Recovering Corrupted M4a Recordings

This works but the values use in dd are not adequate for every case. Here the author of the original post explains why:

Original post of this solutionBasically you are stripping the header of the file by skipping 44 bytes with dd but that value varies from file to file, as it happened to me.The solution is to use a hex editor (I suggest on a copy of the broken file) and delete everything from the beginning up to the end of the word "mdat". In my case it was 28 bytes instead of 44.I use 0xED as a hex editor on mac (it's free and runs on the latest mac OS, Mojave, as of this writing). Also, for mac you can install faad using Homebrew by runningYou may need to specify the file sample rate if different from 44,100Hz when using faad with the switch -sIf faad returns this error Error: Maximum number of bitstream elements exceeded it could mean that you deleted too many bytes from the beginning of the file, as it happened to me at first.Lastly, once you process the raw file with faad you will want to reencode the m4a file to make sure you have a proper and compatible file, this can easily be done with ffmpeg

I have been using Ubuntu on my school computer this year, I usually record the lectures that I can't hope to keep up with the prof, I have permission to do this. I have been using the default audio recorder that you can install with sudo apt-get install audio-recorder because it was the easiest to use. Earlier in the semester they recordings were fine. But now they are corrupt as soon as the recording is done. They are in the .m4a format.

I have tried many tutorials, including editing the hex data of the recording, no luck. I do not know where the recording starts since when I try to make a new recording it is corrupt off the bat. I have tried using ffmpeg to get this error, moov atom not found, which looking up does nothing to help solve the problem. Or I get an error saying protocol not found. Did you mean in.m4a? which is the name of the file, that I typed in correctly. ffmpeg returns a protocol not found error. Then it says do you mean the file that I did put in. Faad returns this error: Unable to find correct AAC sound track in the MP4 file. Also I tried an mp4 repair service and it works so the file should be able to be fixed. But it would cost $86 for it, and I need to fix 6 recordings.

I have tried uninstalling and reinstalling the restricted codecs.

Any help would be greatly appreciated.

·OTHER ANSWER:

I have been using Ubuntu on my school computer this year, I usually record the lectures that I can't hope to keep up with the prof, I have permission to do this. I have been using the default audio recorder that you can install with sudo apt-get install audio-recorder because it was the easiest to use. Earlier in the semester they recordings were fine. But now they are corrupt as soon as the recording is done. They are in the .m4a format.

I have tried many tutorials, including editing the hex data of the recording, no luck. I do not know where the recording starts since when I try to make a new recording it is corrupt off the bat. I have tried using ffmpeg to get this error, moov atom not found, which looking up does nothing to help solve the problem. Or I get an error saying protocol not found. Did you mean in.m4a? which is the name of the file, that I typed in correctly. ffmpeg returns a protocol not found error. Then it says do you mean the file that I did put in. Faad returns this error: Unable to find correct AAC sound track in the MP4 file. Also I tried an mp4 repair service and it works so the file should be able to be fixed. But it would cost $86 for it, and I need to fix 6 recordings.

I have tried uninstalling and reinstalling the restricted codecs.

Any help would be greatly appreciated.

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Speed of Includegraphics Seemingly Dependent on How Many Packages Are Loaded!
This was quite a puzzle.This answer will be long, to match the long time it took me to get to the bottom of this, but the sections are titled and numbered so you can skip over the ones you don't care about. You can even skip to the one-sentence summary at the end. :-)This will describe how I arrived at the answer. If you don't care, and only want the answer, you can skip to the next section.I took the file at the top of the question, saved it into a file jfbu1.tex, also created foo.pdf by copying it as cp $(kpsewhich example-image-a.pdf) foo.pdf, then ran pdftex jfbu1.tex, and sure enough, saw output like:where the numbers are increasing.As what was being measured involved includegraphicsfoo.pdf, I tried to unpack the definition of includegraphics to see if it could be further simplified. (I also tried other things, like replacing D with 10000 occurrences of the expansion of A directly, but that didn't make a difference.) Well, showincludegraphics shows that its definition is leavevmode @ifstar Gin@cliptrue Gin@i Gin@clipfalse Gin@i , so let's replace includegraphics in our file with that, see if the phenomenon is still observed, and then try removing parts of it. (E.g. the first case of the @ifstar conditional is probably irrelevant, as we don't have a * in this example, so we won't take that path.)I did this a little, mostly relying on show, and cursing the complexity of LaTeX (just writing out the full definition of includegraphics in terms of TeX primitives would be immense). (Small tip: next time use the LaTeX source code rather than show; it's a bit easier to read.)Anyway, after a few steps of this (a few steps deep into the definition of includegraphics), I observed that we could replace the original file'swith (using just an early part of the definition of includegraphics):and the phenomenon of time increasing as we load more packages was still observed (though it ran faster). In fact, proceeding a bit, this was sufficient: apparently, simply testing whether a file exists takes longer as we load more packages!A few more steps, and we can get down to TeX primitives (no loading of graphicx necessary): which simply opens and closes the file (apparently this is part of how IfFileExists works internally).After making a few more changes  for example, we don't need the trick to convert pdfelapsedtime into seconds(?) as we care more about the fact that it's increasing than about its actual value, and the phenomenon is consistently observed even with much fewer repetitions instead of 10000 (say 81, replacing 10 with 3)  we arrive at the following