Partial Dependency (Databases)

Question: I fabricated a definition that a partial dependency is when fields are indirectly dependent on the primary key or partially dependent but are also dependent on other keys that depend on the primary such that if the field which another field depends on is deleted then that field will still exist due to its dependence on the primary key. I am not sure if it is correct. I have researched and every definition sounds misleading. Is my definition correct and if not what is?
Answer: A FD (functional dependency) that holds in a relation is partial when removing one of the determining attributes gives a FD that holds in the relation. A FD that isn't partial is full.
Eg: Suppose {A,B} → {C} but also {A} → {C}. Then {A,B} → {C} is partial; {C} is partially functionally dependent on {A,B}; {C} is functionally dependent on a part of {A,B} that is not all of it. The consequent partial FD is not {A} → {C}. Whether that is partial depends on (per the definition of partial FD) whether a subset of {A} determines {C}; whether {} → {C}.
Eg: Here's a relation value where that example condition holds. (A FD holds in a relation variable when it holds in every value that can arise.)
A  B  C
1  1  1
1  2  1
2  1  1

The non-trivial FDs that hold: {A,B} determines {C}, {B,C}, {A,C} & {A,B,C}; {A}, {B} & {} also determine {C}. Of those: {A,B} → {C} is partial per {A} → {C}, {B} → {C} & {} → {C}; {A} → {C} & {B} → {C} are partial per {} → {C}; the others are full.

A functional dependency X → Y is a full functional dependency if removal of any attribute A from X means that the dependency does not hold any more; that is, for any attribute A ε X, (X – {A}) does not functionally determine Y. A functional dependency X → Y is a partial dependency if some attribute A ε X can be removed from X and the dependency still holds; that is, for some A ε X, (X – {A}) → Y.
-- Fundamentals OF Database Systems 6th Edition, Ramez Elmasri & Navathe

Notice that whether a FD is full vs partial doesn't depend on CKs (candidate keys), let alone one CK that you might be calling the PK (primary key).
(A definition of 2NF is that every non-CK attribute is fully functionally determined by every CK. Observe that the only CK is {A,B} & the only non-CK attribute C is partially dependent on it so this value is not in 2NF & indeed it is the lossless join of components/projections onto {A,B} & {A,C}, onto {A,B} & {B,C} & onto {A,B} & {C}.)
(Beware that that textbook's definition of "transitive FD" does not define the same sort of thing as the standard definition of "transitive FD".)
Comment: Does partial dependency occur only when there is a composite primary key? Database Systems: Design, Implementation, & Management
 By Carlos Coronel, Steven Morris states that Conversion to 2NF occurs only when the 1NF has composite primary key. If the 1NF has a singleiattribute primary key, then the table is automatically in 2NF.
I am so much confused in this too, please help
Comment: @JeffPuckettII I gave an example. I don't know what you think makes a definition "abstract" vs not or an example "concrete" vs not. (Maybe for you, by definition of "definition" & "example"?) I suppose you mean, an example consisting one full FD, one partial FD, for each a relation/table value satisfying it, an enumeration of all the FDs that one can get by dropping a determining attribute from each FD, and the observations that none of the new FDs from the full FD are satisfied, hence it's full, and at least one of the new FDs from the partial FD is satisfied, hence it's partial?
Comment: (You should really post this as a question.) No. There can be partial dependencies not involving CKs (candidate keys). Eg there are partial FDs for for every full FD whose left hand side isn't all the attributes because its right hand side is partially dependent on every proper superset of that left hand side. Read the last sentence in my answer. Partial/full is a property of FDs. The FDs collectively determine the CKs and highest NF up to BCNF. PS: PKs have no role in normalization. One simply picks one CK and calls it "the PK".
Comment: @sagar See my edited post with example data. But--Please read my last comment, re "example". I already gave an "example"--"Eg if {A,B} → {C} but also {A} → {C} then {C} is partially functionally dependent on {A,B}." If you don't know how to determine whether an FD holds then you need to find out. Where do I stop explaining? You need to memorize definitions. Then to know whether you have a thing of a certain kind determine whether the definition of that kind of thing applies, ie determine whether the defining condition of that sort of thing holds, ie is satisfied.
Comment: PPS: 2NF needs no partial FDs of non-prime attributes on CKs. The book is saying that for non-2NF there can't be a FD from a proper subset of a one-attribute CK. But the book is wrong. They forgot the empty set as proper subset: One can have non-2NF with CK {A} yet a partial FD of non-prime B on it when {}->B (ie B values are the same). Textbooks & the SQL world often forget about the empty set in FDs. Eg [this](http://stackoverflow.com/a/16617091/3404097) & [this](http://www.dcs.warwick.ac.uk/~hugh/M359/FD-demystification.html#emptyset) & [this](http://www.dpxo.net/articles/zerodegree.htm).
Comment: Your abstract definition could benefit from a concrete example.
Comment: @philipxy; Can you please edit your answer with an Example consisting of arbitrary relational table So that we could get your point without any confusion. Thanks for your efforts.
Answer: Partial dependency means that a nonprime attribute is functionally dependent on part of a candidate key. (A nonprime attribute is an attribute that's not part of any candidate key.)
For example, let's start with R{ABCD}, and the functional dependencies AB->CD and A->C.
The only candidate key for R is AB. C and D are a nonprime attributes. C is functionally dependent on A.  A is part of a candidate key. That's a partial dependency.
Comment: C is partially dependent on AB, ie AB->C is a partial FD, because C is dependent on a proper subset of AB, A. C is fully dependent on A, ie A->C is a full FD, because C is not functionally dependent on a proper subset of A.
Comment: Every FD that holds is either full or partial; keys don't enter into it.
Comment: Hi. What is your reference for your definition of "partial FD"? See my answer for a different one--per the quoted textbook. Here is Codd's original definition of "full FD" in Further Normalization of the Data Base Relational Model: "Suppose D,E are two distinct subcollections of the attributes of a relation R and R.D -> R.E. If, in addition, E is not functionally dependent on any subset of D (other than D itself) then E is said to be fully dependent on D in R." (That's not defined for X->X. More to research.)
Comment: @philipxy: I don't have a reference. I have no formal training in anything to do with computers. I'm entirely self-taught. I'd be surprised if I got everything right.
Comment: Thanks. Unfortunately this answer is wrong & people come to this post & think wrong things. Actually I suspect that they don't even get to the page to think those wrong things, because at page top above any links when I google 'partial functional dependency' is text from this page's posts saying wrong things. Just now that text was the start of your post, but other times it's from other wrong posts. (I haven't seen my answer though. OK I may have learned something about ranking & grammar there.) PS Your & dportas/sqlvogel/nvogel's DB theory posts are (typically) of exceptionally high quality.
Comment: The last paragraph of your answer incorrectly says that A -> C is partial, but it is not, and the partial FD that violates 2NF is AB -> C. Which I didn't make clear in first comments on this answer.
Answer: Partial dependency implies is a situation where a non-prime attribute(An attribute that does not form part of the determinant(Primary key/Candidate key)) is functionally dependent to a portion/part of a primary key/Candidate key.
Comment: What is your reference for your definition of "partial FD"?
Answer: Partial Dependency is one kind of functional dependency that occur when primary key must be candidate key and non prime attribute are depends on the subset/part of candidates key (more than one primary key).
Try to understand partial dependency relate through example :
Seller(Id, Product, Price)
Candidate Key : Id, Product
Non prime attribute : Price
Price attribute only depends on only Product attribute which is a subset of candidate key, Not the whole candidate key(Id, Product) key . It is called partial dependency.
So we can say that Product->Price is partial dependency.
Comment: What is your reference for your definition of "partial FD"?
Comment: I have written this based on my intuition. That's why I can not able to give reference. If find any error, obviously inform .
Comment: Technical terms have meanings & histories. "Partial FD" was defined to mean a certain thing & it has consistently been used with that meaning in research & textbooks. It is easy to find a definition in a textbook. It is not defined in terms of CKs or PKs. See my answer. But this post by you is not consistent with what it means. (Also your English is not clear.) So I was interested in why you think it means whatever you think it means--although your post is not clear enough to know what you think it means. "Intuition" is irrelevant & it is very strange that you mention it.
Answer: I hope this explaination gives a more intuitive appeal to dependency than the answers previously given.
Functional Dependency
An analysis of dependency operates on the attribute level, i.e. one or more attribute is determined by another attribute, it comes before the concept of keys. 'The role of a key is based on the concept of determination. 'Determination is the state
in which knowing the value of one attribute makes it possible to determine the value
of another.' Database Systems 12ed
Functional dependency is when one or more attributes determine one or more attributes. For instance:
Social Security Number -> First Name, Last Name.
However, by definition of functional dependency:
(SSN, First Name) -> Last Name
This is also a valid functional dependency. The determinants (The attribute that which determines another attribution) are called super key.
Full Functional Dependency
Thus, as a subset of functional dependency, there is the concept of full functional dependency, where the bare minimal determinant is considered. We refer those bare minimal determinants collectively as one candidate key (weird linguistic quirk in my opinion, like the concept of vector).
Partial Functional Dependency
However, sometimes one of the attributes in the candidate key is sufficient to determine another attribute(s), BUT not all, in a relation (a table with no rows). That, is when you have a partial functional dependency within a relation.
Comment: What is your reference for your definition of "partial FD"?
Answer: Partial dependence is solved for arriving to a relation in 2NF but 2NF is a "stepping stone" (C. Date) for solving any transitive dependency and arriving to a relation in 3NF (which is the operational target).
However, the most interested thing on partial dependence is that it is a particular case of the own transitive dependency. This was demostrated by P. A. Berstein in 1976: IF {(x•y)→z but y→z} THEN {(x•y)→y & y→z}. The 3NF synthesizer algorithm of Berstein does not need doing distintions among these two type of relational defects.
Answer: Partial Functional Dependency occurs only in relation with composite keys. Partial functional dependency occurs when one or more non key attribute are depending on a part of the primary key.
Example:
Table:
Stud_id, Course_id, Stud_name, Course_Name
Where:
Primary Key = Stud_id + Course_id
Then:
To determine name of student we use only Stud_id, which is part of primary key.
{Stud_id} -> {Stud_Name}
Hence,Stud_name is partially dependent on Stud_id. This is called partial dependency.
Comment: What is your reference for your definition of "partial FD"?
Comment: The first sentence is wrong, see my answer & my comments on it. The second sentence is wrong & unclear, see my answer. The rest is unclear.
Answer: If there is a Relation R(ABC)
-----------
|A | B | C |
-----------
|a | 1 | x |
|b | 1 | x |
|c | 1 | x |
|d | 2 | y |
|e | 2 | y |
|f | 3 | z |
|g | 3 | z |
 ----------
Given,
F1: A --> B
F2: B --> C

