Gifts to take from US to Sweden
What gifts would be welcome for a Swedish host family?
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$? I would like to prove inductively that $${2n\choose n}=\sum_{i=0}^n{n\choose i}^2.$$  I know a couple of non-inductive proofs, but I can't do it this way. The inductive step eludes me. I tried naively things like $${2n+2\choose n+1}={2n+2\over n+1}{2n+1\choose n}=2\cdot {2n+1\over n+1}{2n\choose n},$$  But I don't think it can lead me anywhere. I would like the proof to be as simple as possible. The proof I have starts of with $\;xy=0\;$ in a field.   Then $x^{-1}$ exists because it is a field.  Then $x^{-1} xy=x^{-1} 0$.  Therefore $y=0$.  But surely if an integral domain can not have any zero divisors, how can we end the proof by saying $y=0$? Surely then y is a zero divisor and hence the field is not an integral domain? How are second order nonlinear ordinary differential equations solved? Execute program from within a C program How should I run another program from within my C program? I need to be able to write data into STDIN of the launched program (and maybe read from it's STDOUT)  I am not sure if this is a standard C function. I need the solution that should work under Linux. Can the Next/Prev Post links be ordered by menu order or by a meta key? I have a series of posts that are ordered by a meta_key value. They could also be arranged by menu order, if necessary.  The next/prev post links (generated by next_post_link, previous_post_link, or posts_nav_link all navigate by chronology. While I understand this default behaviour, I don't understand how to change it. I found that it maps through to adjacent_post_link in link-template.php, but then it starts to seem fairly hard-coded. Is it recommended to re-write this from scratch to replace it, or is there a better solution. I bought a new SSD with 750 GB and made two partitions: 600 GB and 150 GB. The smaller one was thought to be a Bootcamp partition one day, but to date it was just another unused partition. When I needed more space, I decided to merge these two partitions. The partition was created with Mavericks, the merge was done with Yosemite.  I opened Disk Utility and the "minus" button. Disk Utility told me both partitions would be merged then. However it miserably failed. My main hard disc suddenly had errors which couldn't be repaired and even two of my other external hard discs could not be mounted any longer.  I eventually restored the hard disc from Time Machine, which worked well.  My second partition is now listed as free:    Unfortunately I can't resize the 600 GB partition nor can I create a new partition using the free space.  Diskutil reveils the following:  ~  diskutil list /dev/disk0    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *750.2 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:          Apple_CoreStorage                         599.6 GB   disk0s2    3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3 /dev/disk1    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:                  Apple_HFS Macintosh HD           *599.3 GB   disk1                                  Logical Volume on disk0s2                                  XXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX                                  Unencrypted   Also diskutil brought up this:  ~  diskutil cs list CoreStorage logical volume groups (1 found) | +-- Logical Volume Group 9D2BA4BA-xxxx-xxxx-xxxx-xxxxxxxxxxxx     =========================================================     Name:         Macintosh HD     Status:       Online     Size:         599640592384 B (599.6 GB)     Free Space:   6111232 B (6.1 MB)     |     +-&lt; Physical Volume 29A9A02B-xxxx-xxxx-xxxx-xxxxxxxxxxxx     |   ----------------------------------------------------     |   Index:    0     |   Disk:     disk0s2     |   Status:   Online     |   Size:     599640592384 B (599.6 GB)     |     +-&gt; Logical Volume Family 2FA7892F-xxxx-xxxx-xxxx-xxxxxxxxxxxx         ----------------------------------------------------------         Encryption Status:       Unlocked         Encryption Type:         None         Conversion Status:       NoConversion         Conversion Direction:    -none-         Has Encrypted Extents:   No         Fully Secure:            No         Passphrase Required:     No         |         +-&gt; Logical Volume 7BF42B7B-xxxx-xxxx-xxxx-xxxxxxxxxxxx             ---------------------------------------------------             Disk:                  disk1             Status:                Online             Size (Total):          599282155520 B (599.3 GB)             Conversion Progress:   -none-             Revertible:            No             LV Name:               Macintosh HD             Volume Name:           Macintosh HD             Content Hint:          Apple_HFS   I have tried this:    fsck -fy (The volume Macintosh HD appears to be OK.)   but it wouldn't help. It said I couldn't recover because it wasn't created in a way it would support (sorry for missing the exact message).  I then have learned that Apple_CoreStorage might indicate my disk is encrypted, which might explain why I can't resize it. It doesn't explain why I can't create a new partition to me.  What are my options to make my hard disk available in a single partition with size 750 GB? How do I create a very long delay with Redstone? The only things I've found so far are a cart method (which ceased working in 1.6), a dispenser method (utilizing the decay on dropped items, but this requires occasional feeding), and a binary counter (which won't work for a single input but rather a fluctuating one).  