How to boot into Ubuntu?
Can't boot into Ubuntu in Windows 10 / Ubuntu dual boot
Laptop power supplies, does current matter? I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6&nbsp;V at 8.0&nbsp;A. The output on the second laptop's power supply is 15.6&nbsp;V at 5&nbsp;A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop? Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$ Evaluate $$\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$$   I tried to create a telescoping sum but I couldn't. The last step I could reach was turning the limit into $$\lim_{n\to \infty} \sum_{r=1}^n \left(\frac {1}{2^r(1-\tan (2^{-r+1})} -\frac {1}{2^r(1+\tan (2^{-r+1})}\right) $$  But couldn't proceed further. Also I thought about Riemann sums but it was a pure dead end.  Any help would be greatly appreciated Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal I want to find the rank of this $n\times n$ matrix \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; 1 &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; a &amp; 1 &amp; a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; a&amp; \ddots &amp; &amp; \vdots\\ \vdots &amp; \vdots &amp; \vdots &amp; &amp; \ddots &amp; \vdots \\ a &amp; a &amp; a &amp; \cdots  &amp;\cdots &amp; 1 \end{pmatrix}  that is, the matrix whose diagonals are $1's$ and $a$ otherwise, where $a$ is any real number.  My first observation is when $a=0$ the rank is $n$ and when $a=1$ the rank is $1.$ Then I can assume $a\neq 0, 1$ and proceed row reduction to find its pivot rows. I obtain  \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots  &amp; a \\ 0 &amp; 1+a &amp; a &amp; \cdots &amp; a \\ 0 &amp; a &amp; 1+a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ 0 &amp; a &amp; a &amp; \cdots  &amp; 1+a \end{pmatrix} by subtracting the first row multiplied $a$ for each row below the first, and then divides the factor $(1-a)$,  and stuck there. Any hints/helps? Input field value - remove leading zeros I have a textbox in Javascript. When I enter '0000.00' in the textbox, I want to know how to convert that to only having one leading zero, such as '0.00'. How to securely delete files stored on a SSD? While working in a Java app, I recently needed to assemble a comma-delimited list of values to pass to another web service without knowing how many elements there would be in advance. The best I could come up with off the top of my head was something like this:  public String appendWithDelimiter( String original, String addition, String delimiter ) {     if ( original.equals( "" ) ) {         return addition;     } else {         return original + delimiter + addition;     } }  String parameterString = ""; if ( condition ) parameterString = appendWithDelimiter( parameterString, "elementName", "," ); if ( anotherCondition ) parameterString = appendWithDelimiter( parameterString, "anotherElementName", "," );   I realize this isn't particularly efficient, since there are strings being created all over the place, but I was going for clarity more than optimization.  In Ruby, I can do something like this instead, which feels much more elegant:  parameterArray = []; parameterArray &lt;&lt; "elementName" if condition; parameterArray &lt;&lt; "anotherElementName" if anotherCondition; parameterString = parameterArray.join(",");   But since Java lacks a join command, I couldn't figure out anything equivalent.  So, what's the best way to do this in Java? Matrix Ring of a Semisimple Ring I recently read the concept of semi-simplicity of a (not necessarily commutative) ring.  A ring $R$ is said to be semi-simple if $R$ as a left module over itself is a semi-simple module (This in turn means that each submodule (i.e, left ideal) of $R$ is a direct summand for $R$.)  I am grappling with the following question:     If $R$ is semi-simple, then so is the matrix ring $M_n(R)$.   It is a theorem that each left module of a semi-simple ring is a semi-simple module. Thus $M_n(R)$ is a semi-simple module of $R$. But this doesn't help me.  I need to show that each left ideal of $M_n(R)$ is a direct summand for $M_n(R)$. Is there a characterization  of the left ideals of $M_n(R)$ in terms of the left ideals of $R$?  Lastly, does the converse also hold?     If $M_n(R)$ is a semi-simple ring, then is $R$ necessarily a semi-simple ring?   Thanks. An arithmetic function is defined as follows:$f(1)=1$,  $f(2k)=k$ and $f(2k+1)=f(k)+f(k+1)$. When (for which $k$) is $f(k)$ even?  While it is obvious that $f(4n-1)=f(4n)=2n$, therefore $f(k)$ is even for $k=4n$ and $k=4n-1$, which is possible to prove using induction (isn't it?), I don't know how to prove the converse.  I tried to solve the recurrence or make use of constant difference between certain elements of the sequence $\ldots$ What am I missing?  Thank you. How can I know if my macbook is hacked? what are the meanings of &quot;treated observation&quot; and &quot;non-treated observation&quot; in this context ?  Further, propensity score matching is a more robust method of matching that quantitative accounting researchers frequently use (Rosenbaum &amp; Rubin, 1983). With this technique, the researcher first estimates a logit or probit regression with the treatment effect as the dependent variable (i.e., S&amp;P 500 membership, continuing with our earlier example) and independent variables that are known determinants of the treatment (possibly economic performance, firm size, age, industry, etc. in our example). From this first-stage regression, the researcher obtains propensity scores. 6 The researcher then matches each treated observation to a non-treated observation based on the distance between their propensity scores (i.e., those observations with the closest propensity scores are matched). 