The Primary Key and Candidate Key is: A
As the closure of A+ = {ABC} or R  --- So only attribute A is sufficient to find Relation R.
DEF-1: From Some Definitions (unknown source) - A partial dependency is a dependency when prime attribute (i.e., an attribute that is a part(or proper subset) of Candidate Key) determines non-prime attribute (i.e., an attribute that is not the part (or subset) of Candidate Key).
Hence, A is a prime(P) attribute and B, C are non-prime(NP) attributes.
So, from the above DEF-1,
CONSIDERATION-1:: F1: A --> B (P determines NP) --- It must be Partial Dependency.
CONSIDERATION-2:: F2: B --> C (NP determines NP) --- Transitive Dependency.
What I understood from @philipxy answer (https://stackoverflow.com/a/25827210/6009502) is...
CONSIDERATION-1:: F1: A --> B; Should be fully functional dependency because B is completely dependent on A and If we Remove A then there is no proper subset of (for complete clarification consider L.H.S. as X NOT BY SINGLE ATTRIBUTE) that could determine B.
For Example: If I consider F1: X --> Y where X = {A} and Y = {B} then if we remove A from X; i.e., X - {A} = {}; and an empty set is not considered generally  (or not at all) to define functional dependency. So, there is no proper subset of X that could hold the dependency F1: X --> Y; Hence, it is fully functional dependency.
F1: A --> B
If we remove A then there is no attribute that could hold functional dependency F1. Hence, F1 is fully functional dependency not partial dependency.
If F1 were, F1: AC --> B;
and F2 were, F2: C --> B;
then on the removal of A;
C --> B that means B is still dependent on C;
we can say F1 is partial dependecy.

So, @philipxy answer contradicts DEF-1 and CONSIDERATION-1 that is true and crystal clear.
Hence, F1: A --> B is Fully Functional Dependency not partial dependency.
I have considered X to show left hand side of functional dependency because single attribute couldn't have a proper subset of attributes. Here, I am considering X as a set of attributes and in current scenario X is {A}
-- For the source of DEF-1, please search on google you may be able to hit similar definitions.  (Consider that DEF-1 is incorrect or do not work  in the above-mentioned example).
Comment: This is not clear. Use enough words, sentences & references to parts of examples to clearly & fully say what you mean. Don't try to cram everything into one phrase or sentence. Also this says wrong things. Those FDs need to form a cover or you can't determine the CKs. PKs are irrelevant. "sufficient to find" is just everyday words. "we can say B is partially dependent on A as well as C"--no, B is partially dependent on AC. Def-1 garbles "partial FD" with "2NF". How can a source you quote be unknown?--And what is the point of giving it?--And what are you doing with it? ...
Comment: ... See my comments on my answer & my edited answer re how a FD with a single attribute as determinant can be partial because {} can be a determinant. "because B is completely dependent on A" is wrong, it is because B is not dependent on not all of A--obviously in X->Y Y is *always* dependent on all of X. What is the point of your example data?--You don't use its content for anything. Etc etc.
Comment: @philipxy updated my answer for more clarification that might help you to get my point. However, in a practical scenario, I have never seen empty attribute or empty set -- {} is determining anything. It might be possible theoretically. But there is no practical usage of this.
Comment: This still has most of the problems--I guess we disagree. PS My last comment already contradicts your last comment re [{}](https://stackoverflow.com/q/10936387/3404097). (Just apply the definition of FD.) PS {}->{X} when/iff X must have at most one value. We don't see that much because it's typically an obviously bad design. But 2 examples from practice are a 1-row table of parameter values ({} is the one CK) & a certain SQL idiom for constraining declaratively where a subtype table has a column with only its own type tag as FK to a subtype tag column in the supertype table.
Comment: PS re "Given" FDs: What does "I have these FDs" mean? "These are all the FDs that hold"?--Not possible. "These are all the non-trivial FDs that hold"?--Not possible. "These are some FDs that hold"?--Question can't be answered. Find out what a *cover* is & what the exact conditions are to apply a particular definition/rule/algorithm. To determine CKs & NFs we must be given FDs that form a cover. Sometimes a minimal/irreducible cover. [See this answer.](https://stackoverflow.com/a/53386492/3404097)
Answer:
consider a table={cid,sid,location}
candidate key: cidsid (uniquely identify the row)
prime attributes: cid and sid (attributes which are used in making of candidate key)
non-prime attribute: location(attribute other than candidate key)

if candidate key determine non-prime attribute:
i.e cidsid--->location (---->=determining)
   then, it is fully functional dependent

if proper subset of candidate key determining non-prime attribute:
 i.e sid--->location (proper subset are sid and cid)
         then it is term as partial dependency

to remove partial dependency we divide the table accordingly .

Partial Dependency (Databases)


The preimage of continuum on Torus

Question: Let $p:\mathbb{R}^2\rightarrow\mathbb{R}^2/\mathbb{Z}^2$ be the natural  projection, obviously $\mathbb{R}^2/\mathbb{Z}^2$ is the torus $\mathbb{T}^2$, if $K$ is a connected and compact subset of $\mathbb{T}^2$, and $Q$ is the component of $p^{-1}(K)$, then whether $p(Q)=K$? What is the relation between $Q$ and other components of $p^{-1}(K)$?
Comment: If I remember my topology correctly Decktransformationsshould help you with the relations between the components of $Q$. Also since $K$ is connected, $p(Q)$ has to be $K$. you should be able to proof that by using the connectedness of $K$ and lifting of paths to the universal cover ($\mathbb{R}^2 \to \mathbb{T}^2$)
Answer: The answer is no. Take a cylinder, $C=R\times T$, where $T$ is the unit circle. And consider the universal covering $f:R^2\to C$ given by the formula
$(x,y)\mapsto (x,e^{iy})$. Now the set
$$X=\{ (x,y)\in R^2: y=1/x,0<x\leq 1\}\cup \{(x,y):x=0\}$$
is disconnected, while its image $K=f(X)$ is closed and connected, it consists of a circle and a spiral accumuating on this circle. No component
of $f^{-1}(K)$ is mapped surjectively: one has the circle as the image,
and another the spiral.
To make a torus glue the ends of this cylinder together.
Comment: I agree with your example, thanks a lot ! I wonder if I assume that the component $Q$ of $p^{-1}(K)$ is bounded, is it true?

The preimage of continuum on Torus


Should I use a separate content type?

Question: In drupal 6 I have a content type with a lot of fields, voting, referenced nodes (as answers), etc. Now I would like to create a very similar content type - same behaviour and everything, there are only 2-3 fields that are different, but everything else is the same. Now comes the question: Should I create a separate content type, setup everything, use separate voting, etc? Or is there a way to somehow 'inherit' everything and change only 2-3 fields that need to be changed?
Answer: If you are going to do this often, or expect changes that require these two types to be in sync in the future, you might investigate the http://drupal.org/project/features module, which packages stuff up like this.  But, if it's a one off thing, I'd just go and create a new content type and reuse the existing fields plus the new/different ones in the second content type.  If you don't want to type everything in again, you should be able to use the CCK export feature and then just change the name and type of the result and import it, which if all goes well, will create the second type for you identically to the first.  Then just add the new/different fields manually.
Comment: SO it means that if I have a ontent type trousers - with fields size, colour, brand, some voting and images and I would like to add additionaltypes - such as shirts, shoes, skirts and so on, which differ slightly from each other I would have to create a content type for each of these? I think there is a potential for improvement here for Drupal...
Comment: To Vafellos comment, that, or your create a content type called "item" with all the fields you could possibly need, and just hide the ones from the various edit/add/view pages and forms based upon a field or other criteria.  Off the cuff, for example, if you had a field in it called type, that could be a dropdown for shirt/shoe/skirt etc and then based upon this, fields could be displayed that are valid for whatever is chosen.  To Jim, I don't know enough about D7 yet to comment on that, let alone D8, but you don't HAVE to do anything, there are many solutions to almost every Drupal issue.
Comment: I'd like to know the answer to this to. Say I have twenty-five content types and they share enough fields to make the "field inheritance" concept that Vafello is talking about make sense. Do I have to make 25 separate content types? Is the answer the same for Drupal 6 and 7? What about Drupal 8?
Comment: For Drupal 7 there is something - http://drupal.org/project/bundle_inherit
Comment: Also see http://drupal.stackexchange.com/questions/27741/inheriting-fields-from-a-base-content-type

Should I use a separate content type?


Fresh water in a Earth-like planet with substantially less oceanic water than Earth

Question: What about the rivers? How would the lack of oceanic water affect the amount and / or characteristics of the fresh water available on the planet?
Comment: The only answer to this question is Yes. You're going to have to be a bit more specific about what you want to know
Comment: I answered this question, and in the answer linked to another question you asked that I answered. That's how I realized this was a duplicate.
Answer: Salt water is the product of fresh water dissolving sodium and chloride ions from the ground it flows over and pools on, taking billions of years. Rivers on a world with a hydrologic cycle but significantly less ocean water would still have fresh water rivers and lakes, as long as there is rain and aquifers to filter and store it.
Answer: The thing to remember about rivers is that you need precipitation to make them possible. Much smaller oceans means much less moisture in the precipitation cycle; if it rains at all. Unless you can get enough water in the atmosphere as 'clouds' to reach a critical mass, it might not rain at all. You'd probably get (at best) dew on the ground on cold mornings, when the latent humidity reaches dew point.
Dew wouldn't be enough to get rivers to happen as these need sustained rainfall or snow-melts to form. (Snow melts are just another form of delayed precipitation - snow falls and then builds up until it melts to form a stream)
So; rivers and streams would be (at best) rare. Shame really; the rain cycle acts as a form of purification for water, allowing it to be cleaned and returned to the land, eventually forming rivers. Without this, fresh water is unlikely given the sustained mineral absorption of water in the ocean.
Answer: See the answer to this related question
It depends what you mean by substantially and where the water is.
Someone has actually posted what the oceans would look like with 95% less water (based on a simulation I believe) in the above question and there are still enormous areas covered by water so almost certainly enough to drive the hydrological cycle.
But most of Earths water is in the Mantle - also see the above question. So it might well be that the above much smaller shallower oceans simply drain away into the mantle to replace some of the water lost from there. It really depends on the exact conditions.