slightly simpler file jfbu2.tex, where the phenomenon is still observed:and this still prints output like (not always the same numbers, but the pattern of increase is consistent):(About the useless thepdfelapsedtime before the D, which simply inserts "0" into the typeset output, I'll say more below.)And the mystery remains: the A above seems like it should just do a constant number of operations, why does it take longer as more packages are loaded?Now that we're down to TeX primitives, there's nothing further to unpack at the macro (the TeX programming) level, and we need to look into the TeX program itself.We can step through the TeX program with a debugger like gdb.To do this it would usually be easier to work with the LuaTeX source code, as that's (sort of) written directly in C, rather than the source code of TeX/pdfTeX/XeTeX, as they undergo several rounds of mangling from the .web source to the C code before being compiled. (So the C code that is finally compiled is more readable in the case of LuaTeX.) But it turns out (after appropriate definitions of pdfelapsedtime) that this phenomenon we're interested in does not happen in LuaTeX, so we're stuck with pdfTeX. (It does happen in TeX / XeTeX, where without the convenience of pdfelapsedtime we can just observe visually that it takes longer.)To use gdb, the program needs to be compiled with -g, and also binaries shouldn't be stripped. Fortunately I'd done this before: the trick is, when building from TeX Live sources (see here and here), instead ofto useand update $PATH to use the new binaries appropriately. (Or, if using make install strip, should replace with make install.)One can start gdb with a command like gdb pdftex (make sure PATH is right, or else specify the full path to our specially compiled pdftex binary). Then, one can set breakpoints, before running the program (as if we'd run pdftex jfbu2.tex on the commandline) with run jfbu2.tex.Which breakpoints to set? We'd like to stop when some particular function is called, which doesn't get called too often. My choice was the function called by pdfelapsedtime (though in hindsight I guess using the one for pdfresettimer would have been better) which with some looking at the source code and/or gdb, happens to be (or call) getmicrointerval. (This is the reason for the extra thepdfelapsedtime in the file above, because I want to break there.)So we can start gdb, set break getmicrointerval, and run the program, and it will stop after reaching the place where the function is called. Then we can type continue to continue until the next breakpoint (or end of program), or type next to invoke the next statement of the program (stepping over function calls, i.e. not descending into them) or step to do the same while stepping into function calls. As you keep hitting Enter, it will show you each function that's called, and each line of source that's executed.After doing this a little, it's clear that it will take a long time to do this manually.Long story short: put the following in /.gdbinit:This is like typing "step" and hitting Enter a few million times manually until the program finishes, and everything that gdb outputs will be written to file gdb.txt.With this, the whole thing ran for a few hours, and produced a gdb.txt that was over 700 MB in size, from over 20 million lines.The start of the file looks something like this:(The first Breakpoint 1 at 0x84bad: file pdftex0.c, line 3471 is printed when we set the breakpoint; we had continue after the first time gdb paused at the breakpoint so there's no output until the next.) The part shown in the output above is common to each time pdfelapsedtime is called (we haven't even got to the D part yet).Of course we can't process this 20-million several-hundred-megabyte file by reading through it manually. In fact, grep --line-number Breakpoint gdb.txt can be used to see the number of program steps executed between successive occurrences of pdfelapsedtime (calls to getmicrointerval):This shows thatwhere we can see the increase in the numbers in bold above. (Missed the first D because of the continue.)The main idea is that although the file is 20 million lines long, the set of different lines executed is much smaller, and what we want to compare is which lines were executed more frequently between each successive pairs of breakpoints.We can keep counters of which lines were executed how many times between successive occurrences of Breakpoint 1, getmicrointerval in the file. Used the following Python script:This is the first few lines of output for 2 (the second occurrence of D). The first column is the number of times executed, then what's printed by gdb (usually the line number and source line).Compare with that for 4 (the third occurrence of D, after tikz is loaded):and for 6 (the last one, after xlop is loaded):We can just do this visually, by say opening each in a separate tab and switching between them. For example, the (most frequent) while ( s > 255 ) loop or test is performed 2502900 times after tikz.tex is loaded, compared to 975726 times before. Everything after (less frequent than) zsearchstring is run the same number of times (among statements executed at least 500 times say), and everything above that is from inside the zsearchstring function, or from the zstreqstr function just above (called from zsearchstring). So the culprit is entirely this zsearchstring function in pdftex0.c.If we understand what this zsearchstring is and why it's called, it concludes the debugging process.If you skipped the previous section: so far we've found that all the additional work between different calls of D happens in the function zsearchstring in pdftex0.c, which seems to be invoked more times (and executes a lot more operations) as more packages are loaded. Why?We can see the entire definition of zsearchstring in pdftex0.c or for that matter in tex0.c (which are both inside Build/source/Work/texk/web2c/ in the texlive directory):But at first glance it does not appear to be used anywhere else in the file. That's because in pdftexcoerce.h (or texcoerce.h) you'll find a declaration and a macro defined as it:and you can indeed find searchstring used a few times in pdftex0.c or tex0.c.This C code is somewhat harder to read than necessary though. In fact, the list of files where searchstring is found includes tex.p, which is presumably the result of tangling tex.web. Yet if you look in the TeX source code (with texdoc tex say), you will not find this function, as it's not part of the