A continues non-increasing function satisfying $f(x)\leq f(2x)$ for all $0\leq x$
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
PDOException when creating the table: Base table or view not found I have Drupal running on MariaDB 5.5.33. When I run update.php (after upgrade to Drupal 7.28 from Drupal 6) I get an error:     Failed: PDOException: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'webdb.location_country' doesn't exist: CREATE TABLE {location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter ISO Country Code', name VARCHAR(255) NOT NULL DEFAULT '' COMMENT 'Full Country Name ', PRIMARY KEY (code) ) ENGINE = InnoDB DEFAULT CHARACTER SET utf8 COMMENT 'Country data managed by location.module.'; Array ( ) indb_create_table() (line 2720 of /home/web/public_html/includes/database/database.inc).   When I try to run command     CREATE TABLE {location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter ISO Country Code', name VARCHAR(255) NOT NULL DEFAULT '' COMMENT 'Full Country Name ', PRIMARY KEY (code) ) ENGINE = InnoDB DEFAULT CHARACTER SET utf8 COMMENT 'Country data managed by location.module.';   in phpMyAdmin I get an error     #1064 - You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near '{location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter IS' at line 1   But I wasn't able to find out where is the problem. How can I launch a GameObject at a target if I am given everything except for its launch angle? I am trying to launch an object at a target, given its position, its target position, the launch speed, and the gravity.  I am following this formula from :  $$ \theta = arctan \bigg( \frac{v^2 \pm \sqrt{v^4-g(gx^2 + 2yv^2)}}{gx} \bigg) $$  I have simplified the code to the best of my ability, but I still cannot consistently hit the target.  I am only considering the taller trajectory, of the two available from the +- choice in the formula.  Does anyone know what I am doing wrong?  using UnityEngine;  public class Launcher : MonoBehaviour {     public float speed = 10.0f;      void Start()     {         Launch(GameObject.Find("Target").transform);     }      public void Launch(Transform target)     {         float angle = GetAngle(transform.position, target.position, speed, -Physics2D.gravity.y);         var forceToAdd = new Vector2(Mathf.Cos(angle), Mathf.Sin(angle)) * speed;         GetComponent&lt;Rigidbody2D&gt;().AddForce(forceToAdd, ForceMode2D.Impulse);     }      private float GetAngle(Vector2 origin, Vector2 destination, float speed, float gravity)     {         float angle = 0.0f;          //Labeling variables to match formula         float x = Mathf.Abs(destination.x - origin.x);         float y = Mathf.Abs(destination.y - origin.y);         float v = speed;         float g = gravity;          //Formula seen above         float valueToBeSquareRooted = Mathf.Pow(v, 4) - g * (g * Mathf.Pow(x, 2) + 2 * y * Mathf.Pow(v, 2));         if (valueToBeSquareRooted &gt;= 0)         {             angle = Mathf.Atan((Mathf.Pow(v, 2) + Mathf.Sqrt(valueToBeSquareRooted)) / g * x);         }         else         {             //Destination is out of range         }          return angle;     } } An acquaintance recently posted an image to FB from his recent trip to the JFK Historic Site asking for an explanation of a visible artifact he states was not visible to the naked eye but was visible through the EVF of his camera and in the final image.    The artifact is a series of bright, nearly-vertical bars and a longer, almost horizontal bar superimposed over the lower part of the door frame and the radiator.  I found a very similar artifact in another image of the same room from a blogger which isn't as compressed:    In both cases the artifact seems to be a vertically inverted image of the post and rail outside the saturated window.  From looking at other images of the room available online I know there is spherical glass ornament topping the table lamp whose shape is visible at the left of the photo.  One response to the OP's question is as follows:     RK: It is lens flare. So, even on an iPhone, the camera lens is made   up of multiple lenses. Each designed to focus the image and make sure   it isn't distorted. Remember a lens bends light.  Sometimes, based on   angle and intensity of the incoming light, some stray light bounces   back and forth while traveling through the various elements that make   up what we think of as a camera lens (some of mine have 16 elements   inside a single lens.) Even the best glass is capable of reflecting   some light instead of passing it through the lens elements to the   sensor.  This is what you are seeing. The railing is overexposed, and   some stray light is bouncing around a bit inside the lens.   My response:     DJ: I don't think it's lens flare or ghosting. Those usually form an   image of starbursts, rings, or circles in a row across the image or in   the shape of the aperture; or a veiling glare or haze. This is forming   an image of the light outside minus objects in its path. It is more   likely a direct reflection/projection off a mirror or the glass in a   picture frame elsewhere in the room onto the opposite wall and the   radiator. There are two other clues which seem to confirm this. First,   the image has a gradiated appearance, it is less distinct in the   relatively bright area on the door frame and brighter in the   relatively darker areas behind and on the radiator. You would expect   lens flare to be more evenly specular. Second, the image representing   the light from below the horizontal rail changes angle on the   different faces of the door frame. Unlike a projection, lens flare is   an image created within the lens, the physical shape of the objects it   superimposes do not change its shape.      OP: If that were the case, would I have been able to see said   reflection in the room without the camera? There was no image I could   see with the naked eye. I notice the image in my phone before I took   the pic and did a double, triple and quadruple take before I took it   so I'm sure.      DJ: It would have been visible at the moment the image was taken, but   it may not have appeared nearly as bright and distinct because your   eyes were accommodating for the bright light coming in the window. The   projection could have easily been obscured by you or anyone around you   changing position or moving through the path of the projected   reflection. Also, it's been caught by other people... (see Image 2)   Notice that, in the linked example, the projection is again distorted   by the surface it falls on.   