Why a page that works returns a 500 error?

Question: I have this url that seems to work fine but it returns a 500 error.
http://comehike.com/outdoors/hike_widget.php?hike_id=164&height=700&width=500
Any idea why that is possibly happening? I have like 10k such errors in my google webmaster tools :(
Answer: If you can create a .htaccess file (or already have one), put this code at the top:
# enable PHP error logging
php_flag  log_errors on
php_value error_log  /path/to/htdocs/PHP_errors.log

Create a blank PHP_errors.log file in the directory specified in your .htaccess file and set its permissions to 777. Now refresh the page that's giving the 500 error and check if that log file now contains an error(s).
Answer: hike_widget.php is returning an error 500. Check in chrome developer tools under Network. These are the headers for that file
Click on the file in the Networks left side window then view the headers on the right
Answer: HTTP response headers are separate to the actual content that is returned. You can return any page with any response code (that's how custom 404 errors work).
The problem most likely lies with your server or PHP code. Check that there is no 500 error being sent in PHP (it would use the header() function), check there are no errors in .htaccess and that your server settings are not breaking anything.
If you are on shared hosting you'll probably need to contact your host since it may be their fault.


Mac system application extension

Question: I'm trying to modify the functionality of mission control which belongs to dock.app and I'm wondering what the preferred method of doing so would be. I've looked into using the simpler method of defaults but that won't give me enough control. I'm curious if people use something like Application Enhancer by Unsanity to execute custom code for these purposes.
Answer: Application Enhancer is effectively a dead project at this point -- while the current version does advertise support for Lion, Mountain Lion is slated for release within the next month, and it is unlikely that they will ever support it (as neither the Unsanity site nor their Twitter account has not been updated at all since last November). I would recommend strongly against using it for new products.
Under previous releases of OS X, SIMBL and PlugSuit have been popular, but neither one is available on Lion. The options seem to be more limited now; however, Rentzch's mach_star (mach_override / mach_inject) code seems to still be working.

Mac system application extension


Why size of the reflecting surface must be greater than the wavelength of sound wave?

Question: My book says that "the only requirement for the reflection of sound wave is that the size of the reflecting surface must be bigger than the wavelength of sound wave". Why is that so? Shouldn't the amplitude be the factor?
Answer: To get a specular reflection (angle of incidence equals angle of reflection), the surface must be large in comparison with the wavelength. A small object will scatter all around.
And a row of trees or a a wall with corrugation can act as a diffraction grating.
Answer: You are correct, there is a nonzero amplitude reflexion from a subwavelength surface. Its reflexion will simply look like a point source in the farfield, and it is an inefficient scatterer. That is, for greater than wavelength breadth reflectors, the reflected power from an incident plane wave is roughly proportional to the area of the reflecting surface. For smaller than wavelength scatterers, the decrease in reflected power with decreasing wavelength is much faster than linear.
The corresponding phenomenon with light / electromagnetic waves is called Mie scattering, and, for very small reflectors, Rayleigh scattering. In the Rayleigh régime, the decrease is with the square of the cross sectional area, not linearly.
There are analogous phenomena for scalar acoustic waves, which, like electromagnetic waves, fulfill the Helmholtz equation. The final equations are slightly different because the electromagnetic boundary conditions force slightly different expressions, but the broad principles will be the same.
Below is a plot I made some years ago to check that some software I was working with would reproduce Figure 13-14 in Born and Wolf, "Principles of Optics". It is a plot of the effective cross-section of a scatterer as a function of its physical size. The vertical axis is twice the ratio of power scattered from a homogeneous sphere of water to the power one calculates assuming ray theory. The horizontal axis is the size factor $\sigma = \frac{2\,\pi\,a}{\lambda}$.

The curve is saying that for size factors of 2 or greater, the scattered power can be calculated by ray theory, by thinking of light as little pellets that bounce off a macroscopic object blocking them. That is, the scattering cross section roughly equals the cross sectional area of the target. For much lower size factors, the scattering cross section is much smaller than the "physical" target cross sectional area, and indeed as the object gets very small, the scattering is proportional to the inverse fourth power of the wavelength - much smaller than the linear decrease you would expect from ray theory.
Answer: Sound is a longitudinal wave which travels through the medium (it can't travel without a medium), by creating a wave of compression and rarefaction alternatively and being a wave it has a fundamental property called diffraction which means when a wave passes through an obstacle it bends towards its edges as you might have observed in case of light passing through a hole or a slit it spreads outwards. You can verify it by using a Laser torch, point it on a wall you will see a small red dot now put a needle or a pen in between the beam of light so that only a part of light can hit the wall, you will see the red line instead of dot, thats diffraction. The diffraction is maximum if the obstacle is smaller and its maximum if the obstacle is smaller then the wavelength of the wave in such case most of the wave is diffracted from the edge and that's why the amount of wave reflected is negligible. That answers your first question
Now, Scattering is the phenomenon in which the wave get deflected from its path multiple times and in random directions. Its more like the wave gets diffused in the medium. Reflection is one of the causes of scattering, refraction and diffraction being other causes. Tyndall Effect on foggy morning is a perfect example of scattering.
The size of the particles is an important factor in scattering. If the size is more then the wavelength of wave then the scattering is caused by multiple geometric reflections, which is justified by the first paragraph. Tyndall effect, muddy water are examples of this type of scattering. If the size of the particles is smaller then the wavelength of the wave, for example size of the air molecules is in order of 10^(-12) Picometers whereas the wavelength of visible light is of the order of 10^(-7) (100 nanometers), in such cases the photon (the light particles) hits the gas molecules like oxygen and nitrogen which are very abundant in our atmosphere, the electron of the molecule jumps in the higher energy levels by absorbing the photon and then re-emitting a photon of equal or smaller energy. But the absorption happens only when a single photon has sufficient energy to make the electron jump, two photons can't contribute to make a single jump. Which is why in our example the blue light which has higher frequency (or smaller wavelength) which means higher energy get scattered by the atmospheric gases almost 9.5 times more then the red light which has lover frequency which means less energy, and thats why we see the sky blue, This is called Raman Scattering.
I didn't plan for such a long answer but just couldn't finish in any less. There is a lot more to scattering which you can check in the books or on the Internet


Need help with recreating organic microscopic material in blender

Question: So i have been trying to recreate a specific material in blender for quite a while now, but i just can' seem to get it working. the picture attached shows what i am trying to recreate, basically what you would see if you were to put a mold capsule under a microscope, very translucent, but not reflective almost gelatineous, but more importantly i want to get the effect where it darkens as the material gets "thicker" around the edges and such. i would show my progress, but i really haven't done anything substantial other than messing with subsurface nodes and translucency nodes, i don't even know where to start as far as the darkened edges go.
Comment: Have you used available vectors and a dot product?
Comment: as atomicbezierslinger says in his answer, Input > Fresnel or LayerWeight nodes may help you
Answer: Dot Product and Fresnel

In your nodes you should consider the dot product node depicted in the image below or fresnel node

VectorA • VectorB

computes the strength of the parallel component for the two vectors as a scalar.

VectorA and  VectorB are normalized for ease of understanding.
A result of [1.0] would mean the vectors are parallel
A result of [0.0] would mean the vectors are orthogonal
A result of [-1.0] would mean the vectors are antiparallel

In the image provided in the question the color is different at the glancing angles and more transparent when looking directly at the faces of an imagined 3D model.
[viewing vector] dot product the [face geometric normal vector]
Using the result of VectorA • VectorB  can be used to determine the mix of two colors or transparency and et cetera.  When they are not so parallel use different color.  vector1 and vector2 can be normalized.  When the dot product is close to zero [0.0] then the vectors are at right angles.  You will be able to identify looking at the edge silhouette or directly at a face. Experimenting with this will be a start.
dot product and those vectors are  available in the nodes

https://en.wikipedia.org/wiki/Normal_(geometry)
https://en.wikipedia.org/wiki/Dot_product
This has been used in 3D CG long ago 40+ years

Image above with dot product calculations.  When your viewing vector is more orthogonal to the [face normal] the color will be more opaque.  When your viewing vector is more parallel to the [face normal] the color will be more transparent.  Transparent factor is the property that was designated to be affected by the calculation.

Please also secondarily search Fresnel which is related.
Depending on your models.  You could consider textures and the compositor.
At this moment this is not a tutorial.  I am trying to give you some quick action tips.
Comment: Good.  The best way to convey that is to ... upvote this candidate answer or downvote it.
Comment: Hi, thank you very much for a good answer, these are great tips and just messing around a little with fresnel and dot product i have already gotten much more pleasing results!
Comment: can't unfortunately :( my account is too new so it doesn't let me add an upvote, but thanks for the great tips.


How to explain why a force fielder can't ride their force fields?

