or k) is a measure of the ability of a material (typically a rock or unconsolidated Within these reservoirs, fluids will typically organize themselves like a three-layer cake with a layer of water below the oil layer and a layer of gas above it, although the different layers vary in size between reservoirs.
The vast majority of oil that has been produced by the earth has long ago escaped to the surface and been biodegraded by oil-eating bacteria. Biodegradation is the process by which organic substances are broken down by the enzymes produced by living organisms Oil companies are looking for the small fraction that has been trapped by this rare combination of circumstances. Oil sands are reservoirs of partially biodegraded oil still in the process of escaping, but contain so much migrating oil that, although most of it has escaped, vast amounts are still present—more than can be found in conventional oil reservoirs.
On the other hand, oil shales are source rocks that have not been exposed to heat or pressure long enough to convert their trapped kerogen into oil. [11]
The reactions that produce oil and natural gas are often modeled as first order breakdown reactions, where kerogen is broken down to oil and natural gas by a set of parallel reactions, and oil eventually breaks down to natural gas by another set of reactions. The first set was originally patented in 1694 under British Crown Patent No. 330 covering, "a way to extract and make great quantityes of pitch, tarr, and oyle out of a sort of stone. "
The latter set is regularly used in petrochemical plants and oil refineries. Petrochemicals are chemical products made from raw materials of Petroleum or other Hydrocarbon origin An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline
The biogenic origin of petroleum (liquid hydrocarbon oils) has recently been reviewed in detail by Kenney, Krayushkin, and Plotnikova who raise a number of objections. [12]
### Abiogenic theory
The idea of abiogenic petroleum origin was championed in the Western world by astronomer Thomas Gold based on thoughts from Russia, mainly on studies of Nikolai Kudryavtsev in the 1950s. The hypothesis of abiogenic petroleum origin is an alternative hypothesis to the biological origin theory which was popular in Russia and Ukraine between The hypothesis of abiogenic petroleum origin is an alternative hypothesis to the biological origin theory which was popular in Russia and Ukraine between The term Western world, the West or the Occident ( Latin: occidens -sunset -west as distinct from the Orient) can have multiple meanings Thomas Gold ( May 22, 1920 &ndash June 22, 2004) was an Austrian born Astrophysicist, a professor of Astronomy Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending Nikolai Alexandrovich Kudryavtsev Николай Александрович Кудрявцев ( Opochka, October 21, 1893 - Leningrad, December Gold's hypothesis was that hydrocarbons of purely inorganic origin exist in the planet Earth. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is Since most petroleum hydrocarbons are less dense than aqueous pore fluids, Gold proposed that they migrate upward into oil reservoirs through deep fracture networks. Although biomarkers are found in petroleum that most petroleum geologists interpret as indicating biological origin, Gold proposed that Thermophilic, rock-dwelling microbial life-forms are responsible for their presence. A biomarker is a substance used as an indicator of a biologic state An extremophile is an Organism that thrives in and may even require Physically or Geochemically extreme conditions that are detrimental to the A microorganism (also spelled micro organism or micro-organism and also called a microbe) is an Organism that is Microscopic (usually
This hypothesis is accepted by only a small minority of geologists and petroleum engineers. A hypothesis (from Greek) consists either of a suggested explanation for a phenomenon (an event that is observable or of a reasoned proposal suggesting a possible "The success of the abiogenic theory can be seen by the fact that more than 80 oil and gas fields in the Caspian Sea district have been explored and developed in crystalline basement rock on the basis of this theory. "[13] Methods of making hydrocarbons from inorganic material have been known for some time, but no substantial proof exists that this is happening on any significant scale in the earth's crust for any hydrocarbon other than methane (natural gas). Abundant liquid methane (though not any form of petroleum) has been inferred to be present on Titan, a moon of Saturn, by research data from NASA's Cassini probe. TemplateInfobox Planet.--> Titan (ˈtaɪtən, or as Cassini–Huygens is a joint NASA / ESA / ASI Robotic spacecraft mission currently studying the planet Saturn and its However, Titan has completely different geology from Earth, and is 1,200 gigametres (750,000,000 mi) or 8. 0 AU away. The astronomical unit ( AU or au or au or sometimes ua) is a unit of Length based on the distance from the Earth to the [14]
## Classification
A sample of medium heavy crude oil
The petroleum industry generally classifies crude oil by the geographic location it is produced in (e. Crude oil benchmarks, also known as an oil marker, were first introduced in the mid 1980s The petroleum industry includes the global processes of exploration, extraction, refining, transporting (often by Oil tankers and pipelines g. West Texas, Brent, or Oman), its API gravity (an oil industry measure of density), and by its sulfur content. West Texas is a region in Texas that has more in common geographically with the Southwestern United States than it does with the rest of the state The Brent oilfield operated by Shell UK Limited was once one of the most productive parts of the UK's offshore assets but is now nearing the end of its useful life Oman, officially the Sultanate of Oman ( Arabic: سلطنة عُمان) is an Arab Country in Southwest Asia on the southeast Crude oil may be considered light if it has low density or heavy if it has high density; and it may be referred to as sweet if it contains relatively little sulfur or sour if it contains substantial amounts of sulfur. Light crude oil is Crude oil with a low Wax content The clear cut definition of 'light' and ' heavy ' crude is hard to find simply because the classification Heavy crude oil or Extra Heavy oil is any type of Crude oil which does not flow easily Sweet crude oil is a type of Petroleum. Petroleum is considered "sweet" if it contains less than 0 Sour crude oil is crude oil containing the impurity Sulfur. It is common to find crude oil containing some impurities
The geographic location is important because it affects transportation costs to the refinery. Light crude oil is more desirable than heavy oil since it produces a higher yield of gasoline, while sweet oil commands a higher price than sour oil because it has fewer environmental problems and requires less refining to meet sulfur standards imposed on fuels in consuming countries. Each crude oil has unique molecular characteristics which are understood by the use of crude oil assay analysis in petroleum laboratories. A crude oil assay is essentially the chemical evaluation of Crude oil feedstocks by Petroleum testing laboratories
Barrels from an area in which the crude oil's molecular characteristics have been determined and the oil has been classified are used as pricing references throughout the world. Crude oil benchmarks, also known as an oil marker, were first introduced in the mid 1980s Some of the common reference crudes are:
• West Texas Intermediate (WTI), a very high-quality, sweet, light oil delivered at Cushing, Oklahoma for North American oil
• Brent Blend, comprising 15 oils from fields in the Brent and Ninian systems in the East Shetland Basin of the North Sea. West Texas Intermediate ( WTI) also known as Texas Light Sweet, is a type of Crude oil used as a benchmark in oil pricing and the Underlying Cushing is a city in Payne County, Oklahoma, United States. The population was 8371 at the 2000 census. Brent Crude is the biggest of the many major classifications of oil consisting of Brent Crude Brent Sweet Light Crude, Oseberg and Forties The Brent oilfield operated by Shell UK Limited was once one of the most productive parts of the UK's offshore assets but is now nearing the end of its useful life The East Shetland Basin is a major oil-producing area of the North Sea between Scotland and Norway. The North Sea is a marginal, Epeiric sea of the Atlantic Ocean on the European Continental shelf. The oil is landed at Sullom Voe terminal in the Shetlands. Sullom Voe is an Inlet between North Mainland and Northmavine on Shetland in Scotland. Shetland (formerly spelled Zetland, from etland; Old Norse non Hjaltland; Sealtainn is an Archipelago off the northeast coast of Oil production from Europe, Africa and Middle Eastern oil flowing West tends to be priced off the price of this oil, which forms a benchmark
• Dubai-Oman, used as benchmark for Middle East sour crude oil flowing to the Asia-Pacific region
• Tapis (from Malaysia, used as a reference for light Far East oil)
• Minas (from Indonesia, used as a reference for heavy Far East oil)
• The OPEC Reference Basket, a weighted average of oil blends from various OPEC (The Organization of the Petroleum Exporting Countries) countries
There are declining amounts of these benchmark oils being produced each year, so other oils are more commonly what is actually delivered. Dubai Crude is a light sour crude oil extracted from Dubai. Dubai Crude is used as a price benchmark or Oil marker because it is one of only The Pacific Ocean is the largest of the Earth 's Oceanic divisions For the biogeographical region see Malesia Malaysia (məˈleɪʒə or /məˈleɪziə/ is a country that consists of thirteen states and The Republic of Indonesia ( (Republik Indonesia is a Country in Southeast Asia. The OPEC Reference Basket (ORB, also referred to as the OPEC Basket is a weighted average of prices for Petroleum blends produced by OPEC countries The Organization of the Petroleum Exporting Countries ( OPEC) is a Cartel of thirteen countries made up of Algeria, Angola, Ecuador While the reference price may be for West Texas Intermediate delivered at Cushing, the actual oil being traded may be a discounted Canadian heavy oil delivered at Hardisty, Alberta, and for a Brent Blend delivered at the Shetlands, it may be a Russian Export Blend delivered at the port of Primorsk. Hardisty Alberta is a town in Flagstaff County in Alberta, Canada. Primorsk (Примо́рск Koivisto Björkö is a coastal town in Vyborgsky District of Leningrad Oblast, Russia, and the [15]
## Petroleum industry
Main article: Petroleum industry
The petroleum industry is involved in the global processes of exploration, extraction, refining, transporting (often with oil tankers and pipelines), and marketing petroleum products. The petroleum industry includes the global processes of exploration, extraction, refining, transporting (often by Oil tankers and pipelines Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum Geologists for Hydrocarbon deposits beneath the Earth's surface The extraction of petroleum is the process by which usable Petroleum is extracted and removed from the earth An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline History The technology of oil transportation has evolved alongside the oil industry Pipeline transport is the transportation of goods through a pipe. The largest volume products of the industry are fuel oil and gasoline (petrol). Fuel oil is a fraction obtained from Petroleum Distillation, either as a distillate or a residue Petroleum is also the raw material for many chemical products, including pharmaceuticals, solvents, fertilizers, pesticides, and plastics. Petrochemicals are chemical products made from raw materials of Petroleum or other Hydrocarbon origin The industry is usually divided into three major components: upstream, midstream and downstream. See also Extraction of petroleum The Petroleum industry is usually divided into three major components Upstream Midstream and downstream. The Petroleum industry is usually divided into three major components upstream, midstream and downstream. The petroleum industry is usually divided into three major components Upstream, Midstream and downstream Midstream operations are usually included in the downstream category.
Petroleum is vital to many industries, and is of importance to the maintenance of industrialized civilization itself, and thus is critical concern to many nations. For other uses of this term see Industry (disambiguation An industry (from Latin industrius, "diligent industrious" A Civilization is a society in which large numbers of people share a variety of common elements Oil accounts for a large percentage of the world’s energy consumption, ranging from a low of 32% for Europe and Asia, up to a high of 53% for the Middle East. The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. Other geographic regions’ consumption patterns are as follows: South and Central America (44%), Africa (41%), and North America (40%). The world at large consumes 30 billion barrels (4. 8 km³) of oil per year, and the top oil consumers largely consist of developed nations. In fact, 24% of the oil consumed in 2004 went to the United States alone. The United States of America —commonly referred to as the [16] The production, distribution, refining, and retailing of petroleum taken as a whole represent the single largest industry in terms of dollar value on earth.