7 Hoi et al. (2013) utilize propensity score matching in their study that links irresponsible CSR activities with tax aggressiveness. They first generate predicted propensity scores for each firm-year using a model of the determinants of a firm engaging in a high level of negative, irresponsible CSR activity. Then, they match a treatment firm (one with a high level of negative CSR activities) to a non-treatment firm (one with a low level of, or no, negative CSR activities) by matching observations with the closest propensity scores. Hoi et al. (2013) then re- test the relation between negative CSR activities and tax aggressiveness using this matched sample. These matching techniques help mitigate the researcher’s potential failure to consider certain firm characteristics that differ between treatment and non-treatment firms (Dhaliwal et al., 2012). how to replace multiple strings together in Oracle I have a string coming from a table like "can no pay{1},as your payment{2}due on {3}". I want to replace {1} with some value , {2} with some value and {3} with some value .  Is it Possible to replace all 3 in one replace function ? or is there any way I can directly write query and get replaced value ?   I want to replace these strings in Oracle stored procedure the original string is coming from one of my table I am just doing select on that table   and then I want to replace {1},{2},{3} values from that string to the other value that I have from another table Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent Let $X$ and $Y$ be independent random variables. Prove that $f(X)$ and $g(Y)$ are independent for any choice of measurable functions $f$ and $g$.   This sounds very obvious, but I have no idea how to approach it.  EDIT: Two random variables are independent if $\Pr\{X = x \text{ and } Y = y\} = \Pr\{X = x\} \cdot \Pr\{Y = y\}$ Click Answer your own question Check community wiki A dialog box     Are you sure you want to make this post Community Wiki?   will appear, Click OK or Cancel; The same dialog will appear again.   Google Chrome 44.0.2403.107 / Windows8.1 / site rev 2015.7.25.3609 What is the best way to convert seconds into (Hour:Minutes:Seconds:Milliseconds) time? What is the best way to convert seconds into (Hour:Minutes:Seconds:Milliseconds) time?  Let's say I have 80 seconds, are there any specialized classes/techniques in .NET that would allow me to convert those 80 seconds into (00h:00m:00s:00ms) format like to DateTime or something? How does a wheelie work? So I've been trying to create a mathematical model for an electric motorcycle and began to wonder about the maximum possible torque that could be supplied to the rear driven wheel without having the bike begin to lift up on one wheel.  I found ways to calculate this value online; however, the basic concept as to how the bike actually lifts escapes me.    My problem started when I began to think about what axis the bike will rotate about when it is doing the wheelie.  My first intuition was that the frame and front wheel, together, rotate about the rear axle.  But when I drew a free body diagram of the frame/front wheel system just at liftoff (see below) I made note that the only forces acting about the rear axle, point O, is the force of weight.  This means that an increase in applied torque and subsequently, the applied force Fa, should not effect the rotation about the rear axle.  I know that the applied force on the back wheel is indeed correlated with the propensity for a bike to wheelie, so I considered that the axis of rotation I was choosing was wrong.  If we take the free body diagram above and sum the moments about the center of mass, we would find that an increased applied force would in fact cause the solid body to rotate.  The problem with this understanding is that during rotation, the center of mass of the drawn system should actually rises relative to the surface the bike is moving across.  If the bike were to be truly rotating about its center of mass, then the back wheel would begin to dip below the surface of the road like you might see in a glitchy video game.    So I suspect that the bike is in fact rotating about the back axle, but I don't understand why, please help!  edit: I added the external torque from the back wheel to the frame, which would allow the bike to rotate about the back axle  edit 2:  I suppose that the torque acting on the frame via the engine should not effect the rotation as the movement of a motorcycle can be perfectly replicated by applying a force at the back axle.  A third possible axis of rotation might be the lowest point of the back wheel. I need to find a bottleneck and need to accurately as possible measure time.  Is the following code snippet the best way to measure the performance?  DateTime startTime = DateTime.Now;  // Some execution process  DateTime endTime = DateTime.Now; TimeSpan totalTimeTaken = endTime.Subtract(startTime); Right identity and Right inverse implies a group I am under DDoS. What can I do? How to make a "reflective tape" material in cycles? How can I make a cycles material that gets very bright when a light is shown on it, yet still has normal colors? I'm talking about the "" that can be seen on road signs, the tape on big trucks (like in the image below), traffic barricades and clothing.  Image by TollGroup on    This reflective stuff has a interesting property where the colors show up perfectly well, but when exposed to a light source they seem to reflect much more light the normal.  has lots of good reference images.  I have tried different combinations of glossy and diffuse shaders, but none work as I have yet to get the super bright reflections.  How can cycles make a material that reflects so much light, and keeps the colors correct? How to match all words of one column against words in another column?