Question: In my superhero world, there is a hero. Her name is Monica Fairson. She is able to generate force fields. What might be a plausible reason why Monica wouldn't use her force fields as transportation, like a force field surf board?
Comment: This looks to me like a poll for ideas instead of a clear problem description that allows the community to vote on which answers are better than others. Every reasonable answer seems to exactly equally valid and as such I am voting to temporarily put this question on hold as "primarily opinion-based" until it's been [edit]ed to provide some criteria for what an answer has to account for and what makes an answer *good*.
Comment: Because they are static? as in she can't levitate them.
Comment: I will add this into the question, sorry, but no, they can be moved
Comment: Too late to make it an answer, but look at the physics of Sue Storm's force fields.  Her ability to lift objects by using one (wedging it under it and expanding, etc) is tied to her strength. So she's "strong" enough to make one that could support her weight, but not that of, say, the Titanic. You hero may not be strong enough to generate one that could support her weight.
Answer: It's all relative
In this case the force fields exist in space relative to her rather than to anything else. So while she can use them for shielding, she can't use them to fly. To be able to fly she'd need to be able to place the field relative to the ground.
The force field is utterly unresponsive to external forces
To be used as a surf board it would need to exert return pressure from the water on the rider. It doesn't do this and would just plough straight on relative to the rider's momentum. Action has no reaction.
Answer: Option 1: Force Fields do not affect her. Not just her own Force Fields, but Force Fields in general. If she tried to use one as a "Surf board", she'd fall through.
Option 2: Force Fields can't exist or are unstable close to her. They might flicker or warp.
For more ideas, it would be great if you could give more information about the Force Fields.
Answer: Let's make an experiment. Take a plank of wood : you can lift it, move it, beat someone with it, protect yourself with it... no, try to lift it while you are on the plank. That's hard, isn't it? even if you have enough force, you just can't lift yourself and use the plank of wood as a surf board.
Monica's superpower is not so different. She just control a kind of air plank. She can lift it, move it, beat someone with it, protect herself with it, but can't use force field as a surf board.
Comment: @ironduke97, you don't need to lift a forcefield used as a surfboard either, it just needs to exist relative to the rider and displace water.
Comment: @ironduke97, I was thinking strictly as a surf board, on water
Comment: But a surf board is just a plank, a funny shaped plank but ultimately a plank.
Comment: But you aren't lifting the plank @Separatrix you just stand on top of it.
Comment: Then I suppose the superhero will have to wait for winds to move around just as a surfer has to wait for a wave.
Comment: @Separatrix ah I see.
Answer: Infrisios' options are good so i'll carry them on
Option 3: Perhaps Force Fields have no traction? she could stand on one, but would immediately slip straight off. they can stop things from passing through, but pushing against them would be like pushing against the slippiest ice you've ever experienced so as soon as the force-field moved it would move but wouldn't pull her along with it
Option 4: because it breaks the laws of motion, specifically Law 3, every action has an equal and opposite reaction. she cannot ride it as there is no propulsion pushing away from her to push her in the opposite direction.
Option 4a: this would also mean that if she "pushed" a force field out with her powers, then she would be pushing and then pulling on it when she attempted to stand on it so the forces would cancel out and she'd just drop to the floor
Option 5: it requires focus and concentration to form a force field. so is unable to do that when shes moving
Comment: wouldn't option 3 be more beneficial? If you had a flat plane forcefield with zero traction any momentum something had starting to cross it would continue undiminished for the length of the forcefield. I would think the opposite would be more reasonable to prevent a force field from being used for transport, have it with near infinite friction
Comment: @BKlassen, 0 fraction would still be effective, but i agree one way or another could be the same in terms of limiting movement. but if there was near infinite friction then in theory the wielder would be unable to move the force field at all which the OP stated was needed
Answer: Her force field might work a bit like kevlar. Kevlar is great for stopping bullets, as it soaks up all their kinetic energy, but it's not so great at stopping knives, as the sharp edge sliding against it just cuts straight through. It's only fabric, after all.
So her force fields would be great at deflecting blows that hit them straight on, but the moment they're forced to grind against something (like the floor), they get damaged, or lose their integrity, and end up failing.
(Note: the picture I have in my head is of her skating along the ground on her force field, like in the City Escape level of Sonic Adventure 2. If you picture it more like the Silver Surfer's hoverboard, then this answer wouldn't work (but also please edit that information into the question).)
Answer: Are the force fields movable? If no you can only use them to create a static object like a ladder or a bridge, not a surf board.
Assuming that force fields are movable these could be the reasons why she can't surf them:

She needs to focus a lot to create the force field. It's not uncommon that the caster needs to put most of his/her capability in maintain the force field active, even a static force field. In this case is not "technically impossible" to surf a force field, it only needs so much concentration that it's practically impossible to do both things (create the field and move fast avoiding obstacles).
The force fields are "almost" solid. A force field is not like an adamantium wall but rather an incredibly dense "fluid" or a non-newtonian fluid.  Therefore a force field can easily stop bullets and act as a wall if someone is running against it, but since it's a viscous fluid, over time objects will pierce it. Imagine it like an OObleck surfboard, you can use it as a shield but you can't stand over it.
Even if you can create a magic surfboard, how are you supposed to move it? You need to create a surfboard AND a frictionless slope, then you can move by using gravity, or you need to provide another source of propulsion. The force field can move as a solid body or its movement is technically the creation of f.f. in one place and disruption of f.f. in another place? Since it's a field I imagine it as space's property that the caster can activate and deactivate where he/she wants but this means that the only way to "move" a f.f. is to play with f.f.'s shape and f.f. doesn't actually move.
The reason why the caster can generate force fields actually makes he/she "immune" to them. It's up to you define the caster's origin and his/her source of power.

How to explain why a force fielder can’t ride their force fields?


How much insulation do I really need?

Question: I have been looking at cork sheet insulation for my 200 mm x 300 mm aluminium PCB heatbed, by I am not entirely sure how thick it should be. There seems to be a trade off between losing a few millimeters of print height, and providing adequate installation.
I have seen 10 mm thick table mats, and then 5/3/2 mm thick cork insulation tiles. On some forums people say they use two 2 mm sheets beneath the aluminium heater and then another 1.5 mm aluminium plate under those, to hold it altogether (source: Re: Is a cork board necessary under the heated bed?).
Hopefully this does not come across as a how-long-is-a-piece-of-string type question. I am just trying to get the right amount in the first place whilst spending as little as possible, and keeping the mass/volume and height down. If someone else has already gone through the empirical adjustments themselves, then it might save me the time and expense of having to test various configurations.

Would just 2 mm thick cork backing be sufficient?
Is 10 mm overkill?
Does silver foil backing help considerably, thereby enabling one to reduce the thickness of the cork?
Comment: Cork is bloody cheap. Why worry  -- other than the fact that it's flammable. All that's needed to start a fire is having the thermistor fail or come loose. I'd use a flameproof material if you're going to insulate.
Comment: If you really want to go all out for insulation, buy some [aerogel](http://www.aerogel.org/)!
Comment: @Greenonline I have to admit that you'd have the coolest looking 3D printer with some of that Classic Silica Aerogel insulating your machine!
Comment: @CarlWitthoft - OK, thanks, this is the first time that I have really given thought to the flammability issues, although I had read that cork is preferable to silicon/rubbery insulation, due to less noxious fumes being given off.
Comment: @tbm0115  - :-) That really does look top notch, but is, unfortunately, a bit pricey.
Comment: @CarlWitthoft - As the ignition temperature of cork is 300°C, I wonder if there really is a fire risk. Do you know of any examples of burning, or scorching, of cork, when used as a heatbed insulator? Please see my question [Has anyone experienced scorching or burning of cork heatbed insulation?](http://3dprinting.stackexchange.com/questions/3122/has-anyone-experienced-scorching-or-burning-of-cork-heatbed-insulation)
Comment: Burning cork is difficult even when you WANT it to burn... Cork is the outer layer of trunks and has specifically the goal of protecting the plant from fires. I would say almost no flame risk.
Answer: Since 50% of the bed is uninsulated, you're definately into diminishing returns as soon as you start adding any insulation.
With that area, I think you are looking at 1.2W per kelvin for a 2mm thickness.
I'm guessing a bit with these powers, but roughly, maybe from 100 W un-insulated, 75 with 2mm, 60W with 4mm. You can get a reasonably accurate measure of the power by looking at the duty cycle of the heating element.
Actually, its not clear if your primary goal is to reduce energy/maintain a very high temperature, or speed the initial heating. You can place a temporary sheet of cork on top of the bed (preferably extending over the edges to prevent convection) and this will significantly improve heat-up times.
Comment: Also consider cork on top of the bed during heating.
Comment: Yes, doubling the insulation doesn't double the power saving. The numbers are guesses, I need to work more on the maths for a real answer.
Comment: Yes, that is a good idea... I remember reading somewhere that someone suggested even corrugated cardboard helps.
Comment: Many thanks for the answer. I think that I see what you mean, but just to clarify a few points: By _diminishing returns_, you mean that each increase in insulation thickness gives a correspondingly reduced _increase in actual insulation_ (which, I guess, would make sense)? Are the figures of 100/75/60 W relating to the power used to maintain the heatbed at the same temperature (i.e. 70°C)? Without (necessarily) wishing to get into the mathematics too much, are those figures for the power, _guesstimates_ based on experience or did you arrive at those figures using a formula?

How much insulation do I really need?


Jenkins - passing updated revision to downstream jobs

Question: We have moved build system from CruiseControl to jenkins for a multi-platform product.  This was a  single monolithic job:
 1. check for changes
 2. update product build number in properties file
 3. commit file to subversion
 4. pass svn revision number to other platforms for local checkout (performance reasons)
 5. build (C++, Java)
 6. test
In Jenkins, we have split the build and test into 2 jobs, build triggering the tests.  All platform builds have to succeed for tests to run.  I'd like tests on platform A to run regardless of build failure on platform B, but that's a different issue.
The problem I'm trying to address now is for the build phase.  When Jenkins starts, it knows the SVN_REVISION of the repository at start of job.  We increment the build number before the compilation during the job and it is this svn revision we need to pass to downstream jobs.  We need to ensure the same revision is checked out on all platforms and that the test job also checks out same revision.  The compilation takes 2-3 hours and testing about 7 hours, so it is normal enough for some new commits to happen during the build that will be included in test job.  We have also had commits during build phase that get included in one platform but not the others due to different speeds of checkout.
We have tried Parameterized Trigger plugin which can pass SVN_REVISION - the revision at time job started, but does not pass the revision of modified file with build number.  We use Parameterized Trigger in other cases and it does what we need.
One thing I am thinking of doing to add svn revision number to properties file.  I could read the revision from the property file in other jobs, assuming file has not been changed, which could be risky.
svn uses ':' to separate property, IIRC, other properties use '=' for key=value as we also read properties to be used in shell scripts.  There are other dependent projects, so I'll try this when I get back to office and set up a sandbox (half day's work).
Anyone got any recommendations or comments?
Answer: Thanks to this post and the comments below:
https://itisatechiesworld.wordpress.com/jenkins-related-articles/jenkins-configuration/jenkins-passing-a-parameter-from-one-job-to-another/
Here is the answer that worked for me:

Get the Parameterized Trigger Plugin (How to install: Manage Jenkins->Manage Plugins->Available and check "Parameterized Trigger Plugin" and install, note I also installed "Environment Injector Plugin", this may be necessary as well)
Goto JOB_1 and add a Post-Build action (Trigger parameterized build on other projects)
Type the project to build JOB_2
Add Parameters (Predefined Parameters)
Type the following in the Parameters box: SVN_REV=${SVN_REVISION}
Apply and Save
MOST IMPORTANT: YOU MUST ADD THIS PARAMETER (SVN_REV) to JOB_2
Goto  and check "This build is parameterized" and add a "String Parameter"
Type "SVN_REV" (Must be same name) and put in a default value of 1 or anything
It's now an environment variable, to access it, all you need is %SVN_REV%
In your build step, you can write echo %SVN_REV% and it will display the SVN_REVISION.