code that Knuth wrote. It's instead part of the system-dependent changes  changes made in web2c to produce a working TeX program. Instead you need to look at the complete (pdf)TeX source, with the change files too. Something like the following (assuming that texlive is the texlive directory):to produce a pdftex.tex file, followed by pdftex pdftex.tex (after optionally changing the input webmac to input pdfwebmac). (One could also look in the .ch file directly, but WEB code is ugly and is best not looked at directly.)Now we can look in the resulting PDF for search_string.Here's the definition of search_string; compare with our earlier zsearchstring C code above (generated from this):This finally explains what search_string is and why it exists. (We'll say more below.) Looking at places where it's used makes things even more clear. It's used in three procedures: end_name, start_input, and slow_make_string. Let's look at the first two:Compare with the corresponding sections in the TeX program: 517 and 537, which don't use search_string after calling make_name_string. It's worth looking at the definition (at least the documentation / context) of that too:We saw above that these functions are called when scanning a filename in an input, openin or openout operation. This of course includes the includegraphicsfoo.pdf example in the question, and the openin in the reduced example.Note that sometimes scanning does not require creating a string: we can see this by changing the test case to:where the phenomenon is not observed. (Well I haven't run it through gdb, but the numbers do not increase.)Also see why working with filenames required system-dependent changes in the first place  at the time TeX was developed, file names were very inconsistent across operating systems; in fact in the place where TeX was developed (SAIL), file names consisted of a base, extension and an area that included the user's initials and project (or something like that).Some background, for understanding the context of the code we saw above. At the time Knuth was originally (re)writing TeX (19801982), the programming language Pascal (at least the version available to him and at many places where TeX was going to be used) did not have good support for strings. So TeX basically takes care of allocating all strings manually: there's a giant array of characters called str_pool, initialized at the start of the program, and whenever TeX needs to store a new string, it stores the characters of the new string (as it's being built up, e.g. scanned from the input file) at successive indices into this array. For example, the kth string starts at str_poolstr_startk and goes up to str_poolstr_startk1-1. Or you can read this in the program:Note that the string pool is just an array, and is not optimized for finding strings in it: the TeX program as originally written saves references to whatever strings are needed (e.g. it will save k, and thereby know where to find the kth string). It never needs to look through all strings in the array for a particular string, any more than it's reasonable to search through all bytes of a computer's memory looking for a particular value.But when the system-dependent changes for web2c were made (a long time ago), a function slow_make_string was introduced which before saving a string, searches the entire string pool(!) to see whether it's already present under some other name (number). If so, the same string (number) is reused. This explains the very frequent (executed millions of times) loop ofthat we saw in gdb: it's searching through all string numbers s, starting at the largest (most recent) value.It appears that this may have made sense when memory constraints were tighter than time constraints (you can always wait longer), especially as it would also mean the string pool was small so there was a smaller limit on how much time would be spent searching through the entirety of it. At current memory sizes (and memory access times, which have over the last many decades consistently become more expensive relative to (arithmetic) CPU instructions) it may be worth reconsidering...(TeX as originally written does not do this. From some of the documentation it's worded as though TeX simply creates this new string, stores no reference to it, and moves ahead, which sounds like a typical memory leak bug  possibly worthy of one of those reward cheques from DEK? :P  but from looking at some of the code it seems rather that TeX unconditionally flushes the string, so it's rather the case that the changed (web2c) TeX wants to preserve a reference for some reason, so it needs this workaround... it's not clear to me which is the case.)Apart from TeX Live, I took a look at MiKTeX, and it has nearly identical code for these sections. (Just renamed from 54/web2c-string to 54/MiKTeX-string.) I have not been able to look at other less common (not based on web2c) TeX distributions, like KerTeX or TeX-gpc, nor of course of closed-source (commercial) distributions like BaKoMa TeX or Texpad.At the end of a TeX run, if tracingstats1, the program prints statistics to the log file (Here is how much of TeX's memory you used). These are the results by moving the bye to different places in the above file (after adding tracingstats1):At the top of the file (just after tracingstats1):After A, B, C, D have been first defined:(Doesn't change because single-letter names are not stored separately.)After those and also filename has been defined:(Makes sense: filename is one string, and 8 characters long.)Just before the first D:(The two strings of 19 bytes total are not the primitives pdfresettimer and pdfelapsedtime (those would be already stored), but rather something created by thepdfelapsedtime. Not sure of the details.)Just after the first D, or just after the first message:After input xintexpr is loaded (and any place before input tikz):After input tikz:(Note the large increase compared to earlier.)After input xlop (or end of file):These relative increases in the size of the string pool roughly match the relative increases in the time for executing D.In the common implementations of TeX, commands in which TeX scans for a file name (as in the case of includegraphics) involve searching through the entire string pool, and this gets slower as more packages are loaded because the packages define control sequences (macros) whose names are stored in the string poolHere is test file for (Plain) pdftex. To test it, you need some graphics file foo.pdf in working