See also: Price of petroleum, Oil price increases since 2003, and Gasoline usage and pricing
## Petroleum exploration
### Extraction
The most common method of obtaining petroleum is extracting it from oil wells found in oil fields. This article is about the price of crude oil see Gasoline usage and pricing for information about derivative motor fuels For information on the price of oil see Price of petroleum. The usage and pricing of Gasoline (petrol results Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum Geologists for Hydrocarbon deposits beneath the Earth's surface The extraction of petroleum is the process by which usable Petroleum is extracted and removed from the earth West Texas PumpjackJPG|thumb|right|300px|This Pumpjack located south of Midland TX is a common sight in West Texas. An oil field is a region with an abundance of Oil wells extracting Petroleum (crude oil from below ground With improved technologies and higher demand for hydrocarbons various methods are applied in petroleum exploration and development to optimize the recovery of oil and gas (Enhanced Oil Recovery, EOR). Enhanced Oil Recovery (abbreviated EOR is a generic term for techniques for increasing the amount of Oil that can be extracted from an Oil field. Primary recovery methods are used to extract oil that is brought to the surface by underground pressure, and can generally recover about 20% of the oil present. The extraction of petroleum is the process by which usable Petroleum is extracted and removed from the earth The natural pressure can come from several different sources; where it is provided by an underlying water layer it is called a water drive reservoir and where it is from the gas cap above it is called gas drive. After the reservoir pressure has depleted to the point that the oil is no longer brought to the surface, secondary recovery methods draw another 5 to 10% of the oil in the well to the surface. The extraction of petroleum is the process by which usable Petroleum is extracted and removed from the earth In a water drive oil field, water can be injected into the water layer below the oil, and in a gas drive field it can be injected into the gas cap above to repressurize the reservoir. Finally, when secondary oil recovery methods are no longer viable, tertiary recovery methods reduce the viscosity of the oil in order to bring more to the surface. The extraction of petroleum is the process by which usable Petroleum is extracted and removed from the earth Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. These may involve the injection of heat, vapor, surfactants, solvents, or miscible gases as in carbon dioxide flooding. Surfactants are wetting agents that lower the Surface tension of a liquid allowing easier spreading and lower the Interfacial tension between two liquids Carbon dioxide (CO2 flooding is a process whereby Carbon dioxide is injected into an oil reservoir in order to increase output when extracting oil.
### Alternative methods
During the oil price increases since 2003, alternatives methods of producing oil gained importance. The most widely known alternatives involve extracting oil from sources such as oil shale or tar sands. These resources exist in large quantities; however, extracting the oil at low cost without excessively harming the environment remains a challenge.
It is also possible to chemically transform methane or coal into the various hydrocarbons found in oil. Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, The best-known such method is the Fischer-Tropsch process. The Fischer-Tropsch process (or Fischer-Tropsch Synthesis is a catalyzed chemical reaction in which synthesis gas ( Syngas) a mixture of Carbon monoxide It was a concept pioneered during the 1920s in Germany to extract oil from coal and became central to Nazi Germany's war efforts when imports of petroleum were restricted due to war. Nazi Germany and the Third Reich are the common English names for Germany under the regime of Adolf Hitler and the National Socialist German Workers International trade is exchange of Capital, Goods, and Services across International borders or Territories. It was known as Ersatz (English:"substitute") oil, and accounted for nearly half the total oil used in WWII by Germany. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including However, the process was used only as a last resort as naturally occurring oil was much cheaper. As crude oil prices increase, the cost of coal to oil conversion becomes comparatively cheaper. The method involves converting high ash coal into synthetic oil in a multi-stage process. Synthetic oil is Oil consisting of Chemical compounds which were not originally present in Crude oil ( Petroleum) but were Artificially
Currently, two companies have commercialised their Fischer-Tropsch technology. Shell Oil in Bintulu, Malaysia, uses natural gas as a feedstock, and produces primarily low-sulfur diesel fuels. Bintulu is a coastal town and the capital of Bintulu District (7220 For the biogeographical region see Malesia Malaysia (məˈleɪʒə or /məˈleɪziə/ is a country that consists of thirteen states and Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 Diesel or Diesel fuel (ˈdiːzəl in general is any Fuel used in Diesel engines The most common is a specific fractional distillate of petroleum [17] Sasol[18] in South Africa uses coal as a feedstock, and produces a variety of synthetic petroleum products. Sasol (originally Afrikaans for Suid-Afrikaanse Steenkool en Olie - South African Coal and Oil is a South African company involved in mining energy chemicals The Republic of South Africa (also known by other official names) is a country located at the southern tip of the continent of Africa
The process is today used in South Africa to produce most of the country's diesel fuel from coal by the company Sasol. The Republic of South Africa (also known by other official names) is a country located at the southern tip of the continent of Africa Diesel or Diesel fuel (ˈdiːzəl in general is any Fuel used in Diesel engines The most common is a specific fractional distillate of petroleum Sasol (originally Afrikaans for Suid-Afrikaanse Steenkool en Olie - South African Coal and Oil is a South African company involved in mining energy chemicals The process was used in South Africa to meet its energy needs during its isolation under Apartheid. This process produces low sulfur diesel fuel but also produces large amounts of greenhouse gases. Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 Diesel or Diesel fuel (ˈdiːzəl in general is any Fuel used in Diesel engines The most common is a specific fractional distillate of petroleum Greenhouse gases are gaseous constituents of the atmosphere bothnatural and anthropogenic that absorb and emit radiation at specific wavelengths within the spectrum of thermal infrared
An alternative method of converting coal into petroleum is the Karrick process, which was pioneered in the 1930s in the United States. The Karrick process is a low-temperature Carbonization (LTC of Coal, shale, Lignite or any carbonaceous materials The United States of America —commonly referred to as the It uses low temperatures in the absence of ambient air, to distill the short-chain hydrocarbons out of coal instead of petroleum. Distillation is a method of separating Mixtures based on differences in their volatilities in a boiling liquid mixture
Further information: Destructive distillation
Oil shale can also be used to produce oil, either through mining and processing, or in more modern methods, with in-situ thermal conversion. Destructive distillation is the process of Pyrolysis conducted in a distillation apparatus ( Retort) to allow the volatile products to be collected
Conventional crude can be extracted from unconventional reservoirs, such as the Bakken Formation. The Bakken Formation, initially described by geologist JW Nordquist in 1953is a rock unit from the Late Devonian to Early Mississippian The formation is about two miles underground but only a few meters thick, stretching across hundreds of thousands of square miles. It further has very poor extraction characteristics. Recovery at Elm Coulee has involved extensive use of horizontal drilling, solvents, and proppants. Elm Coulee Oil Field was discovered in the Williston Basin in Richland County, eastern Montana, in 2000
More recently explored is thermal depolymerization (TDP), a process for the reduction of complex organic materials into light crude oil. Thermal depolymerization ( TDP) is a process using Hydrous pyrolysis for the reduction of complex Organic materials (usually Waste products of Organic matter (or organic material) is Matter that has come from a once-living Organism; is capable of Petroleum ( L petroleum, from Greek πετρέλαιον, lit Using pressure and heat, long chain polymers of hydrogen, oxygen, and carbon decompose into short-chain hydrocarbons. A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 In Organic chemistry, a hydrocarbon is an Organic compound consisting entirely of Hydrogen and Carbon. This mimics the natural geological processes thought to be involved in the production of fossil fuels. Geology (from Greek γη gê, "earth" and λόγος Logos, "speech" lit Fossil fuels or mineral fuels are fossil source Fuels that is Hydrocarbons found within the top layer of the Earth’s crust. In theory, thermal depolymerization can convert any organic waste into petroleum substitutes.
## History
Ignacy Łukasiewicz - creator of the process of refining of kerosene from crude oil. Jan Józef Ignacy Łukasiewicz (1822 - 1882 was a Polish Pharmacist of Armenian descent who devised the first method of distilling Kerosene
Petroleum, in some form or other, is not a substance new in the world's history. More than four thousand years ago, according to Herodotus and confirmed by Diodorus Siculus, asphalt was employed in the construction of the walls and towers of Babylon; there were oil pits near Ardericca (near Babylon), and a pitch spring on Zacynthus. Herodotus of Halicarnassus ( Greek: Hēródotos Halikarnāsseús) was a Greek Historian who lived in the 5th century BC ( 484 BC&ndash Asphalt ( is a sticky black and highly viscous liquid or semi-solid that is present in most crude Petroleums and in some natural deposits sometimes termed asphaltum Babylon was a City-state of ancient Mesopotamia, the remains of which can be found in present-day Al Hillah, Babil Province, Iraq [19] Great quantities of it were found on the banks of the river Issus, one of the tributaries of the Euphrates. Issus, a River in Cilicia, Asia Minor, where Alexander the Great defeated Darius in 333 BC. The Euphrates ( ( Arabic: ar نهر الفرات; Turkish: tr Fırat Syriac: syr ܦܪܬ; Hebrew: he פרת Ancient Persian tablets indicate the medicinal and lighting uses of petroleum in the upper levels of their society. The Persian Empire was a series of Iranian empires that ruled over the Iranian plateau, the original Persian homeland and beyond in Western Asia
The earliest known oil wells were drilled in China in 347 CE or earlier. West Texas PumpjackJPG|thumb|right|300px|This Pumpjack located south of Midland TX is a common sight in West Texas. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National They had depths of up to about 800 feet (240 m) and were drilled using bits attached to bamboo poles. For the ficitonal character see Drill Bit (Transformers. Drill bits are cutting tools used to create cylindrical holes Bamboo is a group of Woody perennial Evergreen Plants in the True grass family Poaceae, subfamily [20] The oil was burned to evaporate brine and produce salt. Brine (lat saltus) is Water saturated or nearly saturated with Salt (NaCl For sodium chloride in the diet see Salt. Sodium chloride, also known as common salt, table salt, or Halite, is a By the 10th century, extensive bamboo pipelines connected oil wells with salt springs. Bamboo is a group of Woody perennial Evergreen Plants in the True grass family Poaceae, subfamily The ancient records of China and Japan are said to contain many allusions to the use of natural gas for lighting and heating. For a topic outline on this subject see List of basic Japan topics. Petroleum was known as burning water in Japan in the 7th century. [19]
The Middle East petroleum industry was established by the 8th century, when the streets of the newly constructed Baghdad were paved with tar, derived from easily accessible petroleum from natural fields in the region. The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. The petroleum industry includes the global processes of exploration, extraction, refining, transporting (often by Oil tankers and pipelines A street is a Public thoroughfare in the built environment It is a Public parcel of land adjoining Buildings in an urban context Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous Tar is a viscous black Liquid derived from the Destructive distillation of organic matter In the 9th century, oil fields were exploited in the area around modern Baku, Azerbaijan, to produce naphtha. An oil field is a region with an abundance of Oil wells extracting Petroleum (crude oil from below ground Baku (Bakı sometimes known as Baqy, Baky, Baki or Bakü, is the capital the largest city and the largest port of Azerbaijan Azerbaijan ( English; Azərbaycan officially the Republic of Azerbaijan (Azərbaycan Respublikası is the largest and most populous country in the South Naphtha normally refers to a number of different flammable liquid mixtures of hydrocarbons i These fields were described by the geographer Masudi in the 10th century, and by Marco Polo in the 13th century, who described the output of those wells as hundreds of shiploads. A geographer is a Scientist whose area of study is Geography, the study of Earth 's physical environment and Human habitat TemplateInfobox Muslim scholars --> Abu al-Hasan Ali ibn al-Husayn íbn Ali al-Mas'udi (transl) (born c Marco Polo ( September 15 1254 – January 9 1324 at earliest but no later than June 1325 was a Venetian trader and explorer Petroleum was distilled by Persian chemist al-Razi in the 9th century, producing chemicals such as kerosene in the al-ambiq (alembic). Distillation is a method of separating Mixtures based on differences in their volatilities in a boiling liquid mixture layout and formatting it should ensure no clashes with the top of the infobox A chemist is a Scientist trained in the Science of Chemistry. Kerosene, sometimes spelled kerosine in scientific and industrial usage is a Combustible Hydrocarbon liquid An alembic (from Arabic Al-inbiq الأنبيق is an alchemical Still consisting of two Retorts connected by a tube [21] (See also: Alchemy (Islam), Islamic science, and Timeline of science and technology in the Islamic world. )
The earliest mention of American petroleum occurs in Sir Walter Raleigh's account of the Trinidad Pitch Lake in 1595; whilst thirty-seven years later, the account of a visit of a Franciscan, Joseph de la Roche d'Allion, to the oil springs of New York was published in Sagard's Histoire du Canada. Sir Walter Raleigh or Ralegh (c 1552 – 29 October 1618 was a famed English writer Poet, Soldier, Courtier and Explorer Trinidad ( Spanish: " Trinity " is the largest and most populous of the two major islands and The Pitch Lake is a lake of natural Asphalt located at La Brea in southwest Trinidad. A Russian traveller, Peter Kalm, in his work on America published in 1748 showed on a map the oil springs of Pennsylvania. [19]
In 1711 the Greek physician Eyrini d’Eyrinis discovered asphalt at Val-de-Travers, (Neuchâtel). The Val-de-Travers is a district in the Canton of Neuchâtel, in Switzerland. Neuchâtel ( literally: New Castle in Old French) is the Capital of the Swiss canton of Neuchâtel on Lake He established a bitumen mine de la Presta there in 1719 that operated until 1986. [22][23]
Oil sands were mined from 1745 in Merkwiller-Pechelbronn, Alsace under the direction of Louis Pierre Ancillon de la Sablonnière, by special appointment of Louis XV. Merkwiller-Pechelbronn is a community in the French region of Alsace. Alsace (Alsace alzas Alsatian and Elsass pre-1996 German: Elsaß; Alsatia is one of the 26 Regions of France, located on the eastern In 1745 Louis Pierre Ancillon de la Sablonnière established the Pechelbronn Bitumen mine at Merkwiller-Pechelbronn, Bas-Rhin, Alsace Louis XV (15 February 1710 &ndash 10 May 1774 ruled as King of France and of Navarre from 1 September 1715 until his death in 1774 [24] The Pechelbronn oil field was active until 1970, and was the birth place of companies like Antar and Schlumberger. Schlumberger Limited is the world's largest Oilfield services corporation operating in approximately 80 countries with about 84000 people of 140 nationalities The first modern refinery was built there in 1857. [24]
The modern history of petroleum began in 1846 with the discovery of the process of refining kerosene from coal by Nova Scotian Abraham Pineo Gesner. The term modern period or modern era (sometimes also modern times) is the period of history that followed the Middle Ages between c Kerosene, sometimes spelled kerosine in scientific and industrial usage is a Combustible Hydrocarbon liquid Nova Scotia (ˌnəʊvəˈskəʊʃə ( Latin for New Scotland; Alba Nuadh Nouvelle-Écosse is a Canadian province located on Canada 's Abraham Pineo Gesner, born May 2, 1797 in Cornwallis Township, Nova Scotia, Canada ( – died April 29, 1864 Ignacy Łukasiewicz improved Gesner's method to develop a means of refining kerosene from the more readily available "rock oil" ("petr-oleum") seeps in 1852 and the first rock oil mine was built in Bóbrka, near Krosno in Galicia in the following year. Jan Józef Ignacy Łukasiewicz (1822 - 1882 was a Polish Pharmacist of Armenian descent who devised the first method of distilling Kerosene Bóbrka may refer to the following places Historical Polish name for Bibrka, Ukraine Bóbrka Lesko County in Subcarpathian Voivodeship (south-east Krosno (in full The Royal Free City of Krosno, Królewskie Wolne Miasto Krosno (Krossen 1358) is a town in south-eastern Poland with 48060 inhabitants Galicia (Галичина ( Halychyna) Galicja is a historical region in East Central Europe, currently divided between Poland and Ukraine, In 1854, Benjamin Silliman, a science professor at Yale University in New Haven, was the first to fractionate petroleum by distillation. Benjamin Silliman ( 8 August 1779 &ndash 24 November 1864) was an American Chemist, one of the first American professors These discoveries rapidly spread around the world, and Meerzoeff built the first Russian refinery in the mature oil fields at Baku in 1861. An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline Baku (Bakı sometimes known as Baqy, Baky, Baki or Bakü, is the capital the largest city and the largest port of Azerbaijan At that time Baku produced about 90% of the world's oil.
