Just once switched to OpenGL rendering, but after that changing to Blender Render or Cycles really doesn't help. Even after quitting Blender and then re-starting it and reopening the scene, it's still rendering with OpenGL.  What could possibly go wrong?   Here's my file
Blender is rendering an older version of my project, not the most recent one. I have made it using the Blender Render but it does not want to render in cycles either. A black and grey screen is rendered as if everything is transparent. Checked general camera, lighting and compute devises in case I messed something up but I can't find anything. All my textures and objects look normal, does anybody know what is wrong or what to check?  Ok added link:
I am wondering if my proof is correct? Thank you for whoever willing to take a look at it for me.     Proof $\liminf E_k \subset \limsup E_k $   If $\{E_k\}_{k=1}^\infty$ is a sequence of sets, we define \begin{align*} \limsup E_k &amp; = \bigcap_{j=1}^\infty\left(\bigcup_{k=j}^\infty E_k\right)\\ &amp;= \bigcap_{j=1}^\infty(E_j \cup E_{j+1} \cup \cdots)\\ &amp;= (E_1 \cup E_2 \cup \cdots) \cap (E_2 \cup E_3 \cup \cdots) \cap \cdots. \end{align*}  Therefore, $\limsup E_k$ consists of those points in $\mathbb{R}^n$ which belong to infinitely many $E_k$. \begin{align*} \liminf E_k &amp; = \bigcup_{j=1}^\infty\left(\bigcap_{k=j}^\infty E_k\right)\\ &amp;= \bigcup_{j=1}^\infty(E_j \cap E_{j+1} \cap \cdots)\\ &amp;= (E_1 \cap E_2 \cap \cdots) \cup (E_2 \cap E_3 \cap \cdots) \cup \cdots. \end{align*} Therefore, $\liminf E_k$ consists of those points in $\mathbb{R}^n$ which belong to all $E_k$ for $k \geq k_0$.  Now consider $x \in \liminf E_k$, then $x \in E_1 \cap E_2 \cap \cdots$, or $x \in E_2 \cap E_3 \cap \cdots$ and so on, that is to say, $x \in E_{k_0} \cup E_{k_0+1} \cup \dots$ for some $k_0$. More specifically, $x \in E_k \forall k \geq k_0$. Therefore, $x \in (E_1 \cup E_2 \cup \cdots) \cap (E_2 \cup E_3 \cup \cdots) \cap \cdots$, so we showed $x \in \limsup E_k$. Setting Zero values back to NULL Can I nohup/screen an already-started process? I'm doing some test-runs of long-running data migration scripts, over SSH. Let's say I start running a script around 4 PM; now, 6 PM rolls around, and I'm cursing myself for not doing this all in screen.  Is there any way to "retroactively" nohup a process, or do I need to leave my computer online all night? If it's not possible to attach screen to/nohup a process I've already started, then why? Something to do with how parent/child proceses interact? (I won't accept a "no" answer that doesn't at least address the question of 'why' -- sorry ;) ) Let $n$ is a natural number. Prove that $$\left\lfloor\frac{n}{1}\right\rfloor+\left\lfloor\frac{n}{2}\right\rfloor+....+\left\lfloor\frac{n}{n}\right\rfloor+\left\lfloor{\sqrt{n}}\right\rfloor$$   is even.   I used induction and the inequality $$x-1&lt;\lfloor{x}\rfloor\le{x}$$ to prove it.  Is there any other, nicer way to do it? If Steve Rogers wasn't so weak, could Cap be even stronger? Can a lingering injury that requires "magical healing of 6th level or higher" be healed by an upcast lower-level spell? The  table in the DMG (p. 272) contains some wounds that can only be fixed by powerful healing magic, for instance:     Horrible Scar. You are disfigured to the extent that the wound cannot be easily concealed. You have disadvantage on Charisma (Persuasion) checks and advantage on Charisma (Intimidation) checks. Magical healing of 6th level or higher, such as heal and regenerate, removes the injury.   Can the necessary magical healing described here be a lower-level spell (such as cure wounds) that is upcast to 6th level? Or must it be a healing spell that is already 6th level or above before upcasting? Ignore python multiple return value Proof of relation between divided difference and interpolation polynomial coefficient Given data points $\{(x_i,f(x_i)\}_{i=0}^{m}$, if we define divided difference recursively as: $$f[x_0,\cdots,x_{k+1}] = \frac{f[x_1,\cdots,x_{k+1}]-f[x_0,\cdots,x_k]}{x_{k+1}-x_0} \text{ with the definition that} f[x_0] = f(x_0)$$ then it is true that the unique interpolating polynomial $L_m(x)$ of degree $m$ such that $L_m(x_i) = f(x_i)$ for all $i = 0\cdots m$ is given by: $$ L_m(x) = \sum_{k=0}^mf[x_0,\cdots,x_k]\omega_k(x), \text{ where } \omega_k(x) = \prod_{i=0}^{k-1}(x-x_i). $$ The question asks to show this. That is, show the coefficients of the interpolating polynomial of degree $m$ in the basis $\{\omega_k\}_{k=0}^{m}$ is exactly $a_k = f[x_0,\cdots,x_k]$, the divided differences. To tackle this problem, I've attempted to use induction. The base step is trivial as $a_0 = f(x_0)$, but I am stuck on the inductive step. I supposed the degree $m$ interpolating polynomial of some data $\{(x_i,f(x_i)\}_{i=0}^{m}$ is indeed given by: $$ L_m(x) = \sum_{k=0}^mf[x_0,\cdots,x_k]\omega_k(x) $$ and I want to argue that $L_{m+1}(x) = \sum_{k=0}^{m+1}f[x_0,\cdots,x_k]\omega_k(x)$ is the interpolating polynomial of degree $m+1$ interpolating $\{(x_i,f(x_i)\}_{i=0}^{m+1}$, with any additional point $(x_{m+1},f(x_{m+1}))$ added. Clearly, $L_{m+1}(x)$ interpolates $\{(x_i,f(x_i)\}_{i=0}^{m}$ by definition of the $\omega_k$'s, but I am stuck at showing $L_{m+1}(x_{m+1}) = f(x_{m+1})$. Hints will be extremely appreciated! Attributes from an hstore-column as separate columns in a view? Let's assume we have a table where it has two columns, one an ID and one an hstore column, which stores key/value pairs.  