repertory. Mine is a copy of the file found via kpsewhich example-image-a.pdf. Call the following testspeedgraphics.tex and execute pdftex testspeedgraphics on command line.input graphicx.texdefBnoexpandAnoexpandAnoexpandAnoexpandAnoexpandA% noexpandAnoexpandAnoexpandAnoexpandAnoexpandA%edefCBBBBBBBBBB% 100 AdefAnoexpandC%edefDC% 100 C, each one expanding to 100 AdefAsetbox0hboxfoodeffooincludegraphicsfoo.pdfpdfresettimerD % 10000 usage of includegraphicsedefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput xintexpr.stypdfresettimerD % 10000 usage of includegraphicsedefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput tikz.texpdfresettimerD % 10000 usage of includegraphicsedefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput xlop.texpdfresettimerD % 10000 usage of includegraphicsedefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^JbyeThis file will do 4 times 10000 includegraphicsfoo.pdf in box0. We load more and more packages. On a 2.8GHz computer I get this typically in the console output:**** 1.12306pt****(loading of xintexpr)**** 1.19366pt****(loading of tikz)**** 1.36714pt****(loading of xlop)**** 1.40392pt****Hence there is increase of timings, and one feels the bigger the package the more the impact.Now comment out all loading of extra packages in test file above and repeat experiment. I get typically**** 1.13177pt******** 1.12141pt******** 1.14122pt******** 1.12416pt****i.e. there no timings drift...Now another test file, where we still include graphicx.tex but do no usage of includegraphics, rather we expand a dummy macro foo. This being much faster we do 1000000 repetitions.input graphicx.texdefBnoexpandAnoexpandAnoexpandAnoexpandAnoexpandA% noexpandAnoexpandAnoexpandAnoexpandAnoexpandA%edefCBBBBBBBBBB% 100 AdefAnoexpandC%edefDC% 100 C, each one expanding to 100 AdefAnoexpandD%edefEC% 100 D, each one expanding to 100 CdefAsetbox0hboxfoodeffoofoopdfresettimerE % 1000000 "foo"edefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput xintexpr.stypdfresettimerE % 1000000 "foo"edefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput tikz.texpdfresettimerE % 1000000 "foo"edefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^Jinput xlop.texpdfresettimerE % 1000000 "foo"edefzzzthedimexprpdfelapsedtime spmessage^^J^^J**** zzz ****^^J^^JbyeThis test file does all the input's of extra packages. Typically I get from pdftex testspeedfoo.tex:**** 0.48016pt****(xintexpr)**** 0.49115pt****(tikz)**** 0.48283pt****(xlop)**** 0.47798pt****i.e. no impact at all.Now, why is there impact with includegraphics. Is it simply because its expansion is much more complex, and if yes what is explanation? or is it something specific related to includegraphics dealings and then again what is explanation?Perhaps something having to do with hash-table? the more macros are defined the less efficient TeX is in expanding macros? (then the thing would be not includegraphics specific, I stopped my testing there, leaving the experts to express their intuitions first).Originally, this question arose in the context of a Joseph answer using xfp and includegraphics. I wanted to test if using draft option of includegraphics had an impact and then realized that loading or not xfp changed the timings. Then I realized it had nothing xfp specific, but any big package would do.I also tested with this variant of foo:defAsetbox0hboxfoodeffoofooadeffooafoobdeffoobfoocdeffoocfooddeffoodfooedeffooefoofdeffooffoogdeffoogfoohdeffoohfooideffooifoojdeffoojfookdeffookfooldeffoolfoomdeffoomfoondeffoonfooodeffooofoopdeffoopfooqdeffooqfoordeffoorfoosdeffoosfootdeffootfooudeffooufoovdeffoovfoowdeffoowfooxdeffooxfooydeffooyfoozdeffoozfooAdeffooAfooBdeffooBfooCdeffooCfooDdeffooDfooEdeffooEfooFdeffooFfooGdeffooGfooHdeffooHfooIdeffooIfooJdeffooJfooKdeffooKfooLdeffooLfooMdeffooMfooNdeffooNfooOdeffooOfooPdeffooPfooQdeffooQfooRdeffooRfooSdeffooSfooTdeffooTfooUdeffooUfooVdeffooVfooWdeffooWfooXdeffooXfooYdeffooYfooZdeffooZfooaadeffooaafoobbdeffoobbfooccdeffooccfoodddeffooddfooeedeffooeefooffdeffoofffooggdeffooggfoohhdeffoohhfooiideffooiifoojjdeffoojjfookkdeffookkfoolldeffoollfoommdeffoommfoonndeffoonnfoooodeffoooofooppdeffooppfooqqdeffooqqfoorrdeffoorrfoossdeffoossfoottdeffoottfoouudeffoouufoovvdeffoovvfoowwdeffoowwfooxxdeffooxxfooyydeffooyyfoozzdeffoozzfooAAdeffooAAfooBBdeffooBBfooCCdeffooCCfooDDdeffooDDfooEEdeffooEEfooFFdeffooFFfooGGdeffooGGfooHHdeffooHHfooIIdeffooIIfooJJdeffooJJfooKKdeffooKKfooLLdeffooLLfooMMdeffooMMfooNNdeffooNNfooOOdeffooOOfooPPdeffooPPfooQQdeffooQQfooRRdeffooRRfooSSdeffooSSfooTTdeffooTTfooUUdeffooUUfooVVdeffooVVfooWWdeffooWWfooXXdeffooXXfooYYdeffooYYfooZZdeffooZZfooto try to emulate the case with expansions of many distinct macros. But this does not show any drifting when loading packages, i.e. I don't reproduce with that the includegraphics situation: all four executions of 1000000's A take each about 2.9s--3s on my 2.8GHz computer.
Depth Buffer and Render Target
From the deferred rendering articles/tutorials I read it's a limitation in XNA (likely because the XBox 360 probably discards the depth buffer when you change render targets, hence they apply the limitation to Windows as well). What you need to do is use MRT (Multiple Render Targets) and write/test the depth against another RenderTarget2D that is something along the lines of Single.When you have finished 'compositing' your depth buffer write it out to the real depth buffer using a screen quad and associated pixel shader.The first article in J.Coluna's (quite brilliant) series on LPP describes the problem briefly - and his code should provide a nice reference for working around the issueWhen I use this RenderTarget:renderTarget new RenderTarget2D(GraphicsDevice, GraphicsDevice.Viewport.Width, GraphicsDevice.Viewport.Height, false, SurfaceFormat.Color, DepthFormat.Depth24);and draw something to it:graphicsDevice.SetRenderTarget(renderTarget);// some drawing code heregraphicsDevice.SetRenderTarget(null);and then when I want to continue with drawing depth buffer seams to be clean. Why? Is possible to save it for future use?·OTHER ANSWER:When I use this RenderTarget:renderTarget new RenderTarget2D(GraphicsDevice, GraphicsDevice.Viewport.Width, GraphicsDevice.Viewport.Height, false, SurfaceFormat.Color, DepthFormat.Depth24);and draw something to it:graphicsDevice.SetRenderTarget(renderTarget);// some drawing code heregraphicsDevice.SetRenderTarget(null);and then when I want to continue with drawing depth buffer seams to be clean. Why? Is possible to save it for future use?