Oil field in California, 1938. California ( is a US state on the West Coast of the United States, along the Pacific Ocean.
The first commercial oil well drilled in North America was in Oil Springs, Ontario, Canada in 1858, dug by James Miller Williams. Oil Springs Ontario (population 800 is a Village located along Former Kings Highway 21 in Lambton County Ontario, south of Oil City. Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page James Miller Williams ( September 14 1818 &ndash November 25 1890) was a businessman and political figure in Ontario, Canada The US petroleum industry began with Edwin Drake's drilling of a 69-foot (21 m) oil well in 1859, on Oil Creek near Titusville, Pennsylvania, for the Seneca Oil Company (originally yielding 25 barrels per day (4. For other uses of this term see Industry (disambiguation An industry (from Latin industrius, "diligent industrious" Edwin Laurentine Drake ( March 29, 1819 &ndash November 9, 1880) also known as Colonel Drake, was an American Oil Creek is a river that flows through both Pennsylvania and New York. Titusville is a city in Crawford County, Pennsylvania, United States. 0 m³/d), by the end of the year output was at the rate of 15 barrels per day (2. 4 m³/d)). The industry grew through the 1800s, driven by the demand for kerosene and oil lamps. Kerosene, sometimes spelled kerosine in scientific and industrial usage is a Combustible Hydrocarbon liquid An oil lamp is a simple vessel used to produce light continuously for a period of time from a fuel source It became a major national concern in the early part of the 20th century; the introduction of the internal combustion engine provided a demand that has largely sustained the industry to this day. A nation is a Human Cultural and Social Community. In as much as most members never meet each other yet feel a common bond it may be considered The internal combustion engine is an engine in which the Combustion of Fuel and an Oxidizer (typically air occurs in a confined space called a Early "local" finds like those in Pennsylvania and Ontario were quickly outpaced by demand, leading to "oil booms" in Texas, Oklahoma, and California. The Commonwealth of Pennsylvania ( often colloquially referred to as PA (its abbreviation by natives and Northeasterners is a state located in the Northeastern Ontario (ɒnˈtɛrioʊ is a province located in the central part of Canada, the largest by population and second largest after Quebec Texas ( is a state geographically located in the South Central United States and is also known as the Lone Star State. Oklahoma ( is a state located in the South Central region of the United States of America. California ( is a US state on the West Coast of the United States, along the Pacific Ocean.
Early production of crude petroleum in the United States:[19]
• 1859: 2,000 barrels (~270 t)
• 1869: 4,215,000 barrels (~5. 750×105 t)
• 1879: 19,914,146 barrels (~2. 717×106 t)
• 1889: 35,163,513 barrels (~4. 797×106 t)
• 1899: 57,084,428 barrels (~7. 788×106 t)
• 1906: 126,493,936 barrels (~1. 726×107 t)
By 1910, significant oil fields had been discovered in Canada (specifically, in the province of Ontario), the Dutch East Indies (1885, in Sumatra), Iran (1908, in Masjed Soleiman), Peru, Venezuela, and Mexico, and were being developed at an industrial level. Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page Ontario (ɒnˈtɛrioʊ is a province located in the central part of Canada, the largest by population and second largest after Quebec See http//enwikipediaorg/wiki/WikipediaFootnotes for an explanation of how to generate footnotes using the tags and the template below Sumatra (also spelled Sumatera) is the sixth largest island in the world (approximately 470000 km² and is the largest island entirely in Indonesia (two For a topic outline on this subject see List of basic Iran topics. Masjed Soleiman (also transcribed as Masjid Soleyman and Masjid-e-Soleiman) (مسجد سلیمان in Persian) is a city in the Khuzestan Peru (Perú Piruw Piruw officially the Republic of Peru ( reˈpuβlika del peˈɾu is a country in western South America. Venezuela (ˌvɛnəˈzweɪlə) officially the Bolivarian Republic of Venezuela (Spanish República Bolivariana de Venezuela) is a country on the The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America.
Even until the mid-1950s, coal was still the world's foremost fuel, but oil quickly took over. Following the 1973 energy crisis and the 1979 energy crisis, there was significant media coverage of oil supply levels. The 1973 oil crisis began on October 17 1973 when the members of Organization of Arab Petroleum Exporting Countries (OAPEC consisting of the Arab members of The 1979 (or second) oil crisis in the United States occurred in the wake of the Iranian Revolution. The news media refers to the section of the Mass media that focuses on presenting current News to the public This brought to light the concern that oil is a limited resource that will eventually run out, at least as an economically viable energy source. At the time, the most common and popular predictions were quite dire. However, a period of increase production and reduced demand caused an oil glut in the 1980s. The 1980s oil glut was a surplus of crude oil caused by falling demand following the 1973 and 1979 energy crises.
Today, about 90% of vehicular fuel needs are met by oil. Petroleum also makes up 40% of total energy consumption in the United States, but is responsible for only 2% of electricity generation. Petroleum's worth as a portable, dense energy source powering the vast majority of vehicles and as the base of many industrial chemicals makes it one of the world's most important commodities. A commodity is anything for which there is demand but which is supplied without qualitative differentiation across a market Access to it was a major factor in several military conflicts of the late twentieth and early twenty-first centuries, including World War II and the Persion Gulf Wars (Iran-Iraq War, Operation Desert Storm, and the Iraq War). World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The Iraq War, also known as the Second Gulf War, the Occupation of Iraq, or the War in Iraq, is an ongoing Military campaign The top three oil producing countries are Saudi Arabia, Russia, and the United States. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending The United States of America —commonly referred to as the About 80% of the world's readily accessible reserves are located in the Middle East, with 62. The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. 5% coming from the Arab 5: Saudi Arabia (12. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi 5%), UAE, Iraq, Qatar and Kuwait. For a topic outline on this subject see List of basic Iraq topics. Qatar ( قطر; ˈqɑtˁɑr local pronunciation giṭar officially the State of Qatar (Arabic دولة قطر transliterated The State of Kuwait ( دولة الكويت IPA [dawlatt̪ alkuwajt̪]) is a sovereign Arab Emirate on the coast of the Persian Gulf, enclosed However, with today's oil prices, Venezuela has larger reserves than Saudi Arabia due to crude reserves derived from bitumen. Bitumen is a mixture of organic Liquids that are highly Viscous, black sticky entirely soluble in Carbon disulfide, and composed primarily
## Uses
The chemical structure of petroleum is composed of hydrocarbon chains of different lengths. In Organic chemistry, a hydrocarbon is an Organic compound consisting entirely of Hydrogen and Carbon. Because of this, petroleum may be taken to oil refineries and the hydrocarbon chemicals separated by distillation and treated by other chemical processes, to be used for a variety of purposes. An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline Distillation is a method of separating Mixtures based on differences in their volatilities in a boiling liquid mixture In a " scientific " sense a chemical process is a method or means of somehow changing one or more Chemicals or Chemical compounds Such a chemical See Petroleum products. Petroleum products are useful materials derived from crude oil ( Petroleum) as it is processed in Oil refineries.
### Fuels
Further information: alternative fuel
Generally used in transportation, power plants and heating. Alternative fuels, also known as non-conventional Fuels are any Materials or substances that can be used as a Fuel, other than conventional fuels ETHANE is a mnemonic indicating a protocol used by Emergency services to report situations which they may be faced with especially as it relates to major incidents where Alkanes, also known as Paraffins are Chemical compounds that consist only of the elements Carbon (C and Hydrogen (H (i Diesel or Diesel fuel (ˈdiːzəl in general is any Fuel used in Diesel engines The most common is a specific fractional distillate of petroleum Fuel oil is a fraction obtained from Petroleum Distillation, either as a distillate or a residue Jet fuel is a type of Aviation fuel designed for use in Aircraft powered by gas-turbine engines. Kerosene, sometimes spelled kerosine in scientific and industrial usage is a Combustible Hydrocarbon liquid Liquefied petroleum gas (also called LPG, GPL, LP Gas, or Autogas) is a mixture of Hydrocarbon Gases used as a Fuel Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane,
Petroleum vehicles are internal combustion engine vehicles. The internal combustion engine is an engine in which the Combustion of Fuel and an Oxidizer (typically air occurs in a confined space called a
### Other derivatives
Certain types of resultant hydrocarbons may be mixed with other non-hydrocarbons, to create other end products:
• Alkenes (olefins) which can be manufactured into plastics or other compounds
• Lubricants (produces light machine oils, motor oils, and greases, adding viscosity stabilizers as required). In Organic chemistry, an alkene, olefin, or olefine is an unsaturated Chemical compound containing at least one Carbon Plastic is the general common term for a wide range of synthetic or semisynthetic organic solid materials suitable for the manufacture of industrial products A lubricant (sometimes referred to as a "Lube" is a substance (often a liquid introduced between two moving surfaces to reduce the Friction between them improving Motor oil, or engine oil, is an Oil used for lubrication of various Internal combustion engines While the main function is to lubricate Moving Although the word grease originally described the rendered fat of animals the term is now applied more broadly to mean a Lubricant of higher initial Viscosity Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.
