Using the substitution method on $p(n)=\sqrt{n}p(\sqrt{n})+\sqrt{n}$
Solving the recurrence $T(n) = \sqrt n T(\sqrt{n}) + \sqrt{n}$
Why rationalize the denominator? sObject ' ' type is not supported Hey everyone I've been seeing this a lot lately and am trying to figure out why this error is thrown when querying the SOAP API directly. I've tried several very basic SOQL queries such as  SELECT Body FROM AssetFeed   Only to be met with the sObject type 'AssetFeed' is not supported. error.  The account that I'm currently querying is just a standard user who accepted permission from an app that was created by a Developer Account, so I'm wondering if it might be permissions from the user or permission from the app itself? Possibly because Developer accounts cannot use 95% of whats offered?  The WSDL used is a v27.0 generated Partner WSDL if that helps narrow it down.  I've noticed this in multiple standard objects, so I'm wondering what the trend really is? Seems like a good informational question for future googling of others?  Running describeGlobal()  Array (     [0] =&gt; AggregateResult     [1] =&gt; Attachment     [2] =&gt; ChatterActivity     [3] =&gt; CollaborationGroup     [4] =&gt; CollaborationGroupFeed     [5] =&gt; CollaborationGroupMember     [6] =&gt; CollaborationGroupMemberRequest     [7] =&gt; CollaborationInvitation     [8] =&gt; ContentDocument     [9] =&gt; ContentDocumentFeed     [10] =&gt; ContentDocumentHistory     [11] =&gt; ContentDocumentLink     [12] =&gt; ContentVersion     [13] =&gt; ContentVersionHistory     [14] =&gt; EntitySubscription     [15] =&gt; FeedComment     [16] =&gt; FeedItem     [17] =&gt; FeedLike     [18] =&gt; FeedTrackedChange     [19] =&gt; Group     [20] =&gt; GroupMember     [21] =&gt; HashtagDefinition     [22] =&gt; Name     [23] =&gt; TaskPriority     [24] =&gt; TaskStatus     [25] =&gt; User     [26] =&gt; UserFeed     [27] =&gt; UserPreference     [28] =&gt; UserRecordAccess     [29] =&gt; UserRole )   Where would all the rest of my SOAP SObjects be? This seems like a very thin list compared to the 295 SObjects advertised How to link to apps on the app store I am creating a free version of my iPhone game. I want to have a button inside the free version that takes people to the paid version in the app store. If I use a standard link    the iPhone opens Safari first, and then the app store. I have used other apps that open the app store directly, so I know it is possible.  Any ideas? What is the URL Scheme for the app store? Do immature fruits perform photosynthesis? Most immature fruits are green: peppers, pine cones, plums, lots of them. I want to know if the green is from chlorophyll in the cells. Do the fruit cells perform photosynthesis? When you cover a green stem or leaf, it will turn pale and stretch. That is because the stems have little need for chlorophyll in the dark, which is why they are pale. They stretch because the auxins in the stems are not destroyed by the photons, and the stems stretch out and topple over. If a green fruit is covered, will it turn pale and stretch like that? Should I flag obviously wrong answers as NAA? Where can I get freely available audio, graphics, and other resources for games? Getting higher power output by using more resistors URL Rewriting of a query string in php First of all, am I being crazy in thinking that if $\lambda$ is an eigenvalue of $AB$, where $A$ and $B$ are both $N \times N$ matrices (not necessarily invertible), then $\lambda$ is also an eigenvalue of $BA$?  If it's not true, then under what conditions is it true or not true?  If it is true, can anyone point me to a citation?  I couldn't find it in a quick perusal of Horn &amp; Johnson.  I have seen a couple proofs that the characteristic polynomial of $AB$ is equal to the characteristic polynomial of $BA$, but none with any citations.  A trivial proof would be OK, but a citation is better. Let $A \in {M_n}$ is nonsingular and each eigenvalue of $A$ is either $+1$ or $-1$.Why $A$ is similar to ${A^{ - 1}}$? Mysterious Windows 7 Autorun Location I have Acer Aspire One A521 with brand new SSD disk, on which I've just installed brand new Windows 7 HE 64. After installing system I installed all drivers, including Conexant audio driver. Starting from that moment, after each system restart I see Windows prompt asking me, if I really want to run application C:\Program Files\CONEXANT\cAudioFilterAgent\cAudioFilterAgent64.exe.  Situation like that is quite normal to me, and I always use some "startup scanner" to find such software and purge system out of it. I have very, very old Startup Control Panel 2.8 by Mike Lin. It can have even ten years, but it has never disappointed me, so I continue using it. It scans Startup folders for current user and common one, HKLM Run, HKCU Run and Run Once sections of Windows Registry. For past ten years I thought that these are all locations where application, that is being autorun during system startup can coexist. Turns out, I was wrong.  Since this is brand new Windows, just installed, its autorun locations are empty. The only entry I do have is ATI graphic card driver manager startup string in HKLM Run. I have checked that fact ten times (but only with above mentioned program and manually) and I'm 100% sure, that in none of known to me autorun locations there are no traces of Conexant program startup string.  What do I miss? Does Windows 7 introduces some new startup location or a new method of autorunning programs, that is beyond, what I know and what Startup Control Panel scans?  