Best Method to Determine If a First Order Formula Is Logically Valid?
First order logic is undecidable, so there is (as you note) no mechanical method for determining first order validity. So what's the next best to a mechanical method for trying to establish (in)validity?The trouble with looking for natural deduction proofs is that the introduction rules allow you to deduce more and more complex wffs, and thus don't stop you spinning off down blind alleys (even when there is a proof to be discovered).Better, then, to use a method without introduction rules, where as you grow a proof the length of wffs at least doesn't grow and ideally decreases. Two options spring to mind. One is downward-branching tableau proofs as in Richard Jeffrey's lovely Formal Logic: Its Scope and Limits, or my Jeffrey-for-Dummies, officially titled An Introduction to Formal Logic. The other option is certain sequent systems. The tableau system in particular is very student-friendly, and with a bit of practice, on "nice" examples you'll usually find a closed tableau if there is one to be found, and find an open tableau and be able to read off a valuation which falsifies the wff being tested if the wff is invalid. This is perhaps your best buy!For example, let's use a tableau to test $(forall x P(x) rightarrow forall x Q(x)) rightarrow forall x (P(x) rightarrow Q(x))$. We start by assuming that's false (i.e. its negation is true), which comes to assuming$$forall x P(x) rightarrow forall x Q(x)$$$$negforall x (P(x) rightarrow Q(x))$$The latter is equivalent to$$exists xneg (P(x) rightarrow Q(x))$$So, if that's true there must be an object in the domain which satisfies the condition, which we can dub $a$, so$$neg (P(a) rightarrow Q(a))$$whence $$P(a)$$$$neg Q(a)$$Now look at the first line. We have to consider cases. We have either the negated antecedent or the consequent:$$negforall x(Px)quadquad|quadquad forall xQ(x)$$On the right hand branch we immediately have a contradiction, however, because we can instantiate the universal $forall xQ(x)$ with $a$ to get $Q(a)$.So look at the left branch. We can continue that $$exists xneg P(x)quadquadquadquadquadquad$$ $$neg P(b)quadquadquadquadquadquad$$ where we have to use a new name to dub the witness for the existential. And now we are stymied. So the assumption that the original wff is false doesn't lead to contradiction. So it can't be valid. In fact, we can read off the open branch of the tableau the interpretation with just two elements in the domain -- call them $a$ and $b$ -- where $P(a)$, $neg P(b)$, $neg Q(a)$ and it doesn't matter for $Q(b)$. And that interpretation will falsify the test formula! For a more careful exploration of this kind of thing, if it is unfamiliar to you, see my book.I know there isnt a "standard method" to determine if a formula is logically valid, but i would like to know if there is something you can always try first of all to determine it.Not all formulas look obviously valid like $forall x P(x) rightarrow exists x P(x)$. This can be proven with natural deduction, if its required.For example, i think $(forall x P(x) rightarrow forall x Q(x)) rightarrow forall x (P(x) rightarrow Q(x))$ is valid, and i am trying to prove it by contradiction, asumming there is some intepretation in wich it is false, but i can't figure out how to do it.So, any advices?
Is It Wasteful to Create a New Database Table Instead of Using Enum Data Type?
Option #2, using reference tables, is the standard way of doing it. It has been used by millions of programmers, and is known to work. It is a pattern, so anyone else looking at your stuff will immediately know what is going on. There exist libraries and tools that work on databases, saving you from lots and lots of work, that will handle it correctly. The benefits of using it are innumerable.Is it wasteful? Yes, but only slightly. Any half-decent database will always keep such frequently joined small tables cached, so the waste is generally imperceptible.All other options that you described are ad hoc and hacky, including MySQL's enum, because it is not part of the SQL standard. (Other than that, what sucks with enum is MySQL's implementation, not the idea itself. I would not mind seeing it one day as part of the standard.)Your final option #3 with using a plain integer is especially hacky. You get the worst of all worlds: no referential integrity, no named values, no definitive knowledge within the database of what a value stands for, just arbitrary integers thrown all over the place. By this token, you might as well quit using constants in your code, and start using hard-coded values instead. circumference radius * 6.28318530718;. How about that?I think you should re-examine why you find reference tables onerous. Nobody else finds them onerous, as far as I know. Could it be that it is because you are not using the right tools for the job? Your sentence about having to "encode things and deal with integers", or having to "create elaborate programming constructs", or "creating new object oriented entities on the programming side", tells me that perhaps you may be attempting to do object-relational mapping (ORM) on the fly dispersed throughout the code of your application, or in the best case you may be trying to roll your own object-relational mapping mechanism, instead of using an existing ORM tool for the job, such as Hibernate. All these things are a breeze with Hibernate. It takes a little while to learn it, but once you have learned it, you can really focus on developing your application and forget about the nitty gritty mechanics of how to represent stuff on the database.Finally, if you want to make your life easier when working directly with the database, there are at least two things that you can do, that I can think of right now:Create views that join your main tables with whatever reference tables they reference, so that each row contains not only the reference ids, but also the corresponding names.Instead of using an integer id for the reference table, use a CHAR(4) column, with 4-letter abbreviations. So, the ids of your categories would become "TEST", "DSGN", "PROG", "OTHR". (Their descriptions would remain proper English words, of course.) It will be a bit slower, but trust me, nobody will notice.Finally, when there are only two types, most people just use a boolean column. So, that "standard/exception" column would be implemented as a boolean and it would be called "IsException".Suppose I have 4 types of services I offer (they are unlikely to change often):TestingDesignProgrammingOtherSuppose I have 60-80 of