• Wax, used in the packaging of frozen foods, among others. Wax has traditionally referred to a substance that is secreted by Bees ( Beeswax) and used by them in constructing their Frozen food is food preserved by the process of Freezing. Freezing food is a common method of Food preservation which slows both food decay and by
• Sulfur or Sulfuric acid. Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 Sulfuric (or sulphuric acid, H 2 S[[oxygen O]]4 is a strong Mineral acid. These are a useful industrial materials. Sulfuric acid is usually prepared as the acid precursor oleum, a byproduct of sulfur removal from fuels. Oleum ( Latin oleum = "oil" or fuming sulfuric acid refers to a solution various compositions of Sulfur trioxide in Sulfuric Hydrodesulfurization (HDS is a Catalytic chemical process widely used to remove Sulfur (S from Natural gas and from refined petroleum products
• Bulk tar. Tar is a viscous black Liquid derived from the Destructive distillation of organic matter
• Asphalt
• Petroleum coke, used in speciality carbon products or as solid fuel. Asphalt ( is a sticky black and highly viscous liquid or semi-solid that is present in most crude Petroleums and in some natural deposits sometimes termed asphaltum Petroleum coke (often abbreviated petcoke) is a Carbonaceous solid derived from Oil refinery Coker units or other cracking processes
• Paraffin wax
• Aromatic petrochemicals to be used as precursors in other chemical production. In chemistry paraffin is the common name for the Alkane Hydrocarbons with the general formula C n H2 n +2 Petrochemicals are chemical products made from raw materials of Petroleum or other Hydrocarbon origin A chemical substance is a Material with a definite chemical composition.
### Consumption statistics
Global fossil carbon emissions, an indicator of consumption, for 1800-2004. Total is black. Oil is in blue.
## Environmental effects
Diesel fuel spill on a road
The presence of oil has significant social and environmental impacts, from accidents and routine activities such as seismic exploration, drilling, and generation of polluting wastes not produced by other alternative energies. A society is a Population of Humans characterized by patterns of relationships between individuals that share a distinctive Culture and Institutions See also Natural environment The '''biophysical''' environment is the symbiosis between the physical environment and the Biological Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes Drilling is the process of using a Drill bit in a Drill to produce cylindrical holes in solid materials such as wood or metal Pollution is the introduction of contaminants into an environment that causes instability disorder harm or discomfort to the physical systems or living organisms they are in
### Extraction
Oil extraction is costly and sometimes environmentally damaging, although Dr. John Hunt of the Woods Hole Oceanographic Institution pointed out in a 1981 paper that over 70% of the reserves in the world are associated with visible macroseepages, and many oil fields are found due to natural seeps. John M Hunt (1918 – 2005 was a geologist chemist and oceanographer The Woods Hole Oceanographic Institution (WHOI is a private nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and Offshore exploration and extraction of oil disturbs the surrounding marine environment. [25] Extraction may involve dredging, which stirs up the seabed, killing the sea plants that marine creatures need to survive. Dredging is an Excavation activity or operation usually carried out at least partly underwater in shallow seas or Fresh water areas with the purpose of "Ocean Floor" redirects here For the 2001 song by Audio Adrenaline, see Lift (Audio Adrenaline album. But at the same time, offshore oil platforms also form micro-habitats for marine creatures. An oil platform or oil rig is a large structure used to house workers and machinery needed to drill and/or extract oil and Natural gas through wells
### Oil spills
Volunteers cleaning up the aftermath of the Prestige oil spill
Main article: Oil spill
Crude oil and refined fuel spills from tanker ship accidents have damaged natural ecosystems in Alaska, the Galapagos Islands, France and many other places and times in Spain (i. The Prestige was an Oil tanker whose sinking in 2002 off the Galician coast caused a large Oil spill. For the fictional character see Oil Slick (Transformers. An oil spill is the release of a Liquid Petroleum Hydrocarbon into For the fictional character see Oil Slick (Transformers. An oil spill is the release of a Liquid Petroleum Hydrocarbon into An ecosystem is a natural unit consisting of all plants animals and micro-organisms( Biotic factors in an area functioning together with all of the non-living physical ( Alaska ( Аляска Alyaska) is a state in the United States of America, in the northwest of the North American continent This article is about the country For a topic outline on this subject see List of basic France topics. This is a list of Oil spills throughout the world One tonne of crude oil is roughly equal to 308 US gallons or 7 Spain () or the Kingdom of Spain (Reino de España is a country located mostly in southwestern Europe on the Iberian Peninsula. e. Ibiza). Ibiza (Eivissa is an island located in the Mediterranean Sea about 80 km off the coast of Spain
The quantity of oil spilled during accidents has ranged from a few hundred tons to several hundred thousand tons (Atlantic Empress, Amoco Cadiz. The Atlantic Empress was a Greek Oil tanker that was involved in two large oil spills Sequence of events En route from the Persian Gulf to Rotterdam, the Netherlands via a scheduled stop at Lyme Bay, Great Britain the ship encountered . . ). Smaller spills have already proven to have a great impact on ecosystems, such as the Exxon Valdez oil spill
Oil spills at sea are generally much more damaging than those on land, since they can spread for hundreds of nautical miles in a thin oil slick which can cover beaches with a thin coating of oil. The Exxon Valdez oil spill occurred in Prince William Sound, Alaska, on March 24 1989 A nautical mile or sea mile is a unit of Length. It corresponds approximately to one minute of Latitude along any meridian. For the fictional character see Oil Slick (Transformers. An oil spill is the release of a Liquid Petroleum Hydrocarbon into This can kill sea birds, mammals, shellfish and other organisms it coats. Oil spills on land are more readily containable if a makeshift earth dam can be rapidly bulldozed around the spill site before most of the oil escapes, and land animals can avoid the oil more easily. A dam is a barrier that divides waters. Dams generally serve the primary purpose of retaining water while other structures such as Floodgates, Levees ----A bulldozer is a crawler ( Caterpillar tracked Tractor) equipped with a substantial metal plate (known as a blade) used to push large quantities
Control of oil spills is difficult, requires ad hoc methods, and often a large amount of manpower (picture). The dropping of bombs and incendiary devices from aircraft on the Torrey Canyon wreck got poor results;[26] modern techniques would include pumping the oil from the wreck, like in the Prestige oil spill or the Erika oil spill. The Torrey Canyon was a Supertanker capable of carrying a cargo of 120000 tons of Crude oil, which was wrecked off the western coast of Cornwall The Prestige was an Oil tanker whose sinking in 2002 off the Galician coast caused a large Oil spill. Erika was the name of a tanker built in 1975 and last chartered by Total-Fina-Elf. [27]
### Global warming
Main article: Global warming
Burning oil releases carbon dioxide (CO2) into the atmosphere, which is credited with contributing to global warming. Global warming is the increase in the average measured temperature of the Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Global warming is the increase in the average measured temperature of the Per joule, oil produces 15% less CO2 than coal, but 30% more than natural gas. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, However, the unique role of oil as the main source of transportation fuel makes reducing its CO2 emissions a difficult problem. Transport or transportation is the movement of people and goods from one place to another Fuel is any material that is burned or altered in order to obtain energy While large power plants can, in theory, eliminate their CO2 emissions by techniques such as carbon sequestering or even use them to increase oil production through enhanced oil recovery techniques, these amelioration strategies do not generally work for individual vehicles
### Whales
It has been argued that the advent of petroleum-refined kerosene saved the great cetaceans from extinction by providing a cheap substitute for whale oil, thus eliminating the economic imperative for whaling. A power station (also referred to as generating station, power plant or powerhouse) is an industrial facility for the generation of Carbon capture and storage ( CCS) is an approach to mitigating Global warming based on capturing Carbon dioxide (CO2 from large Enhanced Oil Recovery (abbreviated EOR is a generic term for techniques for increasing the amount of Oil that can be extracted from an Oil field. Whaling is the hunting of Whales and dates back to at least 6000 BC [28]
## Alternatives to petroleum
Main article: Renewable energy
### Alternatives to petroleum-based vehicle fuels
The term alternative propulsion or "alternative methods of propulsion" includes both:
• alternative fuels used in standard or modified internal combustion engines (i. Renewable energy is Energy generated from Natural resources mdashsuch as Sunlight, Wind, Rain, tides and geothermal Alternative propulsion is a term used frequently for Powertrain concepts differing from the Internal combustion engine concept used in only Petroleum fueled Fuel economy in automobiles is the amount of Fuel required to move the Automobile over a given Distance. The hydrogen economy is a proposed method of deriving the Energy needed for Motive power (cars boats airplanes buildings or portable electronics by reacting Alternative fuels, also known as non-conventional Fuels are any Materials or substances that can be used as a Fuel, other than conventional fuels The internal combustion engine is an engine in which the Combustion of Fuel and an Oxidizer (typically air occurs in a confined space called a e. combustion hydrogen or biofuels). Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1
• propulsion systems not based on internal combustion, such as those based on electricity (for example, all-electric or hybrid vehicles), compressed air, or fuel cells (i. The Electric Vehicle was an American Automobile manufactured only in 1899 A hybrid vehicle is a vehicle that uses two or more distinct power sources to propel the vehicle A Compressed air car is an alternative fuel car that uses a motor powered by compressed air A fuel cell is an electrochemical conversion device It produces electricity from Fuel (on the Anode side and an oxidant (on the e. hydrogen fuel cells).
Nowadays, cars can be classified between the next main groups:
• Petro-cars, this is, only use petroleum and biofuels (biodiesel and biobutanol). Biodiesel refers to a non-petroleum-based Diesel fuel consisting of short chain Alkyl ( Methyl or ethyl) Esters made by Butanol may be used as a Fuel in an Internal combustion engine.
• Hybrid vehicles and plug-in hybrids, that use petroleum and other source, generally, electricity. A hybrid vehicle is a vehicle that uses two or more distinct power sources to propel the vehicle A plug-in hybrid electric vehicle ( PHEV) is a Hybrid vehicle with batteries that can be recharged by connecting a plug to an Electric power
• Petrofree cars, that do not use petroleum, like electric cars, hydrogen vehicles. An electric car is a type of alternative fuel Car that utilizes Electric motors and Motor controllers instead of an Internal combustion engine A hydrogen vehicle is a Vehicle that uses Hydrogen as its on-board fuel for motive power . .
## Future of petroleum production
Main articles: Peak oil and Hubbert peak theory
The future of petroleum as a fuel remains somewhat controversial. USA Today news reported in 2004 that there were 40 years of petroleum left in the ground. USA TODAY is a national American daily Newspaper published by the Gannett Company. Some argue that because the total amount of petroleum is finite, the dire predictions of the 1970s have merely been postponed. Others claim that technology will continue to allow for the production of cheap hydrocarbons and that the earth has vast sources of unconventional petroleum reserves in the form of tar sands, bitumen fields and oil shale that will allow for petroleum use to continue in the future, with both the Canadian tar sands and United States shale oil deposits representing potential reserves matching existing liquid petroleum deposits worldwide. [11]
### Hubbert peak theory
The Hubbert peak theory (also known as peak oil) posits that future petroleum production (whether for individual oil wells, entire oil fields, whole countries, or worldwide production) will eventually peak and then decline at a similar rate to the rate of increase before the peak as these reserves are exhausted. It also suggests a method to calculate the timing of this peak, based on past production rates, the observed peak of past discovery rates, and proven oil reserves. The peak of oil discoveries was in 1965, and oil production per year has surpassed oil discoveries every year since 1980. [29]
In 1956, M. King Hubbert correctly predicted US oil production would peak around 1971. Marion King Hubbert (October 5 1903 &ndash October 11 1989 was a Geoscientist who worked at the Shell research When this occurred and the US began losing its excess production capacity, OPEC gained the ability to manipulate oil prices, leading to the 1973 and 1979 oil crises. The Organization of the Petroleum Exporting Countries ( OPEC) is a Cartel of thirteen countries made up of Algeria, Angola, Ecuador The 1973 oil crisis began on October 17 1973 when the members of Organization of Arab Petroleum Exporting Countries (OAPEC consisting of the Arab members of The 1979 (or second) oil crisis in the United States occurred in the wake of the Iranian Revolution. Since then, most other countries have also peaked. China has confirmed that two of its largest producing regions are in decline, and Mexico's national oil company, Pemex, has announced that Cantarell Field, one of the world's largest offshore fields, was expected to peak in 2006, and then decline 14% per annum. Petróleos Mexicanos ( PEMEX) is Mexico 's state-owned Petroleum company Cantarell Field or Cantarell Complex is the largest Oil field in Mexico and one of the largest in the world
Controversy surrounds predictions of the timing of the global peak, as these predictions are dependent on the past production and discovery data used in the calculation as well as how unconventional reserves are considered. Supergiant fields have been discovered in the past decade, such as Azadegan, Carioca/Sugar Loaf, Tupi, Jupiter, Ferdows/Mounds/Zagheh, Tahe, Jidong Nanpu/Bohai Bay, West Kamchatka, and Kashagan, as well as tremendous reservoir growth from places like the Bakken and massive syncrude operations in Venezuela and Canada. [30] However, while past understanding of total oil reserves changed with newer scientific understanding of petroleum geology, current estimates of total oil reserves have been in general agreement since the 1960s. Further, predictions regarding the timing of the peak are highly dependent on the past production and discovery data used in the calculation.