In short (Parameter must be specified in BOTH jobs)
JOB_1 => SVN_REV=${SVN_REVISION}
JOB_2 => Add SVN_REV as a String Parameter, to access type %SVN_REV%
Comment: This should be the correct answer. Works fine. Just call the variable with echo SVN_REV instead of %echo SVN_REV%
Comment: This won't work if the downstream job has different schedule, specially when the builds triggered at irregular time.
Answer: I think the Clone Workspace Plugin would work well for you.  It allows you to clone the workspace so another job can use it.  Using this, I would configure my jobs something like this.

(1) Master Job:  Check out the source, update the build number, make workspace clone
(2) Platform 1: use clone from #1, build for Platform 1, make workspace clone for testing Platform 1
(3) Platform 2: use clone from #1, build for Platform 2, make workspace clone for testing Platform 2
(4) Testing for Platform 1: use clone from #2
(5) Testing for Platform 2: use clone from #3
Answer: We ran into similar issue where we want to call jobs on the slave machines and pass the SVN revision which master is using, following is how we solved this problem:
1) Invoke the child job with predefined parameter say MASTER_SVN_REVISION and assign it value of SVN_REVISION

2) Now in the job which you have invoked in step 1, use following mechanism to use value of MASTER_SVN_REVISION
Answer: One of the source options in the Parameterized Trigger plugin is:

properties from a properties file read from the workspace of the triggering build

If you create this in the original workspace without checking it in, you won't have any risk of change before the downstream jobs are triggered.
Comment: I'll look into this.  However I do need to check the properties file as it is used by this project's build and test as well as other projects.
Answer: In your build step, you can write echo %SVN_REV% and it will display
 the SVN_REVISION. In short (Parameter must be specified in BOTH jobs)
JOB_1 => SVN_REV=${SVN_REVISION}
JOB_2 => Add SVN_REV as a String Parameter, to access type %SVN_REV%

Use ${SVN_REV } to access. It worked for me.


Does Odo lose consciousness when he goes into his bucket?

Question: Not sure if Odo is totally unconscious or if he retains some sort of awareness while "resting" in his bucket. What do the episodes say?
Comment: Interesting question... It's rather likely it's something that was never explained though =\
Comment: I think I remember something about him not able to get mentally tired and spends his time in his room thinking or something. Perhaps he was talking to Kira (towards the end of the series)? I can't seem to find the scene.
Comment: He can lose consciousness; http://scifi.stackexchange.com/questions/67640/can-changelings-be-knocked-out/67646#67646
Comment: He can lose consciousness, but does he do so when he goes into his bucket?
Answer: I would say that he retains a reasonable level of awareness of what's happening around him. There's plenty of references to Odo's need to "regenerate" but it's never made explicitly clear whether this is accompanied by a major loss of consciousness.
When he meets another shapeshifter in DS9 : Chimera, Laas described "solids" thusly

He has bumps on his forehead and          she has a wrinkled nose -- but
            they're basically alike. They're          bipeds that eat, sleep and
            breathe. You and I are nothing          like them.

Later, after he regains his ability to shapeshift in DS9: In Purgatory's Shadow he comments that sleeping in a bed was one of the very few human pleasures (along with eating and drinking) that he enjoyed:

KIRA: I bet you can't wait to get all this put together so you can start shape-shifting around the room again.
ODO: I suppose. Though I did enjoy sleeping in a bed.
KIRA: There's nothing to stop you from sleeping in a bed if you want to.
ODO: Except that now when I'm asleep I tend to revert to my gelatinous state and slide onto the floor. No, the bed goes. I'm a
  changeling, not a solid. There's no use pretending otherwise.
Comment: I don't understand how Odo could say "now when I'm asleep." Could he "fall asleep" as a changeling? Did he, or did he not, retain awareness while "asleep?"
Comment: @T-1000 - He seems to maintain an awareness but there's a lot of change between the earlier seasons and the later ones, after he's met with Laas, after he's joined with the link and after being made human and then merging with an infant changeling. As he grows and matures, his need for restful (unconscious?) sleep seems to disappear
Answer: I do not have a direct reference for this, but later in the series he redesigns his room.  Someone visiting his room found it full of all kinds of weird shapes and structures.  Odo explains that it is not so much that he needs rest as that he couldn't hold one form indefinitely.  He further explains that now, instead of just relaxing in his bucket, he imitates some of the abstract sculptures in his quarters and, for want of a better word, stretches and tests his skill with shapes other than humanoid.  So, no, apparently he is never unconscious, even when resting.
Comment: I'm not sure that the script backs up what you're saying. *" don't use the... bucket anymore. I've kept it  as a reminder of how I used to be.  But now, when I need to regenerate, I simply revert to my gelatinous state... anywhere in these rooms. Here, I can experiment with different
   shapes and textures... bring in
   various forms to emulate... and I
   can do it in private.".*. It isn't obvious that he's doing both at the same time.


What is the difference between the FDR in benjamini-hochberg/bonferonni vs a local FDR?

Question: I am wondering if the local FDR in Efron's literature is different than the FDR associated with Benjamini-Hochberg and if it is perhaps talking about something else.
Comment: Do you hand a link to an example of the specific use you are querying?
Comment: BH stepdown doesn't control the FDR, it controls the FWER.
Answer: Yes, they are different. Local FDR in Efron's literature is easier to understand, and it's a Bayesian idea. We suppose the parameter $\theta$ has a prior distribution, say
\begin{equation*}
  \theta \sim
    \begin{cases}
       0 & \text{with probability } \pi_0 \\
       f_1(\theta) & \text{with probability } 1-\pi_0
    \end{cases}
\end{equation*}
We also suppose that we observe a statistic $z \sim g(\theta)$. The local FDR is basically the posterior probability $p(\theta = 0 | z)$. There's also a related concept in Efron's literature, the Bayes FDR, which is basically $p(\theta=0|z \in \mathcal{Z})$ where $\mathcal{Z}$ is a rejection region (e.g. when the p-value given $z$ is less than 0.05).
Bejamini-Hochberg is more difficult to understand, cos it's a frequentist concept. Suppose you run a large number ($n$) of tests, to test whether $\theta_1=0, \theta_2=0, \ldots, \theta_n=0$. Then, imagine you repeat this set of tests many (infinitely many) times. With each repeat, although $\boldsymbol{\theta}=(\theta_1, \theta_2, \ldots, \theta_n)$ stays the same, $\boldsymbol{z}=(z_1, z_2, \ldots, z_n)$ are generated anew from $z_i \sim g(\theta_i)$. The "false discovery rate" for each repeat $k$ corresponds to $S(k) = Pr(z_{ik} \in \mathcal{Z}, \theta_i = 0 | z_{ik} \in \mathcal{Z}) \equiv \dfrac{\#(z_{ik} \in \mathcal{Z}, \theta_i = 0)}{\#(z_{ik} \in \mathcal{Z})}$, with $Pr(z_{ik} \in \mathcal{Z}, \theta_i = 0 | z_{ik} \in \mathcal{Z}) = 0$ if $\#(z_{ik} \in \mathcal{Z}) = 0$, and $\#$ denotes "counts of". Note that $S(k)$ is a random variable that varies with $k$. In Benjamini Hochberg's definition, $FDR=\mathbb{E}(S(k))$. They are saying if you follow their procedure, given the assumptions (e.g. independence of $z_i$), $FDR \leq \alpha$.
Comment: You are talking about BH as a procedure. The question concerns the definition of FDR in the BH paper, which they use to justify their procedure.
Comment: No wonder 'Bejamini-Hochberg is more difficult to understand' - your explanation is very confusing BH is simply that you rank each test and adjust the p-value by number of tests and check the first test is below the adjusted p-value. If it is you drop that test, adjust the threshold for the lower number of tests and repeat with one less test until you get to the highest p value that fails against the adjusted threshold.
Comment: My point is you can present it simply or complicated, the same as any mathematical operation. If you present the complicated version then it is biased towards being difficult to understand, so difficulty becomes a self fulfilling prophecy. Your answer reads very well without the labels regarding difficulty.
Answer: Efron has a very good explanation of this in local FDR vs BH FDR. Figure 3 in that reference gives a very good geometric view of how the two FDR methods differ. Bonferroni is returned to below.
Fundamental concept of each test
Local fdr (I'm using the capitalisation in Efron's paper) is based on determining the likelihood of the p value being a false positive under null vs the sum of it being a true positive under the prior or a false positive under null. It does this for each test hence the use of 'local' in the name to differentiate it from BH.
BH is based on making long run assumptions about the likelihood of the null giving random false positives. BH recognises that independent probabilities combine using OR logic, so multiple test probabilities sum together. Thus the probability of a false positive occurring within a suite of independent tests is the sum of the probabilities in each each test. In practical use rather than adjust the p-value or z-score itself one common implementation of BH is that the threshold for acceptance or rejection is adjusted to reflect the sum of probable false positives across the suite of tests. The mathematical explanation of this implementation of BH made most sense to me and is firmly grounded in set theory mathematics, in the form of positive regression dependence on a subset of one. here's my understanding of it. To address the point raised in comments about the relevance of this procedure to the question, the implementation may not be what Benjamini and Hochberg originally envisaged, but it is a mathematically sound way of achieving their intent and I found it comprehensible so others may too.
Consequences of differences
This implies that, to quote Efron:

The local nature of fdr(z) is an advantage in interpreting results for individual cases.

Efron states (eq 2.11 in reference) that the relationship at low values in BH is
$$fdr(z) ˙= Fdr(z)/α$$
where $fdr$ is the local FDR and $Fdr$ is the BH.
The full relationship is given by Eq 2.8
$$Fdr(z) = E_f [fdr(Z)|Z ≤ z],$$
where z is the actual z-score realised and Z is the rejection region. I.e. the BH Fdr is the expectation of the fdr given z exceeds the threshold. BH does not worry about how much an individual test exceeds the adjusted threshold, just whether it does or not.
BH requires that each statistic be independent (subject to OR logic), otherwise false positives will be correlated and the adjusted threshold for each test is no longer accurate. Strongly correlated tests need to be handled differently depending on the nature of the correlation. In contrast the local FDR is defined based on the prior specific to each test and so the requirement of independence can be relaxed (I don't see this stated so I am guessing this is because any correlation will be baked into the priors and so explicitly accounted for), but for useful distributions to be defined then the number of tests must be large. To quote Efron:

$N$ must be large for local fdr calculations, at least in the hundreds, but the $z_i$ need not be independent.