actual services that each fall into one of the above categories. For example, 'a service' can be "Test Program using technique A" and it is of type "Testing".I want to encode them into a database. I came up with a few options:Option 0:Use VARCHAR directly to encode service type directly as a stringOption 1:Use database enum. But, enum is evilOption 2:use two tables:service_line_item (id, service_type_id INT, description VARCHAR);service_type (id, service_type VARCHAR);I can even enjoy referential integrity:ALTER service_line_item ADD FOREIGN KEY (service_type_id) REFERENCES service_type (id);Sounds good, yes?But I still have to encode things and deal with integers, i.e when populating the table. Or I have to create elaborate programming or DB constructs when populating or dealing with the table. Namely, JOINs when dealing with the database directly, or creating new object oriented entities on the programming side, and making sure I operate them correctly.Option 3:Don't use enum, do not use two tables, but just use an integer columnservice_line_item ( id, service_type INT, -- use 0, 1, 2, 3 (for service types) description VARCHAR);This is like a 'fake enum' that requires more overhead on the code side of things, like i.e. knowing that 2 'Programming' and dealing with it appropriately.Question:Currently I have implemented it using Option 2, guided under conceptsdo not use enum (option 1)avoid using a database as a spreadsheet (option 0)But I can't help to feel that seems wasteful to me in terms of programming and cognitive overhead -- I have to be aware of two tables, and deal with two tables, vs one.For a 'less wasteful way', I am looking at Option 3. IT is lighter and requires essentially the same code constructs to operate (with slight modifications but complexity and structure is basically the same but with a single table)I suppose ideally it is not always wasteful, and there are good cases for either option, but is there a good guideline as to when one should use Option 2 and when Option 3?When there are only two types (binary)To add a bit more to this question... in the same venue, I have a binary option of "Standard" or "Exception" Service, which can apply to the service line item. I have encoded that using Option 3.I chose not to create a new table just to hold values "Standard", "Exception". So my column just holds 0, 1 and my column name is called exception, and my code is doing a translation from 0, 1 > STANDARD, EXCEPTION (which I encoded as constants in programming language)So far not liking that way either..... (not liking option 2 nor option 3).I do find option 2 superior to 3, but with more overhead, and still I cannot escape encoding things as integers no matter which option I use out of 2, and 3.ORMTo add some context, after reading answers - I have just started using an ORM again (recently), in my case Doctrine 2. After defining DB schema via Annotations, I wanted to populate the database. Since my entire data set is relatively small, I wanted to try using programming constructs to see how it works.I first populated service_types, and then service_line_items, as there was an existing list from an actual spreadsheet. So things like 'standard/exception' and 'Testing' are all strings on the spreadsheet, and they have to be encoded into proper types before storing them in DB.I found this SO answer: What do you use instead of ENUM in doctrine2?,which suggested to not use DB's enum construct, but to use an INT field and to encode the types using 'const' construct of the programming language.But as pointed out in the above SO question, I can avoid using integers directly and use language constructs -- constants -- once they are defined....But still .... no matter how you turn it, if I am starting with string as a type, I have to first convert it to a proper type, even when using an ORM.So if say $str 'Testing';, I still need to have a block somewhere that does something like:switch($str): case 'Testing': $type MyEntity::TESTING; break; case 'Other': $type MyEntity::OTHER; break;The good thing is you are not dealing with integers/magic numbers [instead, dealing with encoded constant quantities], but the bad thing is you can't auto-magically pull things in and out of the database without this conversion step, to my knowledge.And that's what I meant, in part, by saying things like "still have to encode things and deal with integers". (Granted, now, after Ocramius' comment, I won't have to deal directly with integers, but deal with named constants and some conversion to/from constants, as needed).·OTHER ANSWER:Suppose I have 4 types of services I offer (they are unlikely to change often):TestingDesignProgrammingOtherSuppose I have 60-80 of actual services that each fall into one of the above categories. For example, 'a service' can be "Test Program using technique A" and it is of type "Testing".I want to encode them into a database. I came up with a few options:Option 0:Use VARCHAR directly to encode service type directly as a stringOption 1:Use database enum. But, enum is evilOption 2:use two tables:service_line_item (id, service_type_id INT, description VARCHAR);service_type (id, service_type VARCHAR);I can even enjoy referential integrity:ALTER service_line_item ADD FOREIGN KEY (service_type_id) REFERENCES service_type (id);Sounds good, yes?But I still have to encode things and deal with integers, i.e when populating the table. Or I have to create elaborate programming or DB constructs when populating or dealing with the table. Namely, JOINs when dealing with the database directly, or creating new object oriented entities on the programming side, and making sure I operate them correctly.Option 3:Don't use enum, do not use two tables, but just use an integer columnservice_line_item ( id, service_type INT, -- use 0, 1, 2, 3 (for service types) description VARCHAR);This is like a 'fake enum' that requires more overhead on the code side of things, like i.e. knowing that 2 'Programming' and dealing with it appropriately.Question:Currently I have implemented it using Option 2, guided under conceptsdo not use enum (option 1)avoid using a database as a spreadsheet (option 0)But I can't help to feel that seems wasteful to me in terms of programming and cognitive overhead -- I have to be aware of two tables, and deal with two tables, vs one.For a 'less wasteful way', I am looking at Option 3. IT is lighter and requires essentially the same code constructs to operate (with slight modifications but complexity and structure is basically the same but with a single table)I suppose ideally it is not always