It is difficult to predict the oil peak in any given region, due to the lack of transparency in accounting of global oil reserves. Accountancy or accounting is the measurement statement or provision of assurance about financial information primarily used by Lenders managers, [31] Based on available production data, proponents have previously predicted the peak for the world to be in years 1989, 1995, or 1995-2000. Some of these predictions date from before the recession of the early 1980s, and the consequent reduction in global consumption, the effect of which was to delay the date of any peak by several years. Just as the 1971 U. S. peak in oil production was only clearly recognized after the fact, a peak in world production will be difficult to discern until production clearly drops off.
## Petroleum by country
Oil consumption per capita (darker colors represent more consumption).
### Consumption rates
There are two main ways to measure the oil consumption rates of countries: by population or by gross domestic product (GDP). This metric is important in the global debate over oil consumption/energy consumption/climate change because it takes social and economic considerations into account when scoring countries on their oil consumption/energy consumption/climate change goals. Nations such as China and India with large populations tend to promote the use of population based metrics, while nations with large economies such as the United States would tend to promote the GDP based metric.
Selected NationsGDP-to-consumption ratio
(US\$1000/(barrel/year))
Switzerland3. Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation 75
United Kingdom3. The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located 34
Norway3. Norway ( Norwegian: Norge ( Bokmål) or Noreg ( Nynorsk) officially the Kingdom of Norway, is a Constitutional 31
Austria2. Austria (Österreich ( officially the Republic of Austria (Republik Österreich 96
Germany2. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. 89
Sweden2. "Sverige" redirects here For other uses see Sweden (disambiguation and Sverige (disambiguation. 71
Italy2. Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest 57
European Union2. The European Union ( EU) is a political and economic union of twenty-seven member states, located primarily in 52
DRC2. The Democratic Republic of the Congo (République démocratique du Congo often referred to as DR Congo, DRC or RDC, and formerly known or referred to 4
Japan2. For a topic outline on this subject see List of basic Japan topics. 34
Australia2. For a topic outline on this subject see List of basic Australia topics. 21
Spain1. Spain () or the Kingdom of Spain (Reino de España is a country located mostly in southwestern Europe on the Iberian Peninsula. 96
Poland1. Poland (Polska officially the Republic of Poland 87
United States1. The United States of America —commonly referred to as the 65
Belgium1. The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those 59
World1. "The world " is a proper noun for the planet Earth envisioned from an Anthropocentric or Human Worldview, as a place 47
Turkey1. Turkey (Türkiye known officially as the Republic of Turkey ( is a Eurasian Country that stretches 39
Mexico1. The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America. 07
Ethiopia1. NOTE This intro is the result of careful NPOV work Please do not make potentially controversial edits to it without first discussing on the talk page 04
South Korea1. South Korea, officially the Republic of Korea and often referred to as Korea ( Korean: 대한민국 tɛː 00
Philippines1. The Philippines ( Filipino: Pilipinas, officially known as the Republic of the Philippines (fil ''Republika ng Pilipinas'' RP 00
Brazil0. |utc_offset = -2 to -4 |time_zone_DST = BRST |utc_offset_DST = -2 to -5 |cctld 99
Taiwan0. Taiwan ( Taiwanese: Tâi-oân/Tāi-oân (historically 大灣/台員/大員/台圓/大圓/台窩灣 is an Island in East Asia. 98
China0. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National 94
Nigeria0. Nigeria, officially named the Federal Republic of Nigeria, is a federal Constitutional republic comprising thirty-six states and one Federal 94
Pakistan0. Pakistan () officially the Islamic Republic of Pakistan, is a country located in South Asia, Southwest Asia, Middle East and 93
Myanmar0. Burma, officially the Union of Myanmar ( pjìdàunzṵ mjàmmà nàinŋàndɔ̀ is the largest country by geographical area in mainland Southeast Asia. 89
India0. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country 86
Russia0. Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending 84
Indonesia0. The Republic of Indonesia ( (Republik Indonesia is a Country in Southeast Asia. 71
Vietnam0. Vietnam (ˌviːɛtˈnɑːm Việt Nam) officially 61
Thailand0. The Kingdom of Thailand (ˈtaɪlænd ราชอาณาจักรไทย, râːtɕʰa-ʔaːnaːtɕɑ̀k-tʰɑj 53
Saudi Arabia0. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi 46
Singapore0. Singapore 40
Iran0. For a topic outline on this subject see List of basic Iran topics. 35
Selected NationsPer capita energy consumption, oil equivalent
(barrel/person/year)
DRC0. The Democratic Republic of the Congo (République démocratique du Congo often referred to as DR Congo, DRC or RDC, and formerly known or referred to 13
Ethiopia0. NOTE This intro is the result of careful NPOV work Please do not make potentially controversial edits to it without first discussing on the talk page 37
Myanmar0. Burma, officially the Union of Myanmar ( pjìdàunzṵ mjàmmà nàinŋàndɔ̀ is the largest country by geographical area in mainland Southeast Asia. 73
Pakistan1. Pakistan () officially the Islamic Republic of Pakistan, is a country located in South Asia, Southwest Asia, Middle East and 95
Nigeria2. Nigeria, officially named the Federal Republic of Nigeria, is a federal Constitutional republic comprising thirty-six states and one Federal 17
India2. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country 18
Vietnam2. Vietnam (ˌviːɛtˈnɑːm Việt Nam) officially 70
Philippines3. The Philippines ( Filipino: Pilipinas, officially known as the Republic of the Philippines (fil ''Republika ng Pilipinas'' RP 77
Indonesia4. The Republic of Indonesia ( (Republik Indonesia is a Country in Southeast Asia. 63
China4. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National 96
Turkey9. Turkey (Türkiye known officially as the Republic of Turkey ( is a Eurasian Country that stretches 85
Brazil11. |utc_offset = -2 to -4 |time_zone_DST = BRST |utc_offset_DST = -2 to -5 |cctld 67
Poland11. Poland (Polska officially the Republic of Poland 67
World12. "The world " is a proper noun for the planet Earth envisioned from an Anthropocentric or Human Worldview, as a place 55
Thailand13. The Kingdom of Thailand (ˈtaɪlænd ราชอาณาจักรไทย, râːtɕʰa-ʔaːnaːtɕɑ̀k-tʰɑj 86
Russia17. Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending 66
Mexico18. The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America. 07
Iran21. For a topic outline on this subject see List of basic Iran topics. 56
European Union29. The European Union ( EU) is a political and economic union of twenty-seven member states, located primarily in 70
United Kingdom30. The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located 18
Germany32. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. 31
Italy32. Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest 43
Austria34. Austria (Österreich ( officially the Republic of Austria (Republik Österreich 01
Spain35. Spain () or the Kingdom of Spain (Reino de España is a country located mostly in southwestern Europe on the Iberian Peninsula. 18
Switzerland34. Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation 64
Sweden34. "Sverige" redirects here For other uses see Sweden (disambiguation and Sverige (disambiguation. 68
Taiwan41. Taiwan ( Taiwanese: Tâi-oân/Tāi-oân (historically 大灣/台員/大員/台圓/大圓/台窩灣 is an Island in East Asia. 68
Japan42. For a topic outline on this subject see List of basic Japan topics. 01
Australia42. For a topic outline on this subject see List of basic Australia topics. 22
South Korea43. South Korea, officially the Republic of Korea and often referred to as Korea ( Korean: 대한민국 tɛː 84
Norway52. Norway ( Norwegian: Norge ( Bokmål) or Noreg ( Nynorsk) officially the Kingdom of Norway, is a Constitutional 06
Belgium61. The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those 52
United States68. The United States of America —commonly referred to as the 81
Saudi Arabia75. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi 08
Singapore178. Singapore 45
(Note: The figure for Singapore is skewed because of its small
population compared with its large oil refining capacity.
Most of this oil is sent to other countries. )
### Production
Oil producing countries
In petroleum industry parlance, production refers to the quantity of crude extracted from reserves, not the literal creation of the product. This is a list of Countries and their states/provinces that extract Crude oil from Oil wells Africa Algeria (
In order of amount produced in 2006 in thousand bbl/d and thousand /d:
#Producing Nation (2006)(103bbl/d)(103m3/d)
1Saudi Arabia (OPEC)10,6651,704
2Russia 19,6771,537
3United States 18,3311,330
4Iran (OPEC)4,148659
5China3,858610
6Mexico 13,707589
8United Arab Emirates (OPEC)2,945467
9Venezuela (OPEC) 12,803446
10Norway 12,786443
11Kuwait (OPEC)2,675425
12Nigeria (OPEC)2,443388
13Brazil2,166344
14Algeria (OPEC)2,122337
15Iraq (OPEC) 32,008319
1 peak production of conventional oil already passed in this state
2 Although Canadian conventional oil production is declining, total oil production is increasing as oil sands production grows. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the CM3 redirects here If you were looking for the 3rd game in the Cooking Mama series abbreviated as CM3 see here. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi The Organization of the Petroleum Exporting Countries ( OPEC) is a Cartel of thirteen countries made up of Algeria, Angola, Ecuador Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending The United States of America —commonly referred to as the For a topic outline on this subject see List of basic Iran topics. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America. Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page Venezuela (ˌvɛnəˈzweɪlə) officially the Bolivarian Republic of Venezuela (Spanish República Bolivariana de Venezuela) is a country on the Norway ( Norwegian: Norge ( Bokmål) or Noreg ( Nynorsk) officially the Kingdom of Norway, is a Constitutional The State of Kuwait ( دولة الكويت IPA [dawlatt̪ alkuwajt̪]) is a sovereign Arab Emirate on the coast of the Persian Gulf, enclosed Nigeria, officially named the Federal Republic of Nigeria, is a federal Constitutional republic comprising thirty-six states and one Federal |utc_offset = -2 to -4 |time_zone_DST = BRST |utc_offset_DST = -2 to -5 |cctld Algeria ( ar [[Arabic]] الجزائر, Al Jaza'ir ælʤæˈzæːʔir Amazigh: ⴷⵥⴰⵢⴻⵔ Dzayer) officially the People's For a topic outline on this subject see List of basic Iraq topics. Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions If oil sands are included, it has the world's second largest oil reserves after Saudi Arabia.