I want to have a circuit that when I apply an input signal, the output signal doesn't change for 2 to 5 minutes.  When the input turns off, I again want a 2 to 5 minute delay.  I could accomplish this with (roughly) 240 to 600 redstone repeaters, but this is far in excess of being useful.  The only method I can think of, but would require a XOR gate (on the button-input and final output) to start and stop a clock attached to a binary counter.  While I can make room for a device of this size, I was hoping for something simpler. Is there any standard notation for specifying dimension of a matrix after the matrix symbol? I want to explicitly specify dimension of matrices in some expressions, something like   $$\boldsymbol{A}_{m \times n} \boldsymbol{B}_{n \times m} = \boldsymbol{C}_{m \times m} \, .$$  Is there any more or less standard notation for this?    While this notation is generally unambiguous, I think it become ambiguous, for example, in the following case. Suppose that I have some column or row vector which is conjugate transpose of correspondingly row or column vector. If I write it in the following way  $$\boldsymbol{A}_{n \times 1}^{\dagger} \, ,$$ we can have 2 different interpretations:   matrix $\boldsymbol{A}_{n \times 1}$ is $n \times 1$ column vector and by $\boldsymbol{A}_{n \times 1}^{\dagger}$ I'm referring to its conjugate transpose which is $1 \times n$ row vector; matrix $\boldsymbol{A}_{n \times 1}^{\dagger}$ itself is $n \times 1$ column vector which is conjugate transpose of $1 \times n$ row vector $\boldsymbol{A}$. How Many Genius Mixes Are There in iTunes? "wait on" or "wait for"? Officials are waiting on autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin.   I am curious about the preposition on in the sentence, because I usually say "wait for" instead of "wait on". Does it still have the same meaning if I change on to for? Just as follows:     Officials are waiting for autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin. What corrections can you make on galley proofs? When I receive galley proofs of a paper, I look at possible errors introduced by the copy-editing team. But while I proofread the article, there are sometimes small mistakes I'd like to fix, which were not introduced by them (i.e. they were already present in the accepted version of the manuscript).  Usually, the proofs are accompanied by instructions saying that extensive changes should not be introduced at that time, and any such changes would have to be approved by the editor (hence, I suppose, delaying publication). However, the limit is not very clear to me. What is considered extensive changes? In particular, what do you think of the following items (from my experience):   Slight changes in wording, to improve clarity Updating a citation, because an “in press” or “ASAP” article now has page numbers Adding an important (but not crucial) citation one had missed, in the introduction Adding a citation to a paper that has been published since the manuscript was submitted; possibly adding a short sentence to the text     What I have done so far is change everything that I think should be changed to improve the paper (including all the above items), and let the typesetter decide whether he wanted to send it back to the editor. I never received any complaint or comment on my changes, which could indicate that it was the correct course of action. Possible to have the default landing page of my Sharepoint Site be an applicaiton page? So basically when someone goes to:   http://mysite.com   I would like to show an Application Page that I have created, without the giant URL.  Example of the giant URL :  http://mysite.com/_layouts/ap/myAppPage.aspx   Is there any way for me to do this? I know this, but I can't recollect at all.   What is this thing called?   They are usually centered in a book or writing and I'm certain they have a name but I can't remember for the life of me. They also come in all shapes, colors and sizes. Is it possible to generate transcendental numbers of arbitrary irrationality measure ? I am thinking of something like an infinite series which depends on a parameter fixing the irrationality measure.   All I have found so far is bounds on the irrationality measure of famous numbers, I have not been able to find something going the other way around. Show discontinuity of $\frac{xy}{x^2+y^2}$ Why is $1^{\infty}$ considered to be an indeterminate form Often, crontab scripts are not executed on schedule or as expected. There are numerous reasons for that:   wrong crontab notation permissions problem environment variables   This community wiki aims to aggregate the top reasons for crontab scripts not being executed as expected. Write each reason in a separate answer.  Please include one reason per answer - details about why it's not executed - and fix(es) for that one reason.  Please write only cron-specific issues, e.g. commands that execute as expected from the shell but execute erroneously by cron. How do I split a string so I can access item x? Need help recalling name of sci-if story about earth evolving into electronic life forms Read a story once about earth being abandoned for long periods of time. Upon the return of man to earth all life forms, flora and fauna, have evolved into intricate electronic forms of themselves.   Would like to find that story and it's name.