wasteful, and there are good cases for either option, but is there a good guideline as to when one should use Option 2 and when Option 3?When there are only two types (binary)To add a bit more to this question... in the same venue, I have a binary option of "Standard" or "Exception" Service, which can apply to the service line item. I have encoded that using Option 3.I chose not to create a new table just to hold values "Standard", "Exception". So my column just holds 0, 1 and my column name is called exception, and my code is doing a translation from 0, 1 > STANDARD, EXCEPTION (which I encoded as constants in programming language)So far not liking that way either..... (not liking option 2 nor option 3).I do find option 2 superior to 3, but with more overhead, and still I cannot escape encoding things as integers no matter which option I use out of 2, and 3.ORMTo add some context, after reading answers - I have just started using an ORM again (recently), in my case Doctrine 2. After defining DB schema via Annotations, I wanted to populate the database. Since my entire data set is relatively small, I wanted to try using programming constructs to see how it works.I first populated service_types, and then service_line_items, as there was an existing list from an actual spreadsheet. So things like 'standard/exception' and 'Testing' are all strings on the spreadsheet, and they have to be encoded into proper types before storing them in DB.I found this SO answer: What do you use instead of ENUM in doctrine2?,which suggested to not use DB's enum construct, but to use an INT field and to encode the types using 'const' construct of the programming language.But as pointed out in the above SO question, I can avoid using integers directly and use language constructs -- constants -- once they are defined....But still .... no matter how you turn it, if I am starting with string as a type, I have to first convert it to a proper type, even when using an ORM.So if say $str 'Testing';, I still need to have a block somewhere that does something like:switch($str): case 'Testing': $type MyEntity::TESTING; break; case 'Other': $type MyEntity::OTHER; break;The good thing is you are not dealing with integers/magic numbers [instead, dealing with encoded constant quantities], but the bad thing is you can't auto-magically pull things in and out of the database without this conversion step, to my knowledge.And that's what I meant, in part, by saying things like "still have to encode things and deal with integers". (Granted, now, after Ocramius' comment, I won't have to deal directly with integers, but deal with named constants and some conversion to/from constants, as needed).
How Much Does a Hamster Cage Cost?
Getting hamster for your child involves finding the right hamster cage and the feeding and bedding accessories that go with it. Before you bring the hamster, check out the costs of ownership.Hamster  CageThe most important thing that you will need is the hamster cage. This will be where your hamster will live. There are lots of different types of cages. These can be purchased for anywhere between $10 for a small plastic cage up to $100 for a larger cage made of metal or wood.BeddingBedding material is important as it will make your hamster cage comfortable for the hamster. This will cost between $2 and $10 depending on whether you choose basic bedding, or whether you prefer the scented varieties. Prepare to replace bedding weekly as part of your cleaning regimen.Dish and FoodA dish to put food in is a very good idea, it's best to buy a ceramic bowl so that hamsters can not chew and eat it. This should only cost up to a maximum of $10.Food is also necessary and you can buy lots of different mixes of hamster food at your local pet shop. These should not cost any more than a few dollars for a small bag to try out.BottleAll animals need to drink and hamsters are no exception. Expect to pay up to $5 for a water bottle. A bowl of water could be used instead however bottles are much cleaner and less likely to make a mess.Can guinea pigs eat hamster food?Ignore that person above! I feed my guinea pigs hamster food because I have like 7 hamster lol :) they are perfectly fine and I've won loads of pet shows XD they've been alive for years too :PI lost the tablespoon i use to measure my hamster food?Hi Yes, that's ok. It would be just like you hamster chewing his/her cage or plastic igloo, or any other toy or item that's plastic. It is 100% safe if your hamster has chewed the measuring tablespoon. If I were you I would clean the cage to find it. If it's not in the cage do not worry, just look around the cage, in the floor, under the bed, just any place like that. I would also ask your mom where she put it because it might not be in the cage at all. Hope I have helped you!Is it possible to make homemade hamster food? If so do you have any recipes?I have one! Ingredients: Diffrent types of seeds(unsalted) honey put some of the seeds in a bowl. put honey and form balls. let the honey dry for it hardens. put one ball at a time in!is it okay to feed pet mice hamster food?Hamster food is different. Maybe post on craigslist if someone is willing to tradeWhat foods (other than hamster food) can i give to my hamsters?A hamsters diet mainly consists of a dried mix that can be bought in pet stores. This will contain all the vitamins and minerals a hamster needs. Make sure the mix you buy does not contain too many seeds or nuts because too many of these can make your hamster fat. One thing to note when feeding dwarf hamsters is not to feed too many sugary foods as this could lead to diabetes. You should provide two teaspoons of the dry mix each day. Any food that your hamster does not eat should be thrown away. Along with the normal hamster mix you can also feed your hamster fresh fruit and vegetables once or twice a week. Be careful you do not feed too many of these as it may cause the hamster to get diarrhoea. The following is a list of some foods you can feed your hamster: Banana Sweetcorn Cucumber Apple Cheese Turnip Raisins Peas Carrot Celery Bread Grapes Melon Chicken Never feed your hamster these foods: Chocolate Raw Kidney Beans Garlic Onions Raw Potato Sweets Hope this helps.Hamster Food, Treats & Diet: What Types, How Much & OftenFeeding your hamster is going to be relatively easy considering all the food options that are available to you. With that said though, not every type of hamster food is good for them. Some of your options include carefully formulated ingredients that will provide your hamster a well-balanced diet while