3 Though still a member, Iraq has not been included in production figures since 1998
### Export
Oil exports by country
In order of net exports in 2006 in thousand bbl/d and thousand /d:
#Exporting Nation (2006)(103bbl/d)(103m3/d)
1Saudi Arabia (OPEC)8,6511,376
2Russia 16,5651,044
3Norway 12,542404
4Iran (OPEC)2,519401
5United Arab Emirates (OPEC)2,515400
6Venezuela (OPEC) 12,203350
7Kuwait (OPEC)2,150342
8Nigeria (OPEC)2,146341
9Algeria (OPEC) 11,847297
10Mexico 11,676266
11Libya (OPEC) 11,525242
12Iraq (OPEC)1,438229
13Angola (OPEC)1,363217
14Kazakhstan1,114177
1 peak production already passed in this state
2 Canadian statistics are complicated by the fact it is both an importer and exporter of crude oil, and refines large amounts of oil for the U. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the CM3 redirects here If you were looking for the 3rd game in the Cooking Mama series abbreviated as CM3 see here. The Kingdom of Saudi Arabia, KSA ( المملكة العربية السعودية, al-Mamlaka al-ʻArabiyya as-Suʻūdiyya) or Suudi The Organization of the Petroleum Exporting Countries ( OPEC) is a Cartel of thirteen countries made up of Algeria, Angola, Ecuador Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending Norway ( Norwegian: Norge ( Bokmål) or Noreg ( Nynorsk) officially the Kingdom of Norway, is a Constitutional For a topic outline on this subject see List of basic Iran topics. Venezuela (ˌvɛnəˈzweɪlə) officially the Bolivarian Republic of Venezuela (Spanish República Bolivariana de Venezuela) is a country on the The State of Kuwait ( دولة الكويت IPA [dawlatt̪ alkuwajt̪]) is a sovereign Arab Emirate on the coast of the Persian Gulf, enclosed Nigeria, officially named the Federal Republic of Nigeria, is a federal Constitutional republic comprising thirty-six states and one Federal Algeria ( ar [[Arabic]] الجزائر, Al Jaza'ir ælʤæˈzæːʔir Amazigh: ⴷⵥⴰⵢⴻⵔ Dzayer) officially the People's The United Mexican States ( or commonly Mexico (ˈmɛksɪkoʊ () is a federal constitutional Republic in North America. Libya ( ليبيا ar-Latn Lībiyā; Libyan vernacular: Lībya; Amazigh:) officially the Great Socialist People's Libyan Arab For a topic outline on this subject see List of basic Iraq topics. Angola, officially the Republic of Angola (República de Angola Pronounced ʁɛˈpublikɐ dɨ ɐ̃ˈgɔlɐ Repubilika ya Ngola is a country in south-central Kazakhstan, also Kazakstan ( Қазақстан, Qazaqstan, qɑzɑqˈstɑn Казахстан, Kazakhstán,) officially the Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions S. market. It is the leading source of U. S. imports of oil and products, averaging 2. 5 MMbbl/d in August 2007. [2].
Total world production/consumption (as of 2005) is approximately 84 million barrels per day (13,400,000 m³/d).
See also: Organization of Petroleum Exporting Countries. The Organization of the Petroleum Exporting Countries ( OPEC) is a Cartel of thirteen countries made up of Algeria, Angola, Ecuador
### Consumption
In order of amount consumed in 2006 in thousand bbl/d and thousand /d:
#Consuming Nation 2006(103bbl/day)(103m3/day)
1United States 120,5883,273
2China7,2741,157
3Japan 25,222830
4Russia 13,103493
5Germany 22,630418
6India 22,534403
8Brazil2,183347
9South Korea 22,157343
10Saudi Arabia (OPEC)2,068329
11Mexico 12,030323
12France 21,972314
13United Kingdom 11,816289
14Italy 21,709272
15Iran (OPEC)1,627259
1 peak production of oil already passed in this state
2 This country is not a major oil producer
### Import
Oil imports by country
In order of net imports in 2006 in thousand bbl/d and thousand /d:
#Importing Nation (2006)(103bbl/day)(103m3/day)
1United States 112,2201,943
2Japan5,097810
3China 23,438547
4Germany2,483395
5South Korea2,150342
6France1,893301
7India1,687268
8Italy1,558248
9Spain1,555247
10Taiwan942150
11Netherlands936149
12Singapore787125
13Thailand60696
14Turkey57692
15Belgium54687
1 peak production of oil already passed in this state
2 Major oil producer whose production is still increasing
### Non-producing consumers
#Consuming Nation(bbl/day)(m³/day)
1Japan5,578,000886,831
2Germany2,677,000425,609
3South Korea2,061,000327,673
4France2,060,000327,514
5Italy1,874,000297,942
6Spain1,537,000244,363
7Netherlands946,700150,513
Source : CIA World Factbook
## Writers covering the petroleum industry
• List of oil fields
• List of oil-producing states
• List of oil-consuming states
• Partial List of Countries that have already passed their production peak
• List of petroleum companies
• 1990 spike in the price of oil
• Abiogenic petroleum origin
• ANWR (Arctic National Wildlife Refuge)
• Bioplastic
• Crude oil washing
• Ecodollar
• Energy conservation
• Energy crisis: 1973 energy crisis, 1979 energy crisis
• Energy development
• Eugene Island
• Fossil fuel
• Gas oil ratio
• Global warming
• Greenhouse gases
• Gross domestic product per barrel
• History of the Petroleum Industry
• Hubbert peak
• Mineral oil
• Nationalization of oil supplies
• Natural gas, another fossil fuel
• Non-conventional oil
• Oil phase-out in Sweden
• Oil price increases since 2003
• Oil refinery
• Oil reserves
• Oil supplies
• Oil well
• Olduvai theory (not strictly about oil, but it basically assumes that oil and gas are the only significant energy sources)
• Passive margin
• Platts
• Peak oil
• Petroleum disasters
• Petroleum geology
• Petrodollar
• Petro-free : that does not use or sell petroleum (i. Brian Black is an US professor of history and Environmental studies at Pennsylvania State University, Altoona Pennsylvania. Colin J Campbell, PhD Oxford, (born in Berlin, Germany in 1931 is a retired British petroleum geologist who predicts that oil production will Kenneth S Deffeyes is a Geologist who worked with M King Hubbert of Hubbert's peak fame at the Shell Oil Company research laboratory Thomas Gold ( May 22, 1920 &ndash June 22, 2004) was an Austrian born Astrophysicist, a professor of Astronomy David L Goodstein (born 1939 is a US physicist and educator Since 1988 he has served as Vice- provost of the California Institute of Technology Daniel H Yergin (born February 6, 1947) is an American author speaker and economic researcher Derrick Jensen (born December 19, 1960) is an American author and Environmental activist This list of Oil fields includes some of Major oil fields of the past and present This is a list of Countries and their states/provinces that extract Crude oil from Oil wells Africa Algeria ( Countries in decreasing order of oil consumption ( Barrels per day in 2005 These are lists of petroleum companies. List of companies by size of oil reserves A list of the largest petroleum companies is always somewhat arbitrary as state-owned companies The 1990 (or third) energy crisis was milder and more brief than the two previous oil crises ( 1973 and 1979) The hypothesis of abiogenic petroleum origin is an alternative hypothesis to the biological origin theory which was popular in Russia and Ukraine between The Arctic National Wildlife Refuge ( ANWR) is a National Wildlife Refuge in northeastern Alaska. Due to its toxicity, Lead has been phased out of Petroleum used in many countries For information on plastics which are biodegradable see Biodegradable plastic. Crude oil washing (COW is washing out the residue from the tanks of an Oil tanker using the crude oil cargo itself after the cargo tanks have been emptied Energy conservation is the practice of decreasing the quantity of energy used An energy crisis is any great bottleneck (or price Rise) in the supply of energy resources to an economy. The 1973 oil crisis began on October 17 1973 when the members of Organization of Arab Petroleum Exporting Countries (OAPEC consisting of the Arab members of The 1979 (or second) oil crisis in the United States occurred in the wake of the Iranian Revolution. Energy development is the ongoing effort to provide sufficient Primary energy sources and secondary Energy forms to meet civilization's needs Fossil fuels or mineral fuels are fossil source Fuels that is Hydrocarbons found within the top layer of the Earth’s crust. When oil is brought to surface conditions it is usual for some gas to come out of solution Global warming is the increase in the average measured temperature of the Greenhouse gases are gaseous constituents of the atmosphere bothnatural and anthropogenic that absorb and emit radiation at specific wavelengths within the spectrum of thermal infrared Energy efficiency as it relates to oil usage can be described by the Gross domestic product per Barrel (GDP per barrel (GDP/barrel of oil used The petroleum industry includes the global processes of exploration, extraction, refining, transporting (often by Oil tankers and pipelines Mineral oil or liquid Petroleum is a By-product in the Distillation of Petroleum to produce Gasoline and other petroleum The Nationalization of oil supplies refers to the process of deprivatization of oil production operations and is often combined with restrictions on crude oil exports Natural gas is a Gaseous Fossil fuel consisting primarily of Methane but including significant quantities of Ethane, Propane, Fossil fuels or mineral fuels are fossil source Fuels that is Hydrocarbons found within the top layer of the Earth’s crust. Non-conventional oil is oil produced or extracted using techniques other than the traditional Oil well method In 2005 the Government of Sweden announced their intention to make Sweden the first country to break its dependence on Petroleum, Natural gas An oil refinery is an industrial Process plant where Crude oil is processed and refined into more useful Petroleum products, such as Gasoline Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions Oil reserves are the estimated quantities of Crude oil that are claimed to be recoverable under existing Economic and operating conditions West Texas PumpjackJPG|thumb|right|300px|This Pumpjack located south of Midland TX is a common sight in West Texas. The Olduvai theory states that industrial civilization (as defined by per capita energy consumption will have a lifetime of less than or equal to 100 years (1930-2030 A Passive margin is the transition between oceanic and Continental crust which is not an active plate margin Platts is a provider of energy information around the world that has been in business in various forms for more than a century and is now a division of The McGraw-Hill Companies For the fictional character see Oil Slick (Transformers. An oil spill is the release of a Liquid Petroleum Hydrocarbon into Petroleum geology refers to the specific set of geological disciplines that are applied to the search for Hydrocarbons ( Oil exploration) A petrodollar is a US dollar earned by a country through the sale of petroleum Alternative propulsion is a term used frequently for Powertrain concepts differing from the Internal combustion engine concept used in only Petroleum fueled e. petro-free fuel station). A filling station, fueling station, gas station, service station, petrol station, or gasbar, Retail Outlet
• Petroleum politics
• Predicting the timing of peak oil
• Price of oil
• Renewable energy
• Rosneft
• Soft energy path
• Subsea
• Thermal depolymerization
• Thomas Gold
• World energy resources and consumption
## References
1. ^ Bauer Georg, Hoover Herbert (tr.), Hoover Lou(tr.). Petroleum politics have been an increasingly important aspect of international diplomacy since the discovery of oil in the Middle East in the early 1900s See also Peak oil M King Hubbert, who devised the peak theory correctly predicted in 1956 that oil production would peak in the United States between 1965 and 1970 This article is about the price of crude oil see Gasoline usage and pricing for information about derivative motor fuels Renewable energy is Energy generated from Natural resources mdashsuch as Sunlight, Wind, Rain, tides and geothermal OAO Rosneft Oil Company ( Роснефть) () is an integrated petroleum company owned by the Russian Government In 1976 Amory Lovins coined the term "soft path" to describe an alternative future where efficiency and appropriate renewable Energy sources steadily replace a centralized Subsea is a general term frequently used to refer to equipment technology and methods employed to explore drill and develop oil and gas fields that exist below the ocean floors Thermal depolymerization ( TDP) is a process using Hydrous pyrolysis for the reduction of complex Organic materials (usually Waste products of Thomas Gold ( May 22, 1920 &ndash June 22, 2004) was an Austrian born Astrophysicist, a professor of Astronomy Georgius Agricola ( March 24, 1494 – November 21, 1555) was a German scholar and scientist De re metallica xii. translated 1912
2. ^ Speight, James G. (1999). The Chemistry and Technology of Petroleum. Marcel Dekker, pp. 215-216. ISBN 0824702174.
3. ^ IEA Key World Energy Statistics
4. ^ "Crude oil is made into different fuels"
5. ^ EIA reserves estimates
6. ^ CERA report on total world oil
7. ^ Heat of Combustion of Fuels
8. ^ Use of ozone depleting substances in laboratories. TemaNord 2003:516. http://www.norden.org/pub/ebook/2003-516.pdf
9. ^ Petroleum Study
10. ^ Oil Is Mastery
11. ^ a b Lambertson, Giles. "Oil Shale: Ready to Unlock the Rock", Construction Equipment Guide, 2008-02-16. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1249 - Andrew of Longjumeau is dispatched by Louis IX of France as his ambassador to meet with the Khan of the Mongols Retrieved on 2008-05-21. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 878 - Syracuse Italy is captured by the Muslim sultan of Sicily.
12. ^ Kenney et al., Dismissal of the Claims of a Biological Connection for Natural Petroleum, Energia 2001
13. ^ Glasby, Geoffrey P. (2006). "Abiogenic origin of hydrocarbons: an historical overview" (PDF). Resource Geology 56 (1): 83–96.