Solving this problem is a snap for me. I can use brute-force method of removing manually that file or renaming it or I can uninstall Conexant audio driver at all (for the very, very limited use of audio in my laptop, that I have, Windows driver will for sure be enough, I've installed Conexant one "just in case"). But I'm really, really curious, how Windows is possible to run this program each time I restart it? Where autorun string for it can exists? How do I reset my Unity configuration? I've been messing around with Unity and broke something, how do I "start over"? What is the isomorphism between the fields $(Z_2[x]^{<3},+_{x^3+x^2+1},\times_{x^3+x^2+1})$ and $(Z_2[x]^{<3},+_{x^3+x+1},\times_{x^3+x+1})$? Where to find the checksums of Ubuntu ISO images? I just downloaded the ubuntu-10.10-desktop-i386.iso, and am having a hard time burning it, so I'd like to check that the file is intact, but I cannot find the md5sum of the file.    Is there a URL or official FTP mirror which includes the md5sum of the Ubuntu disk images? Zorn's Lemma states that if every chain $C$ in a partially ordered set $X$ has an upper bound then there is at least one maximal element in $X$.  Let $n\in \mathbb{N}$, $C_n \subset \mathbb{N}$ be the set containing the natural numbers $\{1,\dots,n\}$. Then if $k\le n$, $C_k\subset C_n$, so $C_n$ is a chain. Also, $C_n$ has an upper bound, such as $n+1$. But what is the maximal element of $\mathbb{N}$?  There's something I don't get in Zorn's Lemma statement. Where are the evolutionary "inbetweeners"? The problem I've always had with evolution is the actual lack of variation between animals. More specifically, the lack of observable gradual change between species.  Take for example the hammerhead shark. It obviously has a strong connection with a normal shark, but where's the "half-hammerhead" shark? Where's the species that only has a SLIGHTLY wider head?  I really doubt that a single mutation on a normal shark resulted in a head shaped like that, it had to happen gradually. Right? As far as I understand, evolution works by random mutation in a child being somehow slightly beneficial to that animal so it get's to live longer and reproduce more, eventually resulting in it's genetic material in dominating the inferior ones before it. But if it was for whatever reason beneficial to have a slightly wider head, why don't all the sharks have slightly wider heads now? On the other hand, if it wasn't beneficial, how come the hammerhead still exists?  Furthermore, I feel like some characteristics of a certain animal can't really have gradual benefits. There's a lizard that shoots blood out of it's eyes. The original ancestor certainly didn't, and I'm sure that if it's child only bled slightly from it's eyes it wouldn't really help if much in life. So for it to actually become beneficial, it seems to me that there had to be a ton of lizards that had a disadvantage of bleeding slightly. In fact, there had to be so many that they evolved even further in the same direction and kept doing that until they bled so much it's an actual benefit (sorry for this turning so gross). So why did the inbetweeners survive long enough to evolve even more, and why did they THEN die out? There are $25$ horses. You can take $5$ horses at a time and race them. Each horse always finishes the race in the same amount of time, and there are no ties. The only information you get from each race is the order that the $5$ horses finished in. What is the smallest number of races you need to find the $3$ fastest horses, in order?   I found this problem on  and cannot figure out the best answer. Please help. How to return only the Date from a SQL Server DateTime datatype When/Why Did Love Escape Voldemort? We know that Voldemort does not love. He does not understand it, nor (generally) the magic that it possesses. He knows  of the sort.  [...] &quot;you possess in such quantities and which Voldemort has not at all.&quot; [...] &quot;because he could not bear to reside in a body so full of the force he detests. In the end, it mattered not that you could not close your mind. It was your heart that saved you.&quot; (Harry Potter and the Order of the Phoenix, page 1075)  The above confirms it (although I believe there is a better quote), though  reinforces it. The fact that he hugs so awkwardly shows that he does not really know how, due to his lack of love. I realize that Voldemort's appearance started to change after he started to create Horcruxes, but surely he had an ounce of love when he was a child? The hugging scene perhaps shows that he never once loved his whole life (possibly due to the love potion with his parents?). If so, when did Voldemort begin to have no love at all, and why? How can I obtain a Cauchy distribution from two standard normal distributions? I am interested in      Let $X\sim N(0,1), Y \sim N(0,1)$ independently. Show $\frac{X}{X+Y}$   is a Cauchy random variable.   My work:  $f_{X,Y}(x,y)=\frac{1}{2\pi} e^{\frac{-1}{2}(x^2+y^2)}, -\infty&lt;x,y&lt;\infty$ by independence  Let $U=\frac{X}{X+Y},V=X+Y$. (Is there a better $V$ to choose for this bivariate transformation?)  Then, $X=UV, Y=V - UV$. So, $|J|=V$.  $f_{U,V}(u,v)=f_{X,Y}(uv,v-uv)|J|=\frac{v}{2\pi}e^{\frac{-v^2}{2}(2u^2-2u+1)},-\infty&lt;u&lt;\infty$  $f_U(u)=\frac{1}{2\pi}\int_{-\infty}^{\infty}ve^{\frac{-v^2}{2}(2u^2-2u+1)}dv$. Let $y=\frac{v^2}{2}(2u^2-2u+1)$, so $dy=v(1+2u^2-2u)dv$. Then,  $f_U(u)=\frac{1}{2\pi(2u^2-2u+1)}\int_0^{\infty}e^{-y}dy=(\pi[(\frac{u-1/2}{2})^2+1])^{-1}, -\infty&lt;u&lt;\infty$,   which is not exactly a Cauchy distribution. Where did I mess up? More importantly, how would you proceed in solving this problem?