This is simply because to build robust data based metrics you need enough data to provide a robust estimate of derived parameters.
Bonferroni
Bonferroni differs greatly in its intent from Efron or BH, it controls for the possibility of at least one false positive and is a family-wise error rate controllers (all tests treated uniformly as a common family). Bonferroni more tightly controls the risk of any false positives at the expense of power. FDR methods attempt to provide a more nuanced handling of false positive risk (evaluating risk evaluation for each test individually), providing better power at the expense of a higher risk of false positives.
Comment: The so-called BH FDR you referred to is not actually the FDR referred to by Benjamini and Hochberg (1995). As I pointed out in my answer, the FDR in BH1995 is an unobserved r.v.. The main goal of BH1995 is to *control* for this FDR. Your "BH FDR" is a method for *estimating*  the sample's false discovery rate (which, confusingly, is not BH1995's FDR either), inspired, no doubt, by BH1995's *procedure* for FDR control. As Efron said in his paper, this procedure for *estimation* of FDR was first described by Storey (2002) and Efron and Tibshirani (2002).
Comment: Thanks for your feedback, it helps me understand you reaction to my comments under your answer. I don't see a conflict between my answer and your comment. I am discussing BH-FDR on the basis of set theory implementation (PDRS1), which while procedural is still mathematical (modern maths is founded on set theory). I choose this perspective as it provides additional perspective wrt to your answer and it is the one that helped me understand BH-FDR. I appreciate the procedure doesn't give a precise adjusted probability, but it achieves the same goal for a predefined $\alpha$.


In Hadoop Command Line, How do I save all the commands I used as a log in any format for my subsequent reference. Thanks.

Question: In Hadoop Command Line, what is the code to save all the commands I used in a log (in any format that maintains history of transactions performed) for subsequent reference. Thanks
Comment: Have you tried anything at all? At least googling for the answer.
Answer: I don't think there is a direct hadoop command to do that but you can always use ttyrec to record the commands you run.


Use name Geeta in place of Geeta Geeta

Question: My name is Geeta. As first and last name is required to be filled in while creating a Gmail account, I typed Geeta Geeta as first and last name respectively. Please tell me how I can amend my name as Geeta, as my name is Geeta and not Geeta Geeta.
Comment: And you don't have a last name?
Answer: You need to login to http://plus.google.com with your credentials, and then go to your Profile settings.
In the top of the Profile settings page you can see your profile image and name. Place the mouse cursor on your name, and the message Click to edit your name appears, so click it.

Use name Geeta in place of Geeta Geeta


When I download a free app in appstore it says "amd action:authenticate:sm"

Question: When I download a free app in appstore it says "amd action:authenticate:sm". My device is iPhone 5c. How can I solve this problem???
Answer: You can try adjusting your iPhone clock to your current location.
Go to Settings > General > Date & Time on iOS and set your time appropriately -either manually or automatically by switching the "Set Automatically" slider to on.

When I download a free app in appstore it says “amd action:authenticate:sm”


Can't Change expandMain Fedora Partition with GParted

Question: I am trying to expand my main Fedora partition and have live booted but I still cant move sda3 over so I can expand into the allocated space.
Picture of GParted
Comment: You need to use lvm tools.
Comment: @GabrielaGarcia Can you elaborate?
Comment: Unfortunately I can't because I don't use lvm but I know you need special tools for that instead of GParted. A Google search should be enough.
Answer: The picture shows the /dev/sda3 partition as containing a Logical Volume Manager version 2 Physical Volume, or LVM2 PV.  All of the space within the LVM2 PV appears to be allocated to LVM2 Logical Volume(s).  Usually each LVM2 LV will contain a file system such as ext4.  LVM2 is a special type of formatting that permits file systems to span across multiple physical disk drives.
The lock icon beside /dev/sda3 indicates that the partition is active or in-use.  In order to move or resize /dev/sda3 it must first be deactivated by selecting the partition and using the menu option Partition -> Deactivate.  Then the partition and the enclosed LVM2 PV can be moved or resized.
Note that if you increase the size of the LVM2 PV then to use the new space inside you need to use commands like lvmresize to grow  the LVM2 LVs.  I think when the LVM2 LV is grown then you can grow the file system within using a command like resize2fs for ext2/3/4 file systems.
I highly recommend that you make a backup of your data and also read up on LVM2 before changing the disk organization.
Personally I find the added flexibility of LVM2 unnecessarily complex, so I install GNU/Linux directly into partitions with file systems like ext4.


Drawing and Editing in QGIS

Question: Is it possible to carry out vector editing functions in QGIS? In this case I have an imported shapefile of contour lines. I wish to be able to create a copy of a line, in-situ, trim it, then create a number of offsets at a specific spacing. In short, basic CAD tasks.
Comment: Welcome to gis.stackexchange! Please note that a good question on this site is expected to show some degree of research on your part, i.e. what you have tried and - if applicable - code so far. For more info, you can check our [faq].
Answer: You can install QAD plugin which does exactly what you want. It has trimming, extending, and other interesting tool like simple CAD, as you can see below:

This is the only tutorial I found of QAD Plugin, but unfortunately it is not in English. But I think you can still follow because the commands are in English.
Comment: Awesome, any tutorials you know about?
Thanks, N
Comment: I updated my answer.
Comment: Yeah, spotted that one. However my Italian not so great.
Thanks
Comment: If you are familiar with AutoCAD, it will be easy to understand the process. I had experience working with AutoCAD software before that's why I found it very useful.
Answer: The Advanced Digitizing Panel has tools that will be of use for you.  I use it to start a predefined point, move at a specified distance and angle to my point of beginning then begin digitizing from there specifying line lengths and angles.  Here's a video tutorial for more information on the panel and the related trace tool:
https://www.youtube.com/watch?v=QsjmLa16obs
These tools became part of the standard installation as of QGIS 2.8.

Drawing and Editing in QGIS


Is there any quiz or tool that identifies the denomination which is closest to my personal beliefs?

Question: I've looked through the beliefs of several denominations, but I can't seem to find one that has the same positions that I take on many Christian questions. Is there a quiz or test or even just a catalog of each denominations core beliefs that will give me a straight answer to which denomination I should look into rather than the "you're 81% Methodist" or "you're 63% Lutheran" that I get from many online surveys and quizzes?
Comment: It might help to know what are your beliefs and go from there. Let's start with "who is Jesus Christ? I ask because at Matthew 16:13 Jesus ask His disciples the question, "Who do people say the Son of Man is?"
Comment: **(1).** *the same positions that I take on many Christian questions* - Provide us with a relevant list of these positions, and **I**, for one, will **try** to steer you in the directions which are *most* compatible with them. **(2).** *a quiz or test* - The *main* problem with these is that they only provide the user with *a very narrow and limited set of options* (which might work for most, but, by all appearances, you don't seem to fit their bill).
Comment: If some particular Church worships Jesus, but they have some specific differences from you in their interpretation of Biblical verses or facts about God or Jesus, I'd be curious about what difference that really makes to you.
Comment: Unless it's more about socio-political concerns - does this Church match my support/rejection of Trump? Match my support/rejection of gay rights? Match my support/rejection of abortion? In that case, I can see how it would matter quite a bit.
Comment: I don't believe you'll find a denomination with 100% match unless all your beliefs come from a denomination you belonged to earlier, even then I could see cases of not being a full match
Comment: it's a good question, but why don't you simply go to the nearest Bible believing church and shine Jesus. You'll be amazed at how God will use your compliant heart ♡♡♡
Answer: Is there any quiz or tool that identifies the denomination which is closest to my personal beliefs?
Absolutely, but the true problem here is that there are so many denominations and subsets of those denominations.
In the State of California, a new denomination is recognized by the state almost every day!
Go To Quiz is just one example:

Which Christian denomination do you belong to?
There are hundreds of denominations within Christianity, each with their own unique views and history. Ever since the early sixteenth century and the Reformation under Luther, western Christianity has been split by theological and political views. And since then, split after split, especially amongst Protestant groups, has created a very wide spectrum which Christians occupy.
With religion still central to world politics today, find out where you belong on that spectrum. Are you a devout Catholic, proud of Rome's history? Or maybe you are a staunch Calvinist, one of God's elect. Or you could even be a Pentecostal, putting faith and your relationship with God above all else. Or maybe you are an episcopalian, choosing the middle-way between Catholicism and Protestanism. Take the test now, and find out which of nine categories you belong to!

The question on this site are as follows:

Who do you believe decides whether or not someone achieves salvation?
Which of the the options below do you think best sums up the legitimate sacraments?
What are your views on church hierarchy and positions such as that of Priest, Bishop etc?
Do you believe in the idea of a universal church (before the Second Coming), or that people should have religious freedom to pursue their beliefs as God guides them?
Which of the following do you believe to be necessary for salvation?
Do you believe there is any merit in infant baptism?
Do you believe baptism conveys justifying grace, non-justifying grace, or is purely symbolic?
What are your views on speaking in tongues?
What do you believe to by the significance of the holy communion?
How do you believe Satan came to be (in his evil form)?
What are your views on the Trinity?
What do you believe is the best way to organise Christian worshipping?
Do you believe in secularism, and the separation of church and state?
Do you believe that Christ's death on the cross at Calvary is the sole source of atonement?
Do you believe in sovereign grace, and that only God can have mercy and determine who is granted salvation?
Do you believe in the doctrine of total depravity, and the idea that men are born sinners, incapable of resisting sin by their own merit?