14. ^ "Huge fuel reserves are just 1.2 billion km away, scientists say", CBC News, 2008-02-14. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 842 - Charles the Bald and Louis the German swear the Oaths of Strasbourg in the French and German Retrieved on 2008-02-17. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1500 - Battle of Hemmingstedt. 1600 - Philosopher Giordano Bruno is burned alive at Campo de' Fiori
15. ^ Light Sweet Crude Oil. About the Exchange. New York Mercantile Exchange (NYMEX) (2006). Retrieved on 2008-04-21. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 753 BC - Romulus and Remus found Rome ( traditional date)
16. ^ "International Energy Annual 2004". Energy Information Administration. 14 Jul. 2006. Found at http://www.eia.doe.gov/pub/international/iealf/tablee2.xls
17. ^ Shell Middle Distillate Synthesis Malaysia
18. ^ Sasol corporate website
19. ^ a b c d This article incorporates text from the Encyclopædia Britannica Eleventh Edition article "Petroleum", a publication now in the public domain. The Encyclopædia Britannica Eleventh Edition (1910–1911 is a 29-volume reference work that marked the beginning of the Encyclopædia Britannica The public domain is a range of abstract materials &ndash commonly referred to as Intellectual property &ndash which are not owned or controlled by anyone
20. ^ ASTM timeline of oil
21. ^ Dr. Kasem Ajram (1992). The Miracle of Islam Science, 2nd Edition, Knowledge House Publishers. ISBN 0-911119-43-4.
22. ^ [1]
23. ^ Le bitume et la mine de la Presta (Suisse), Jacques Lapaire, Mineraux et Fossiles No 315
24. ^ a b History of Pechelbronn oil
25. ^ Waste discharges during the offshore oil and gas activity by Stanislave Patin, tr. Elena Cascio
26. ^ Torrey Canyon bombing by the Navy and RAF
27. ^ Pumping of the Erika cargo
28. ^ How Capitalism Saved the Whales by James S. The Torrey Canyon was a Supertanker capable of carrying a cargo of 120000 tons of Crude oil, which was wrecked off the western coast of Cornwall Robbins, The Freeman, August, 1992.
29. ^ Campbell CJ (2000-12). Peak Oil Presentation at the Technical University of Clausthal].
30. ^ NCPA - Policy Backgrounder 159 - Are We Running Out of Oil?
31. ^ New study raises doubts about Saudi oil reserves
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2013-06-19 16:24:33
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http://blogs.msdn.com/b/windowssdk/archive/2007/09/08/sdk-workaround-msbuild-reports-a-dependency-on-net-framework-sdk-2-0.aspx
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This workaround applies to:
· The prerelease Windows SDK for Windows Server 2008 and .Net Framework 3.5 (RC0), September, 2007
· The prerelease Windows SDK for Windows Server 2008 and .Net Framework 3.5 (IDS04), July, 2007
· The Windows SDK Update for Windows Vista (RTM), March, 2007
The Windows SDK does not set the HKLM\Software\Microsoft\.NETFramework\sdkInstallRootv2.0 registry key to a string value containing the root directory of the Windows SDK installation. Some MSBuild tasks may expect this registry key to be set. If you already have the .NET Framework SDK 2.0 or Visual Studio 2005, this key will be set and you should not encounter a problem. However, if you install the Windows SDK without either the .NET Framework SDK or Visual Studio 2005, you may receive an error message from MSBuild tasks with a dependency on this key. To work around this issue set the string value of this key to the root directory of the Windows SDK installation. By default, this is: C:\Program Files\Microsoft SDKs\Windows\v6.1
Additionally, in order to use AL.exe, the ALToolPath parameter must be set and passed to msbuild. For the default install location, this can be done using the following command:
msbuild /p:ALToolPath="C:\Program Files\Microsoft SDKs\Windows\v6.1\Bin
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2013-12-04 17:48:21
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https://math.stackexchange.com/questions/2705414/showing-a-functional-sequence-is-not-cauchy-wrt-infty-norm
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# Showing a functional sequence is not Cauchy wrt $\infty$ norm
I’m trying to show that the functional sequence below is not Cauchy Sequence on $C[-1,1]$ space wrt $\|.\|_{\infty}$ which is equal to $\sup_{[-1,1]}|f_n(x)|$ but I cannot obtain something concrete for exact proof. Could you please fix my mistakes or warn me about unecessary things?
$$f_n(x) = \begin{cases} 0, & \text{if -1\le x\le 0} \\ nx, & \text{if 0\lt x\lt 1/n} \\ 1, & \text{if 1/n\le x\le 1} \end{cases}$$
I have used negation of Cauchy Sequence definition
$\exists \varepsilon_0 \gt 0$ $\forall N \in \mathbb N$ $\exists n,m \ge N$ $\|f_n-f_m\|_{\infty} \ge \varepsilon_0$
Let $m\gt n$ and $1/m \lt 1/n$
I’ve written
$\|f_n-f_m\|_{\infty}$ = $\max\{\sup_{0\lt x\lt 1/m}|f_n-f_m|$ , $\sup_{1/m\lt x\lt 1/n}|f_n-f_m|\}$ = $\max \{\sup_{0\lt x\lt 1/m}|(n-m)x|$ , $\sup_{1/m\lt x\lt 1/n}|nx-1|\}$
I cannot find a $\varepsilon_0$
With all due respect, I think there ara many mistakes. I need your help
Thanks
• Suppose $n>m$, note $\|f_n-f_m\|_\infty ≥ |f_n(1/{m})-f_m(1/m)|$. What is the expression on the right? – s.harp Mar 23 '18 at 21:35
• @s.harp Thanks for your concern. Isn’t it 0? – esrabasar Mar 23 '18 at 21:45
• @Math1000 since $1/n<1/m$, $1/n\le1/m\le1$ hence $f_n(1/m)=1$ and $f_m(1/m)=1$ again. Why is it wrong? – esrabasar Mar 23 '18 at 22:03
• Ok, to be correct it has to be evaluated at $1/n$. Then $f_n(1/n)=1$ and $f_m(1/n)=m/n$. If you keep $m$ fixed and make $n$ as large as you like this difference becomes close to $1$. – s.harp Mar 23 '18 at 22:09
• @s.harp I have understood. I missed $f_m(1/n)=m/n$. For an instant, it has seemed as 1. Thanks a lot – esrabasar Mar 23 '18 at 22:14
Let $m \ge n$. The functions $f_m$ and $f_n$ are equal on $[-1, 0] \cup \left[\frac1n, 0\right]$ so we have:
$$f_m(x) - f_n(x) = \begin{cases} mx - nx, & \text{if x \in \left[0, \frac1m\right]} \\ 1-nx, & \text{if x \in \left[\frac1m, \frac1n\right]}\\ 0, & \text{otherwise} \end{cases}$$
Now we calculate $$\|f_m - f_n\|_\infty = \max\left\{\sup_{x \in \left[0, \frac1m\right] } (m-n)x, \sup_{x \in \left[\frac1m, \frac1n\right] } (1-nx)\right\} = 1 - \frac{n}{m}$$
Therefore, if we set $m = 2n$ we get
$$\|f_{2n} -f_n\| = \frac12 \not\to 0$$
so the sequence $(f_n)_n$ cannot be Cauchy.
A more conceptual way to see that $(f_n)_n$ cannot be Cauchy is to recall that $C[-1,1]$ is a Banach space and that the uniform limit of continuous functions is itself a continuous function.
If $(f_n)_n$ were Cauchy, then by completeness of $C[-1,1]$ it would converge to an element of $C[-1,1]$. Since uniform convergence implies pointwise convergence, the only candidate for the uniform limit is the pointwise limit $\chi_{\langle 0, 1]}$. However, this is not a continuous function so the convergence cannot be uniform.
• Thanks a lot. Is $C[-1,1]$ Banach wrt sup norm? – esrabasar Mar 24 '18 at 9:06
• @esrabasar Yes it is. – mechanodroid Mar 24 '18 at 11:36
• thanks a lot :) – esrabasar Mar 24 '18 at 15:09
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2019-11-21 09:23:36
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https://blender.stackexchange.com/questions/139606/rendering-backwards-in-cycles
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# Rendering Backwards in Cycles
There was already a similar question asked, but I want to render the scene backwards for a different reason: render speed.
I want to split the animation rendering between two PCs, so the first PC would start rendering at frame 0 and going up to 5000 and the second would start at the frame 5000 and going down to frame 0.
They would eventually meet at some point, let's say first PC would render 3000 frames and the second one 2000 frames = finished animation.
Is there a way in Blender Cycles to render a scene backwards instead of forward? I mean, you can go backwards on the timeline and everything works just fine so this should be possible, right?
• An other way would be to set up the two computers to save renders in a shared folder (a NAS, a Dropbox or whatever). In Render/Output, check Placeholder (so each computer will create a empty file before rendering, to 'save the slot') ; and uncheck Overwrite (so each computer won't start rendering a reserved frame). – thibsert May 2 at 22:57
• Thanks for your suggestion, that is definitely one way around it, but it is not what I need. The thing is that I have very bad experience with skipping frames or otherwise weirdly behaving meshes when there is .abc mesh sequence in the scene, like water simulation. So with shared HDD, going from frame 1 to e.g. 5 is a risk, it might not follow correctly. Basically an absolute independence of those two PCs is what I want the most and I think rendering backwards would be a great & super simple solution to this. – mikez May 3 at 2:47
## 1 Answer
This Python script will step through your frames in reverse and render them one-by-one. Save as render-backward.py:
import bpy
for frame in range(bpy.context.scene.frame_end, 1, -1):
bpy.context.scene.frame_set(frame)
bpy.ops.render.render(write_still=True)
Run it like so:
blender yourfile.blend -b -P render-backward.py
• If the above answered the question, please mark the answer as "accepted". Thanks! – pixelbath Jun 27 at 17:47
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2019-12-13 00:29:05
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https://www.jiskha.com/questions/244175/a-particle-starts-at-time-t-0-and-moves-along-the-x-axis-so-that-its-position-at-any
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# Calculus
a particle starts at time t = 0 and moves along the x axis so that its position at any time t>= 0 is given by x(t) = ((t-1)^3)(2t-3)
a.find the velocity of the particle at any time t>= 0
b. for what values of t is the velocity of the particle negative?
c. find the value of t when the particle is moving and the acceleration is zero. explain your answer choice
1. 👍
2. 👎
3. 👁
1. a) find x'(t) using the product rule, that will be your velocity
b) set x'(t) from above < 0 and solve
c) acceleration is the derivative of velocity, so differentiate x'(t) again, and set it equal to zero
1. 👍
2. 👎
2. a) Take the deriviative of x(t)
b) Set the derivative = 0 and solve the equation for t
c) Take the derivative of v(t) and set that equal to zero. If there is more than one answer, take the one for which v is not zero.
1. 👍
2. 👎
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2021-01-19 12:38:29
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https://stats.stackexchange.com/questions/360786/estimating-correlation-matrix-using-numeric-likelihood-maximization
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# Estimating correlation matrix using numeric likelihood maximization
I'm performing maximum likelihood estimation on jointly distributed data and I'm having some issues estimating the correlation terms. I am using an approach based on the Cholesky decomposition, but I feel that it has too many free parameters during estimation. Let me clarify the question.
Here's the formal definition of the data/model:
Suppose that $\mathbf{X}_i=(x_{i,1},x_{i,2},...,x_{i,n})$ and that $\mathbf{X}_i\sim Norm(\mathbf{0}_n,\mathbf{\Sigma})$, where $\mathbf{0}_n$ is just an $n$-long vector of zeros and $\mathbf{\Sigma}$ is the correlation (not covariance) matrix between the elements. Stated clearly:
$\mathbf{\Sigma}=\begin{bmatrix} 1 & \rho_{12} & \rho_{13} & \dots & \rho_{1n} \\ \rho_{12} & 1 & \rho_{23} & \dots & \rho_{2n} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ \rho_{1n} & \rho_{2n} & \rho_{3n} & \dots & 1 \end{bmatrix}$
Suppose further that all of my observations $\mathbf{X}_1,\mathbf{X}_2,...,\mathbf{X}_m$ are i.i.d.
What I'm trying to estimate are all the correlation terms contained in $\mathbf{\Sigma}$. Note that $\mathbf{\Sigma}$ contains $(n^2-n)/2$ correlation terms.