Anyone else want to chime in with an explanation? A friend recently got her ID stolen while she was in the Netherlands. She will soon need to fly to her home country Italy, but she doesn't know what to do.  What can one do in such a situation? As far as I know, since it's Schengen, you don't need an ID card to go through borders. On the other hand, this is air travel, so they always require it for security reasons.   Can she show another document that proves her nationality? A copy of the ID card? Anything? I would like to get an alert (with sound) when my laptop battery is fully charged.  How can I do that? reflecting direct light on glossy surface in Cycles Working in Cycles.  Say I have a "disco ball" with a glossy shader. I'm pointing a spot light to it, and I'm trying to have the reflections of that light illuminate the diffuse material on the walls with the patterns from the ball.    I get this:    but I'd like to get something like:    For the illustration I placed a point light inside the ball an removed faces. But what I'd like to do is move the light around the ball so that the light reflected from it changes like it would do in real life.   Is that possible at this point?  EDIT:  Just for the record here's the image rendered in LuxRender (yet another program to learn...) SEO in Stack Overflow We've been out of private beta for only two days, and stackoverflow.com is already ranking high in .  Are there any specific techniques applied in the site? I've been researching the subject for some time and haven't found it to be so easy.   even returns site-links.  () Entering U.S. exactly on the day of visa "expiration date" I want to know by an example how prices in stock market changes Let us assume there is a listed company x. Currently it has 100 shares issued to trade in free float market. Current price of stock is let say 10. Now please let me know if I purchase one share of company x at the market price of 10. How it will effect the stock price. And please add and exemplify some other scenarios whichever you find good to explain more. For more information let say promoters of the company holds 100 shares with them like 50% of the company is with promoters and the other half is with people who invest or trade in that company. If I've missed to tell or assume any other vital info. needed please assume it yourself while mentioning it. Thank You How to automatically hyphenate within \texttt? This question was phrased as a bug report for LaTeX and I thought it would be helpful to be presented here (including an answer).  The person had a lot of "common words" in typewriter font sprinkled around his text and he was surprised that this text would not automatically hyphenate and he had to manually insert \- to mark hypenation points. Automorphisms of the complex plane How can it be shown that $$Aut(\mathbb{C})=\{f|f(z)=az+b,a\neq 0\},$$ where an automorphism of $\mathbb{C}$ is defined as a bijective entire function with entire inverse?  If $f$ is of the form $f(z)=az+b$, with $a\neq 0$, then obviously $f$ is in $Aut(\mathbb{C})$. How can I prove the converse? I have the following reference:  @MISC{EX2012,   author = {{S}ingle {A}uthor {O}rganization},   year = {2012},   title = {Example} }   A citation for this is breaking after "Author", but extending beyond the margin, as shown in the following example layout in the PDF:  Demo text demo text demo to margin Demo text which cites it (Single Author Organization, 2012) and flows over the margin.   How can I solve this? I am using natbib and citing with \citep{EX2012}. Singular verb after two noun phrases joined by "and" that can be thought of as a single thing I am having trouble with the following sentence:      "The complexity and diversity of the new platforms is worrying us."   If "complexity" and "diversity" constitute two subjects, then the verb should presumably be "are"; however, the sentence feels more natural with "is". Is this correct? Is there a linguistic term for this occurrence?    The following questions address the general topic of compound subjects, but not specific cases like this:             And the following question seems to have somewhat inconclusive answers:         So this question is not really a duplicate of these three. How is Leibniz's rule for the derivative of a product related to the binomial formula? Possible Duplicate:          The  describes the expansion of the $n$th power of the sum $(a+b)$:  $$(a+b)^n = \sum_{k = 0}^n {n\choose k}a^kb^{n-k}$$  In calculus, there is a generalization of the product rule called , which describes the expansion of the $n$th derivative of the product of two functions $f$ and $g$:  $$(fg)^{(n)} = \sum_{k = 0}^n {n\choose k}f^{(k)}g^{(n-k)}$$  It's not difficult to prove using the product rule and induction, what I'm really trying understand here is why the formula is true. Is there a way to prove it using the binomial formula? How are these two formulas related? Is there a combinatorial proof for Leibniz's rule like there is for the ?   I understand this question is a bit vague, but I hope you'll agree that these two formulas look so similar it just feels like there should be some relation between the two. Of course this is not necessarily true, but I'm hoping it's not just a crazy coincidence. How can I access the apache basic-auth username in a PHP script? Prove that a finite union of closed sets is also closed Terminating with Master's after several years in a PhD program. How to indicate on CV/Resume? I am not happy with my PhD program, and after several years I am graduating with a master's this month. I earned the M.S. along the way as a PhD student, but have never formally requested it before this semester. What is the best way to indicate this situation on a CV or resume? I don't want to put just M.S. because then it looks like it took me a really long time to get a master's and I can't put that I am a PhD student because I no longer am.  Right now, I am thinking something like  M.S. in &lt;field&gt;, &lt;University&gt;, May 2016 PhD student in &lt;field&gt;, &lt;University&gt;, Aug. 2011 - May 2016 B.S. in &lt;field&gt;, &lt;Undergrad University&gt;, Aug. 2007 - May 2011   Would that be clear what's going on? Alternatively, should I list PhD above M.S. even though I didn't complete it? Should I list both M.S. and PhD in same line since it is the same university and span of time? Control Cycles/Eevee material nodes and material properties using python? Get current URL with jQuery? I am using jQuery. How do I get the path of the current URL and assign it to a variable?  Example URL:  http://localhost/menuname.de?foo=bar&amp;amp;number=0 How can a single Curve Interpolation Mode set to Constant?