You could query that column as such:  SELECT name, attributes-&gt;'device' as device FROM products WHERE attributes-&gt;'edition'= 'ebook'   Can you create a view for this table where the keys/values appear as columns in the view instead of all in the hstore column?  Example: I have an hstore key where it might have the key of amenity.  I want to create a view showing the the ID and the amenity values in a new view. I'm trying to prove that $(ma, mb) = $|$m$|$(a, b)$ , where $(ma, mb)$ is the greatest common divisor between $ma$ and $mb$. My thoughts: If $(ma, mb) = d$ , then $d$|$ma$ and $d$|$mb$ → $d$|$max + mby$ → $d$|$m(ax+by)$. This implies that $d$|$m$ or $d$|$(ax+by)$. This is the same as  $d$|$m$ or $d$|$a$ and $d$|$b$, so $d$|$m$ or $d$|$(a,b)$. This is the same as $d$|$m|$ or $d|(a,b)$, so $d$|$|m|(a,b)$. I don't know what to do. Let     $$ \mathbb{Z}^{'}_{\mathbb{C}}=\{ z \in \mathbb{C} | \exists f \in \mathbb{Z}[X] \text{ monic such that } f(z)=0\} $$   be the integral closure of $ \mathbb{Z} $ in $ \mathbb{C} $. Prove that $ \mathbb{Z}^{'}_{\mathbb{C}} $ is not finitely generated as a $ \mathbb{Z} $-module.  My attempt: Suppose $ \mathbb{Z}^{'}_{\mathbb{C}}=\mathbb{Z}\alpha_{1}+...+\mathbb{Z}\alpha_{n} $ for some $ \{ \alpha_{i}\}_{i=\overline{1,n}} \subset \mathbb{Z}^{'}_{\mathbb{C}} $. I know that given $ \alpha , \beta \in \mathbb{Z}^{'}_{\mathbb{C}} $ with minimal polynomials of degrees $ m $ and $ n $ respectively, then we can construct a monic polynomial with integral coefficients $ P(z)=\prod(z-(\alpha_{i}+\beta_{j})) $ where $ \alpha_{i},\beta_{j} $ are the conjugates of $\alpha $ , $\beta $ and therefore the minimal polynomial of $ \alpha + \beta $ has degree $ \leq mn $.   I was thinking that then the degrees of the minimal polynomials of the elements of $ \mathbb{Z}\alpha_{1}+...\mathbb{Z}\alpha_{n} $ could be somehow bounded by a certain constant, whereas $ \mathbb{Z}^{'}_{\mathbb{C}}$ contains elements whose degrees of the minimal polynomials are arbitrarily large, take $ 2^{\frac{1}{n}} $ for example,$ n\geq 2$. I think this works when we are asked to prove that the set of all algebraic numbers $ \overline{\mathbb{Q}} $ is not a finitely dimensional $\mathbb{Q}$-vector space, but I don't know how to proceed in my case.  I would really appreciate any ideas, hints or solutions. Thank you very much! Around 3 months ago, I submitted a paper to a Math journal for peer-review through an online submission system. The same day I received in my e-mail an acknowledgement saying that the paper had been received.  The problem is that the status of the paper on the online submission system is still "Manuscript submitted".  I think this means that the paper has not even been assigned to an editor yet (once this happens, the editor will probably start looking for reviewers), but as far as I know submissions are assigned to editors within a few weeks (I once submitted a paper to another journal and when an editor had been assigned, the status on the online system changed to "Editor handles" or something like that).  I know that publishing is a long and complicated process and I'm not trying to rush anybody, but sometimes manuscripts are lost in the system. In fact, this has once happened to me, so I just want to make sure that the paper was not lost in the system.  Should I send an e-mail asking for the status of the paper?  PS: I think that, at the time of submitting the paper, I didn't choose any specific editor to submit the paper to. I connect my phone to a Bluetooth speaker to play music. When engage Siri or try to use dictation, the phone wants to use the microphone on the Bluetooth device, which is either too crappy or too far away for it to understand what I am saying.  So, I would like a way to restrict the iPhone to using its own microphone even when connected to a Bluetooth speaker.  I am open to doing this via a setting, buying an app, or jailbreaking or whatever.  Is there a way to do this? How do I determine the size of an object in Python? In the various Zelda video games, there seems to be a common mythology, and at least some potential to be in the same place. Do the various Zelda games take place in the same world, or is there no intent to do so? Does the Rule of Two Serve any Actual Purpose? I know Darth Bane came up with the Rule of Two to ensure the survival of the Sith, but, in reality (or in the Star Wars reality), does it (or any Sith rule) serve a true purpose?  