I know that I can't try to estimate the correlation terms directly, because during the estimation process that approach might generate correlation matrices that aren't positive semi-definite. What I am doing, however, is using the Cholesky decomposition approach.
Here, I generate a random vector of size $(n^2-n)/2+n$, place those elements in a lower triangular matrix, and multiply the result by its own transpose. Then, I normalize this new matrix by the using the square roots of the main diagonal. Formally:
$k = ((n^2-n)/2+n)$
$\mathbf{z} =(z_1, z_2, ..., z_k)=k$-$long \ vector \ with \ iid \ random \ draws \ from \ any \ distribution$
$\mathbf{L} = \begin{bmatrix} z_1 & 0 & 0 & \dots & 0 \\ z_2 & z_3 & 0 & \dots & 0 \\ z_4 & z_5 & z_6 & \dots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ z_{k-(n-1)} & z_{k-(n-2)} & z_{k-(n-3)} & \dots & z_k \end{bmatrix}$
$\mathbf{Q} = \mathbf{L} \mathbf{L}'$
$\mathbf{D} = (\sqrt{diag(\mathbf{Q})})^{-1}$
$\mathbf{R} = \mathbf{D} \mathbf{Q} \mathbf{D}'$
Here, I have guaranteed that $\mathbf{R}$ is a positive semi-definite correlation matrix that was generated from $\mathbf{z}$, which contains a bunch of randomly generated numbers.
But I feel like there's a fundamental problem in the way I've set this up. I am using a numeric optimization procedure (in this specific case, python's scipy.optimize) to estimate $(n^2 - n)/2$ terms by searching within a $((n^2 - n)/2 +n)$-dimensional parameter space.
So there might be a bunch of places where the optimization surface is just flat because there are (almost?) infinite $\mathbf{z}$s that generate the same correlation matrix.
So finally, after all this, my question is: given the model stated up top, is there a better way to estimate all correlation terms through likelihood maximization in a way that guarantees positive semi-definiteness?
Any kind of guidance would be greatly appreciated!
Edit As suggested by @Mark L. Stone, Here is the implementation of the problem in Python with appropriate comments to make things a bit clearer, pointing out what parts of code are analogous to the formal/mathematical description I gave.
# Importing libraries used
import numpy as np
from scipy.stats import norm
from scipy.stats import multivariate_normal as mvn
from scipy.optimize import minimize
# Setting seed for replication
seed = 666
np.random.seed(seed)
# Number of dimensions in my jointly-distributed data.
# Analogous to n.
ndim = 13
# Number of observations in the dataset.
# Analogous to m.
nobs = 1000
# Number of elements in parameter vector to be estimated.
# Analogous to k.
num_chol = int(((ndim*ndim)-ndim)/2+ndim)
# k-long vector of random numbers.
# Analogous to z.
true_chol_vec = norm(loc=0,scale=2.5).rvs(num_chol)
# Function that makes a covariance matrix using the random parameters.
def make_cov_mtx_from_chol_vec(chol_vec):
chol_mtx = np.zeros((ndim,ndim))
chol_mtx[np.tril_indices(ndim)] = chol_vec
cov_mtx = np.dot(chol_mtx,chol_mtx.T)
return(cov_mtx)
# Function that normalizes covariance matrix down to a correlation matrix.
def make_cor_mtx_from_cov_mtx(cov_mtx):
stdevs = (1/np.sqrt(np.diag(cov_mtx))).reshape((ndim,1))
cor_mtx = stdevs * cov_mtx * stdevs.T
return(cor_mtx)
# Creating true covariance matrix. Analogous to Q.
true_cov_mtx = make_cov_mtx_from_chol_vec(true_chol_vec)
# Creating true correlation matrix. Analogous to R.
true_cor_mtx = make_cor_mtx_from_cov_mtx(true_cov_mtx)
# Mean of the jointly distributed data. Analogous to 0_n.
means = np.zeros(ndim)
# Generating correlated data to use in estimation.
# Analogous to X.
joint_values = mvn.rvs(mean=np.zeros(ndim),cov=true_cor_mtx, size=nobs)
# Fixes cases where likelihoods are too small
prob_fix = 1e-10
# Log-likelihood function used in optimization.
def neg_log_lik(params):
cov_mtx_estim = make_cov_mtx_from_chol_vec(params)
cor_mtx_estim = make_cor_mtx_from_cov_mtx(cov_mtx_estim)
likelihood = mvn.pdf(x=joint_values,mean=means,cov=cor_mtx_estim, allow_singular=True)
likelihood[likelihood < prob_fix] = prob_fix
log_likelihood = np.log(likelihood)
return(-log_likelihood.sum())
# Optimization starting values
start_params = norm(loc=0,scale=2.5).rvs(num_chol)
# Running optimization
param_optim = minimize(fun=neg_log_lik,
x0=start_params,
method="BFGS",
options={"maxiter":10000,
"disp":True})
print("\n\nTrue cor mtx:")
print(true_cor_mtx)
print("\n\nEstimated cor mtx:")
print(make_cor_mtx_from_cov_mtx(make_cov_mtx_from_chol_vec(param_optim["x"])))
In the implementation above, the estimation terminates after a single iteration and spits out a correlation matrix that isn't even close to what's expected. Is this because of the difference between the search-space dimension and the actual solution-space dimension?
In summary: what is the best way to estimate the correlation matrix of jointly correlated data using a numerical likelihood maximization approach? Is it possible that using this approach - where a $((n^2 - n)/2 + n)$-long parameter vector is used to fit $((n^2 - n)/2)$ correlation terms - might generate problems for the numerical optimization/search procedure? If so, how can that be avoided?
Thanks again!
• You don't seem to have told us what optimization problem you are solving with scipy.optimize. Despite your long presentation, I have essentially no idea what you've done, other than relying on a Choelsky factorization to ensure positive semidefiniteness. You apparently populate a Choelsky factor with a random entries, but is that just an initialization (starting value) for numerical optimization via some unstated optimization problem formulation? – Mark L. Stone Aug 5 '18 at 17:32
• Good point. I'll edit the original post to reflect that. Thx for the heads up! – Felipe D. Aug 5 '18 at 18:40
• What output is displayed when the optimizer terminates after one iteration? By virtue of your approach (even if no mistakes), you may have introduced spurious saddle points. .Is there a reason why you can;t just form the empirical covariance matrix - do you have unclean, inconsistent data (not all variable components measured together)? If not, then other than roundoff errors, empirical covariance should be psd. You can adjust eigenvalues or use other methods to adjust an almost psd "covariance" or correlation matrix to be psd, or have minimum eigenvalue. – Mark L. Stone Aug 5 '18 at 20:00
• The output I get is this: "Optimization terminated successfully. Current function value: 23025.850930 Iterations: 0 Function evaluations: 1277 Gradient evaluations: 1" – Felipe D. Aug 5 '18 at 20:16
• The thing is that this is a small part in other larger estimation problems I have to solve. The main problem I deal with is the Generalized Ordered Probit Model, where I have multiple (discrete) ordered outcomes and the error terms are jointly distributed. In this problem, we estimate the influence of a bunch of exogenous covariates as well as the correlation terms between the errors (more info here). So I tried to translate the simplest version of the problem to a clean-cut context to present it here. – Felipe D. Aug 5 '18 at 20:18
After almost giving up on this, I finally found a good paper that talks about unconstrained parametrizations for the covariance matrix.
The basic idea is to extract the upper triangle Cholesky decomposition and to apply several sequential spherical-coordinate transformations on each of the Cholesky's matrix's columns. It gets really messy and writing a generalized code is pretty tricky, but it's totally doable.
When performing the spherical transforms, you need to calculate two "sets" of parameters: $$r$$s and $$\phi$$s. Since you're working with a correlation matrix, however, you know that all of the $$r$$s are equal to 1, thus reducing the number of values for your optimization process.
Unconstrained parametrizations for variance-covariance matrices (link 2): gives you the general idea of using the Cholesky decomposition with spherical coordinate transformations. The step about spherical coordinates, however, isn't very clear here.
Parameterizing correlations: a geometric interpretation: Another look at a similar question.
n-dimension Spherical coordinates and the volumes of the n-ball in $$\mathbb{R}^n$$: How to generalize the spherical-coordinate transformation for n-dimensions.
Spherical Parameterization of Variance-Covariance Matrix in Mixed-Effects Regression: Question about the first paper.
Spherical Parametrization of a Cholesky Decomposition: Question about the first paper, specifically about the spherical coordinate transformation.
There is I believe a much easier way to parameterize correlation matrices vis the cholesky decomposition. Form the matrix
$$\begin{bmatrix}1 & 0 & 0 & \ldots & 0 & 0 \\ x_{21} & 1 & 0 & \ldots & 0 & 0 \\ x_{31} & x_{32} & 1 & \ldots & 0 & 0 \\ \ldots \\ x_{n-1,1} & x_{n-1,2} & x_{n-1,3} & \ldots & 1 & 0 \\ x_{n1} & x_{n2} & x_{n3} & \ldots & x_{n,n-1} & 1 \\ \end{bmatrix}$$
Now normalize this by dividing each row considered as a vector by its norm. This results in the Cholesky decomposition of the correlation matrix. There are $$n(n-1)/2$$ $$x$$'s. Note that there are no constraints necessary on the $$x$$'s. To get the Cholesky decomposition of the covariance matrix multiply the $$i$$'th row by $$\exp(y_i)$$. So there are $$n$$ parameters for the $$y$$'s. Again note that there are no constraints necessary for the $$y$$'s. Notice that there is a natural starting value for the $$x$$'s, that is $$x_i=0$$ for all $$i$$. However the problem is singular at that point so you should start with small random values for the $$x$$'s.
I have used this parameterization for a lot of models and it seems to perform well. Consider a $$4\times 4$$ matrix so that the dimension of x is 4x3/2=6. Let
$$x=(0.6379 , 0.4829 , 0.2525 ,-0.2435,-0.09326 ,-0.3671)$$
Then the matrix before normalizing is $$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0.6379 & 1 & 0 & 0 \\ 0.4829 & 0.2525 & 1 & 0 \\ -0.2435 & -0.09326 & -0.3671 & 1 \\ \end{bmatrix}$$
and after normalizing it is
$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0.5378 & 0.8431 & 0 & 0 \\ 0.4241 & 0.2217 & 0.8781 & 0 \\ -0.2221 & -0.08504 & -0.3347 & 0.9118 \\ \end{bmatrix}$$
If you multiply this matrix times its transpose you get the correlation matrix.
$$\begin{bmatrix} 1 & 0.5378 & 0.4241 & -0.2221 \\ 0.5378 & 1 & 0.4149 & -0.1911 \\ 0.4241 & 0.4149 & 1 & -0.4069 \\ -0.2221 & -0.1911 & -0.4069 & 1 \end{bmatrix}$$
• Thanks for the answer, Dave! I'm trying this out with a small example and I'm running into some issues, which makes me think I didn't quite get your explanation. For example, consider a case with 3 dimenstions: $$A_{lowmat}=\begin{bmatrix} 1 & 0 & 0 \\ 0.5 & 1 & 0 \\ 0.25 & 0.5 & 1 \end{bmatrix}$$ Here, when I divide each row by its norm, I get this: $$\begin{bmatrix} 1 & 0 & 0 \\ 0.447 & 0.894 & 0 \\ 0.218 & 0.463 & 0.872 \end{bmatrix}$$ But multiplying this matrix by its transpose does not recover the original $A_{lowmat}$ matrix. Am I off? – Felipe D. Apr 22 '19 at 20:49
• Also, you mention $y$ parameters, but it's not clear to me where they came from. Thanks! – Felipe D. Apr 22 '19 at 20:57
• OK, if you are just doing the correlation, not the covariance matrix then there are no y's. – dave fournier Apr 22 '19 at 23:29
• Ah, ok. But this is a one-way process, right? You can only go from random draws (parametrized version) to an actual correlation matrix (unparametrized version), right? In other words, this method doesn't allow you to start off with a given correlation matrix and find the decomposition that, multiplied by its own transpose, would recover the original correlation matrix. Is that right? – Felipe D. Apr 23 '19 at 6:37
• It should be reversible. – dave fournier Apr 23 '19 at 17:48
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2020-01-19 02:39:26
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