There are some flaws to the questionnaire because the answer can only be for certain major Christian denominations only. Subsets are not included.The denominations that this quiz refers someone to are as follows:

Catholic
Episcopalian
Lutheran
Methodist
Restorationist
Puritan
Calvinist
Baptist
Pentecostal

Apart from such online quizzes, to get down to the nitty gritty, one must research the core values and beliefs of particular denominations in order to find out where one fits in.
To say with exactitude which breach or denomination you fit in with would sound like giving personal advice, which is not allowed on this site.
I would recommend that you talk to someone of a particular denomination that interests you and with whom you are comfortable speaking with for more guidance than what we can do here.
Good luck and keep looking. You will eventually find your answer.
Comment: Those aren't the "major denominations". Orthodoxy, the third largest by numbers isn't even included. Neither are the various branches of Anglicanism which account for [more than 100 million followers](https://en.wikipedia.org/wiki/List_of_Christian_denominations_by_number_of_members#Anglicanism_%E2%80%93_110_million). That looks like it is simply a parochial site focusing on the denominations most common in the USA. Not a very good example quiz.
Comment: @curiousdannii I agree, it might be the best there is.  I think we are in a position to develop our own quiz.  We can start by creating a meta question with a table with *rows* representing Question+Option, *columns* representing denomination, and *cells* containing empty or X.  I volunteer to host the web app incorporating the table for the quiz.
Comment: @OneGodtheFather Yes, I'm also interested in studying Coptic tradition as a foil for other mainstream tradition.  I recently was struck by how much I agree with [Irenaeus's recapitulation theology](https://digitalcommons.georgefox.edu/seminary_masters/18/), a foil not only for Penal-Substitution but even Christus Victor atonement theory (because Irenaeus's recapitulation is so much more than Jesus's work on the cross).
Comment: I wish the answers to the quiz were more varied, even an other option. I did match with my denomination but many questions did not hold an answer that I agreed with
Comment: @terdon That is why I said there are flaws in the system!
Comment: Fair. I was just annoyed and felt the need to, um, add noise, basically. Sorry :)
Comment: Not a great quiz, question 4 in particular doesn't make sense to me. But it might be the best there is!
Comment: @curiousdannii Found a few other quizzes, but the questions were so poorly phrased, I thought it would be inappropriate to make mention here as references.
Comment: Q4 is hilarious. It implies the teachings of a (hypothetical) Universal Church are not "guided by God". Oh wait, I just thought of an example where a lot of people who claim to be Christians would agree with that assertion ...
Comment: Not a perfect quiz, but correctly categorized me as a Restorationist.
Comment: @GratefulDisciple I have no real objection to your idea, if the other moderators can be onboard with this initiative and if it would be permitted by SE rules and guidelines (not sure)? Post an inquiry question on meta, if you want.
Comment: @KenGraham [Another quiz hosted by GotoQuiz.com](https://www.gotoquiz.com/with_which_christian_denomination_do_your_vie) is less detailed but has all the major Trinitarian denominations: Catholic, Eastern, Oriental, Anglican, Lutheran, Methodist, Presbyterian/Reformed, Baptist, Pentecostal.
Comment: @GratefulDisciple According to that second quiz, I'm going to have to start exploring Oriental Orthodoxy! My guess is it didn't work as well for me as the first one, but ... who knows?
Comment: @GratefulDisciple Interesting - thanks for the link!


Why no bracha on the Torah commandment of watching matzah?

Question: There is a Torah obligation to guard matza (Exodus 12, 17) (shemur matza).  But there does not seem to be a bracha said on doing this.  Why?  (The watching is not just mental exercise. You have to walk or otherwise get yourself to where the flour is, and then be active in watching. It is not just a mental activity.)
Comment: Also consider that the shemirah is not a specific action but over the months. That is, it is not that it is being watched, but that it should **have been** watched.
Comment: @sabbahillel  Yes, the mitzva has a long duration, but so does dwelling in the succa (but much shorter). In any case, what do you mean it "should have been watched".  The mitzva is to watch, not to think it should be watched. Also, when watching begins the watching should continue uninterrupted, as I understand it.
Comment: @YehudaW The mitzvah of succah is a specific action with the bracha at the time the action is being done. The shmira is a general action and not a specific one. There is no explicit action being done at a speific time.
Answer:
At first glance shimur is a Lo taasse (a negative commandment) despite that we have an  additional shimur leshem matsat mitsva, it remains a Lo taasse. There is generally  no Bracha for A mitsvat Lo taasse.

The source for the pure lo taasse nature of  shimur: Mechilta (on Shemot 12, 17):

[יב, יז] ושמרתם את המצות - שמרהו עד שלא תביאהו לידי פסול.
to ensure that there are no disqualifying event.

See Gemara Pesachim 38b:

ושמרתם את המצות מצה המשתמרת לשם מצה יצתה זו שאין משתמרת לשם מצה אלא לשום זבח.
And ye shall guard the unleavened bread: [it must be] unleavened bread which is guarded for the sake of [the precept of eating] unleavened bread, thus excluding this, which is guarded not for the sake of unleavened bread but for the sake of a sacrifice.

Rashi:

כל שימור שאתה משמרה שלא תחמיץ התכוון לשם מצה של מצוה:
All monitoring which is to avoid fermentation, would be in intent to get matsa of mitsva,  not a mincha of sacrifice.

Bedikat Chamets regard Chamets but  is a mitsvat asse of Tashbitu.
In birkat Chatanim also "והתיר לנו ... עלי ידי חופה וקדושין" points to a Mitsvat asse.
But  Bracha of "lishmor chukav"  of bene Maarava when they remove tefilin is linked to cancelation of  a Mitsvat asse to wear them at day only  (see Menachot 36b Machloket if hishamer deasse is asse or  lo taasse) is at least a bit similar to a blessing for a Mitsvat lo taasse. Anyway Gemara Nidda 51b regarded  it as bracha acharona of mitsvat asse of tefillin.

"ושמרת את החוקה הזאת
      למועדה מימים ימימה"

to exclude nights.

But a stronger argument to substantiate the lack of beracha is the following Gemara in Menachot.

Menachot 42b: Wherever a precept is completed by a single act, e.g. , circumcision, although it may be performed by a gentile, when an Israelite performs it he must pronounce a blessing; and wherever a precept is not completed by a single act, e.g. , the tefillin (manufacturing) , although it may be made by a gentile, when an Israelite makes it he does not pronounce a blessing.

In matsot, the mitzva is completed by eating, so there is no bracha  on shimur which is not the last part of the mitsva.
Tosfot report that Talmud Yerudhalmi doesn't follow this rule.

ואילו לעשות תפילין לא מברך. ויודע היה [שלא לברך לעשות תפילין] ששאלו כל ענייני ברכות ופ' הרואה ירושלמי מצריך לברך אעשיית ציצית סוכה ותפילין ובערוך הביאו בערך צץ ג' וחולק על הש"ס שלנו ובתוספתא דברכות (פ"ו) תני העושה ציצית לעצמו מברך שהחיינו ובפ' הרואה (ברכות דף נד.) נמי אמר דאכלים חדשים מברך שהחיינו וכ"כ רב שרירא גאון:
And in the last chapter of Brachot from the Yerouchalmi, it is regarded as necessary to bless when making Tsitsit,  Succa,  Tefillin, The Sefer Haaruch (from Rabbi Nathan  from Rome) reported the text of the Yerushalmi without mentioning the Bavli.  Tosfot concluded that the Aruch pasken the Yerushalmi.

But we don't follow the Aruch opinion.
Comment: OK. Bedikat hametz (searching) is taasse (positive), and we say the bracha: v'tzivanu al biur hametz.  What is the difference between destroying and not eating that causes bedikat to be positive and shemur (guarding) to be negative?  The logic of taking clear positive wording of shemur in the Torah and calling it negative because there is a related commandment seems illogical.


Adding conditions to the nikah contract after nikah has taken place

Question: Asalaamu Alaykum.
My husband and I are new to Islam. We had an Islamic Nikah, but we did not realise that the marriage was a type of contract. We assumed it had the same principles of a non-Islamic marriage. But since learning that we can put conditions in our nikah contract the both of us would like to.
Is too late to add conditions to the nikah contract?
If we are able to add conditions how would we do this?
Many thanks!
Answer: First of all what i'm saying is only my opinion and if somebody could give you any clear reference from Quran or Sunna you could consider it as nonsense.
Usually when you get married in Islam you have some Imam or someone considered as an earnest "scriber" this means someone you trust who writes down your conditions as a contract. Also you will need at least two witnesses. The Bride may need a Waly. And a Mahr (dowry) should be given to the bride or at least declared in the contract! And normally (this is a Sunna) the parents should announce (or at least the father of the bride) that you got married in your mosque/community/street/quarter.
Now you missed to do a contract and i can't see any reason why you couldn't catch this up. This means you will need an earnest scriber and at least two witnesses. I think (and this is really only my opinion) there is no harm if the scriber is a notary. You can read about contracts according to Islam in the surah al Baqara :

[282] O Believers, when you contract a debt for a fixed; term, you
  should put it in writing. Let a scribe write with equity the document
  for the parties. The scribe whom Allah has given the gift of literacy
  should not refuse to write. Let him write and let the one under
  obligation (the debtor) dictate, and he should fear Allah, his Lord,
  and should not diminish from or add anything to the terms which have
  been settled. But if the borrower be of low understanding or weak or
  unable to dictate (for any reason), then let the guardian of his
  interests dictate it with equity. And let two men from among you bear
  witness to all such documents. But if two men be not available, there
  should be one man and two women to bear witness so that if one of the
  women forgets (anything), the other may remind her. The witnesses
  should be from among such people whom you approve of as witnesses.
  When the witnesses are asked to testify, they should not refuse to do
  so. Do not neglect to reduce to writing your transaction for a
  specified term, whether it be big or small. Allah considers this more
  just for you, for it facilitates the establishment of evidence and
  lessens doubts and suspicions. Of course, there is no harm if you do
  not put in writing the common transactions you conclude daily on the
  spot, but in case of commercial transactions you should have
  witnesses. The scribe and the witnesses should not be harassed: if you
  do so, you shall be guilty of sin. You should guard against the wrath
  of Allah; He gives you the knowledge of the right way for Allah has
  the knowledge of everything.
  [283] If you are on a journey and cannot
  find a scribe to write the document, then transact your business on
  the security of a pledge in hand. And, if any one transacts a piece of
  business with another merely on trust, then the one who is trusted
  should fulfill his trust and fear Allah, his Lord And never conceal
  evidence for he who conceals it, has a sinful heart: Allah knows
  everything that you do.
(Surah 2/Verses 282 and 283)