And why does each successive Sith bother with it?  Due to the nature of the Sith, Sith Lords tend toward arrogance and self-importance.  Both the Sith master and Sith apprentice seem to regularly break the rule by training others.  Deceit and personal interest over loyalty is a way of life for the Sith.  What is to keep any Sith from following the Rule of Two (or any rule, for that matter) if it is against their own self interest?  If a Sith Master can stay in power longer by training a 2nd apprentice and pitting the two against each other, is he really going to worry about the Rule of Two more than his own plans and survival?  The Rule of Two also assumes that every Sith Master would place the survival of the Sith over his own survival, as opposed to attempting to ensure his own immortality in whatever way he could (like Plagueis).  When you have a group that, by default, is arrogant and self-serving, as well as deceptive, why would they want the Sith to survive themselves?  I can see how the Rule of Two, and any other Sith beliefs would be possible guidelines, but it terms of the nature of ambitious people (and the Sith are ambitious), it's hard to believe that each new Sith Master would follow this rule faithfully.  So does this rule, or any Sith rule, actually work?  Or is it more of a suggestion that is broken when convenient? Find four groups of order 20 not isomorphic to each other. How can I get a pure white background in jewelry photography, without losing sparkle and shine? I've read through several threads similar to this, but I'm looking for a comparison of two options here.   I currently take photos on a raised glass platform against a white foam board background and run about 300w of lights (3 100x LEDs @ 5000k, Home Depot Specials in softboxes and umbrellas). As you can imagine, it takes me about 15 minutes of post processing to achieve a perfect white background, and sometimes I have a particular photo that I am unable to get there.  I want to upgrade to either a photography table with a translucent background that I can place a speedlight under, or a cyclorama infinity background such as the MyStudio MS20. The latter option may require an upgrade to my lighting, which I am planning to do anyways.  The idea of course is to get a blown out 255 background with no post processing, other than color correction on the jewelry or product as needed. This would cut my time after the shoot to a ridiculously small amount of time.   Which option would make my life easier?   For reference, I currently use a D5300 with a Tamron 90mm f2.8 macro lens.  This is the best shot I got after quite a lot of effort, before and after processing:      Note that the silver is not shiny like it should be, and the sparkle on the gems is lost. What is the difference between a desktop environment and a window manager? I'm having a really hard time trying to understand what the differences between a desktop environment and a window manager are?  EDIT: From this :  There are basically three layers that can be included in the Linux desktop: X Windows – This is the foundation that allows for graphic elements to be drawn on the display.  builds the primitive framework that allows moving of windows, interactions with keyboard and mouse, and draws windows. This is required for any graphical desktop. Window Manager – The Window Manager is the piece of the puzzle that controls the placement and appearance of windows. Window Managers include: , , , , , etc. Requires X Windows but not a desktop environment. Desktop Environment – This is where it begins to get a little fuzzy for some. A Desktop Environment includes a Window Manager but builds upon it. The Desktop Environment typically is a far more fully integrated system than a Window Manager. Requires both X Windows and a Window Manager.  Examples of desktop environments are , , ,  among others) Get lists of dependent picklist options in Apex I have a pair of dependent picklists.  In Apex code, how can I determine what options are valid in the dependent field for each option in the controlling field?  I've tried using getPicklistValues(), but there doesn't seem to be any way of getting dependency information.  Example  Controlling_Field__c  Fruit, Vegetable, Dairy  Dependent_Field__c  (Fruit): Apple, Banana, Pear  (Vegetable): Tomato, Egglant, Lettuce  (Dairy): Milk, Cheese, Yogurt  What I'm Looking For  (In pseudocode, something like:)  controllingOptions = dependentfield.getPicklistValues(); for (option : controllingOptions) {     dependentOptions = dependentfield.getPicklistValuesFor(option);     do_something_with_it(); }