I would recommend you to do this as soon as possible and if you both agree about the contract everything should be fine! If not you should only put in the contract what you agree about (that again is only my suggestion). And maybe you should ask some Muslim friends for advices about the contents of the contract.
Answer: Assalamualaikum,
Welcome to Islam, you will soon witness the beauty of the religion, the peace and tranquility it brings to you and please don't be disappointed by the indiscipline among majority of its followers, we're trying, make supplication for us.
Congratulations on your marriage. May Allah put barakah in it and grant you pious children.
In Islam it is permissible for a man and woman to get married. And marriage is nothing but a word, a contract. Something that binds a man to be dutiful and obedient to his wife and fearful and obedient to commandments of Allah and the same goes for the wife.
Now only sane people can give a word and hold on to it. So we are talking about sane people. And since this question is about two muslims getting married, this answer isn't applicable for other scenarios.Sane people can also trick others and are also humans and can legitimately forget the vow they have taken so Islam requires that there be witnesses.
Now that this is such an auspicious event as it is helping stop corruption in the world (man and woman committing to each other and taking oath to stop adultery) , the Imam or the preacher recites a few verses from the Quran and takes an oath from you and you can get to private business.
Now things sometimes don't go as planned and comes in the issue of separation or divorce (which is very undesirable act in the eyes of Allah but Islam is practical and there is a space for exceptions).
A woman is under the protection of her wali (a male mahram care taker, simplest meaning) until her marriage, and when she gets married her husband becomes her wali. Now a woman could be in any condition when her divorce happens. So Islam stipulates that a woman seek appropriate Mahar (do not want to say dowry but meaning is close) at the time of Marriage, which she could spend with her own will. (Other intricacies involved here, lets not go there for now).
So going one step back, during the Nikah contract, you may or may not ask for Mahar and your husband may or may not pay it all upfront and may pay in installments. Anyhow all this goes in the contract and this is your right. (poor husband gets nothing right? Well he actually is getting a beautiful bride who will help him be a successful man)
All in all, Nikah is supposed to be simple with slightest of conditions yet a robust contract.
There are possibilities of adding a million things, but in all fairness it is marriage not a business deal to put conditions and stipulations.
Also, unless IMHO if your conditions are like don't touch me until such and such date or you will let me commit haram or I don't want to have kids kind of conditions that could potentially disrupt the marriage then I do not see a reason to go back and change a marriage contract.
Allah knows best.


Find all of homomorphisms $Φ$ from $\mathbb C$[$x$]/$I$ to $\mathbb C$ that satisfies specific condition

Question:
I want to know how can I find ALL homomorphism that satisfies the condition mentioned in the question above. Please give me a method or answer in detail.
Comment: Can you show $\phi(f(x)) = f(1), f \in \mathbb{C}[x]$ isn't an homomorphism
Answer: Because $\phi(a)=a$ for all $a\in\Bbb{C}$ such a homomorphism is surjective, hence its image is a field, hence its kernel is a maximal ideal. The maximal ideals of the quotient $\Bbb{C}[x]/I$ correspond bijectively to the maximal ideals of $\Bbb{C}[x]$ that contain $I$. The maximal ideals of $\Bbb{C}[x]$ are the principal ideals generated by the linear polynomials. An ideal $(x+\alpha)$ contains $I=(x^2(x+1))$ if and only if $x+\alpha$ divides $x^2(x+1)$, i.e. if and only if $\alpha\in\{0,1\}$. What are the corresponding ring homomorphisms?
Answer: Here is another approach:

By the universal property of the quotient,  giving a ring homomorphism $\phi:\Bbb{C}[x]/I\rightarrow \mathbb{C}$ is the same as giving  a ring homomorphism $\psi:\Bbb{C}[x]\rightarrow \mathbb{C}$ with $\psi(I)=0$.
By the universal property of the polynomial ring,  giving a ring homomorphism $\psi:\Bbb{C}[x]\rightarrow \mathbb{C}$ is the same as giving  a ring homomorphism $\rho : \mathbb{C} \rightarrow \mathbb{C}$ and specifying an element $\bar{x}\in\mathbb{C}$ (which will then be the image of $x$).

So combining these two and using that you want $\phi(a)=a$ for all $a\in \mathbb{C}$ such a ring homomorphism is uniquely determined by specifying an element $\bar{x}\in\mathbb{C}$ such that $\bar{x}^2(\bar{x}+1)=0$. What are the two corresponding ring homomorphisms?


How to rotate bezier circle with an object following its path?

Question: I have an object that flies in circles using Bezier Circle curve modifier. I would like to add rotation to the Bezier Circle itself. But once I'm trying to animate the Bezier Circle spin, the object doesn't follow the circle's path, but it just flies away.
Answer: The following animation shows what I think you are asking for.

(i) keyframe the curve using the key-shorcuts i then t while the timeline slider is at the beginning of the animation sequence.
(ii) Add another object and move it to the edge of the curve.
(iii) Now, with the model selected, hold shift and select the curve.  This should leave the model outlined in orange, indicating a secondary selection with the curve highlighted with yellow(the primary selection).
(iv)  Use ctrl+p and select->Follow Path (several options work for this, I'm not sure what the subtleties are for the various types ;)
(v)  now you should be able to move the curve around and keyframe its different transforms along the timeline.
Where the object and curve are, in relation to each other, when you parent them will be affected by where the timeline slider is when you parent the objects.  Here is an animation that shows what happens when I parented the model to the curve mid-way through the animation.
Comment: That is exactly what I was looking for. I believe my mistake was to use curve modifier on the object instead of the Follow Path


Reference for Book Design Theory

Question: First, when i studied group action, i found out about design theory, then i got interested in it. But is there any good book to study design theory? especially for introduction and undergraduate student level. I knew about Design Theory book athor by Thomas Beth, D. Jungnickel, H. Lenz. But i find it too way long and i thought it is not introduction level. Pleas inform me if you know anything about it, thank You so Much!
Comment: Hughes and Piper, *Design Theory*, CUP, 1985.
Comment: Thanks, I'm reading it now!
Answer: Design Theory, by Hughes and Piper for a good introductory text.
Comment: Yes, I'm reading that book now, imo it is good enough for introductory text, so Thank you so much! And i have a plan, after finish it, i'll continue to read about design and structure in a more algebraic way (by reading 'Algebraic Design Theory' by Warwick de Launey & Dane Flannery, and 'Permutation groups and combinatorial structures' by Norman Biggs, do you think is it good plan or not? or i miss something in order (another book i should read to really understand about design theory and it's related algebraic))?
Answer: There is book by Raghav Rao which i have spent about half an hour decades ago. But remember it being more algebraic:: Constructions and combinatorial problems in design of experiments" (corrected reprint of the 1971 Wiley ed.). New York
Comment: yeah, there is also 'Algebraic Design Theory' by Warwick de Launey & Dane Flannery, and 'Permutation groups and combinatorial structures' by Norman Biggs,and since im more in algebra, i will read those book after i finish reading design theory by hughes, anyway thank you for the references!

Reference for Book Design Theory


Received a traffic violation notice in the mail

Question: I live in Illinois. I received a violation from Tollroads.com. I havent driven my car in the state of California. I was on a flight from Brussels to Chicago on the day of the violation.What should I do?
Comment: Please post a scan of the document(s) you received, with your personal data blanked out. As Michael Hampton correctly observes, the URL is not assigned, so there's no actual website at that address. What you received is almost certainly seeking personal information from you via phishing.
Comment: That isn't a real web site. What exactly did you receive?
Comment: Does the notice show a photograph of the vehicle and licence plate, and state it too? In the UK, ownership data is not in the public domain. There is also a possibility of mis-reading the plate. In the pre-tech days I received a real parking violation notice from a town I had never visited. After being stone-walled it turned out the offending car was a different colour, and even then they accused me of re-spraying it. It took sending a copy of the documents to get it cancelled.
Comment: Just how is this a travel question within the scope defined in the [help]?
Answer: The official website of the California Toll Roads is https://thetollroads.com/ (note "the").  There you can verify if the notice is genuine, and if it is, there should be an option to appeal or contest it.
You should carefully check their information about the car involved in the violation; it could be a mistake, or (less likely) that somebody has a fake license plate that matches yours.  In the latter case you may also want to report it to the police.


If the user needs credits to buy stickers/emoticons should the credit no. avail always be visible?

Question: I'm working on an app that allows the single purchase of stickers, not just sticker packs.
This means we need to user a credit system for the sticker purchase since you can't have in app purchases that are lower than $0.99.
The client thinks it's a good idea to have a status bar always displaying the number of credits available.
I think we shouldn't always display to the user how much they're "spending", and that this will make them use credits freely, without thought.
I can't find any research on the subject, so i'm wondering if anyone has any links to research of has an opinion for/against?
Cheers!
Comment: So your question is - should you trick people into spending money they don't have?
Comment: Meaning no disrespect, your stated goal seems a bit shady to me.  The user should know what their current balance is, and what it will cost them, every time they're about to make a purchase or microtransaction.  To do anything else is a blatant abuse of user trust.
Comment: I guess I was misunderstood. I would NOT want to deceive users. If they bought credits they already spent the money. It's not making them spend anything that's not already out of pocket. I do not want to trick people into purchasing something they don't want. I just don't want to obstruct and occlude from the main purpose which is to quickly purchase a single sticker and move on. Like you said - if someone wants to buy something they will, no matter how much it costs. I originally suggested having the credit balance on a different page (like apps such as skype do), as some of you said.
Answer: I tried to do a little research for you as well, but didn't come across anything definite. However, after looking at a number of other apps for phones where purchases are made it seems that they tend to have a separate page where you can check your current "credits" and purchase more if needed. This might prove sufficient for both you and your client. As you won't see your "spending" on each page but rather only if you navigate to it. So they won't be inclined to spend less based on what they are seeing from the "status bar" that the client wanted.
  Just an idea, hope it helps.
Answer: I think you can look at anything in the Envato ecosystem for the best practice on this. Not having enough credits isn't going to stop a user from buying something they want, so I actually think you're approaching conversion from the wrong end.
The goal isn't to trick the user into spending more money, it's to convince them that they should do so in the first place.
Show them their credits, that's normal. Make them easy to add and provide excellent teaser cotnent. The rest should take care of itself.
Answer: I would suggest showing the balance. When people purchase an app in the first place they are willing to spend money which should already be an indicator that they will spend again. Keep a credit balance, maybe have the credit be different from the amount of money its worth depending on the purchase price of the lowest priced sticker. The customer will feel like they can afford the cheapest so its worthwhile and then splurge if they want better. Easy Peezy!