others do not provide any nutritional value and are loaded with nothing but sugars or fats. The hamster food you should look for includes 12-24% protein and 3-6% fat. For Pregnant or baby hamsters, you should get hamster food that contains 18-40% protein and 7-9% fat. The reason pregnant mothers and babies need more protein is that they need all the protein to grow. It's during the first month of a baby hamster's life that does most of it's growing; additional protein will help. In addition to the protein and fats, they need a diet high in carbohydrates. Since they burn so much energy when they are active, hamster food with some needed carbs will give them the energy to do their nightly exercise on the hamster wheel or through their tubes and tunnels. Round out the diet with greens in the forms of lettuces, grasses, fruits, and vegetables. What is in Hamster Food With all the options available and all the guidelines you need to follow, you are probably wondering what exact type of hamster food to get. The problem is, there is no one right answer. We can give you a recommendation on what we think makes a well-balanced hamster diet but by no means is this always going to be right for your situation. In addition to pregnant and baby hamsters, you might need to alter your diet formula for any obese, old, or diabetic hamsters. Obese hamsters should be limited in their fat intake, old hamsters can be fed what the babies eat and diabetic hamsters should have low sugar diets. In regards to prepackaged hamster chow, these should make up more than 50% of the overall diet. There are two main types to choose from; seed mixes and lab blocks of pellets. Variety is the spice of life so it's okay to use both in your hamster's diet. A bag of mixed seeds is a great choice if you want a large variety of options for your hamster to eat. Depending on the brand, theses mixes include not only seeds but also and other types of grasses/grains (oats, wheat) dried fruits and vegetables. If your hamsters ate a bit of all these ingredients, it would probably have a relatively balanced diet. However, just as you see in humans, hamsters will pick and choose what they want to eat. Often they will go for the more fatty foods like sunflower seeds or pumpkin seeds while not eating the other parts of the mix. Thus, they do not get a well-balanced diet. You can pick out the fatty seeds like sunflower and pumpkin seeds and only give them out every so often. You might consider removing some of the corn or alfalfa since some hamster owners say they can cause cancer or liver damage but there is little research to back this up from what we can find. Additionally, dehydrated fruits can get stuck in their mouths or cause a cheek impaction. Finally, avoid mixes that have a lot of molasses in them since they are full of sugar. Lab blocks were originally created as feed in laboratories for research animals. You can now buy these at pet stores but the best ones still come from manufactures that still sell to laboratories. A lab block usually contains a mixture of seed and grains and vitamins and minerals. These are a preferred type of hamster food if you want to make sure your little guys or girls are getting all the vitamins and minerals they need to stay healthy. If you could only get one type of dry food, these would be them. You might think they would taste bad but your hamsters will most likely love them, especially the Syrian breeds. In addition to getting a well-balanced diet, these pellets and blocks will help wear down your hamster's teeth and keep them from becoming overgrown. Lastly, Block and pellets are easier to save while cleaning your hamster cage then the smaller seed mixes. Hamsters in nature rarely drink water but instead get their water from the things they eat (This does NOT mean you do not need a water bottle though). Fresh greens, fruits, and vegetables not only provide your hamsters with the water they need, but they also provide extra vitamins and minerals they need. With that said, you need to be careful how much greens you add into the hamster food; too many greens and they can get a case of diarrhea. A rough guide calls for only feeding it about one square inch (2.54cm) of greens per day. There are greens, fruits, and vegetables that are great for hamsters and there are also ones that should be avoided. The following are some of the greens that are acceptable and some of the greens to avoid (If you collect these from outdoors, make sure there are no pesticides or toxic chemicals that could be on them. Always thoroughly wash them before placing them in your hamster's cage.) • Corn (may or may not cause cancer) • Alfalfa (may or may not cause cancer) In their natural habitat hamsters are mainly herbivores but on occasion, if the opportunity arises, they will snatch up small insects or grubs. This means you will need to provide your pet with some food that contains protein. Many of the prepackaged mixes will have some protein so you wo not have to provide that much more. All you need is a small fingers worth every so often. Try to keep its protein intake down around 12-15% unless otherwise for reasons stated in this article (pregnant and baby hamsters). The following is a list of acceptable forms of protein that can be fed to them (It's best to get any of the live insects/bugs on this list from the pet store so no diseases get spread). Hamsters need access to a fresh source of water 24/7. The best way to do this is by providing them with a water bottle or two throughout their habitat. You need more than one if you have several hamsters or an expansive cage system. In the wild you could observe a hamster licking different rocks or minerals that contain salt. They need salt to help retain water and stay healthy. You can provide your hamster with a salt lick or a mineral salts. These come in various forms and are sometimes added to their accessories as a form of play. If you provide your little guy with a well-balanced diet you probably wo not need to get supplements to add extra vitamins and minerals into their food or water. However, if you want to play it safe and make sure they are getting all the nutrition they need, you can get vitamin and mineral supplements; it more than likely wo not do them any harm as long as you follow the directions. Occasionally a pet owner wants to spoil their hamsters by giving them some treats. For the most part, if you feed it a well-balanced diet it wo not need to be fed any treats. However, every so often it's okay to give your hamster something that is not the best for it in terms of nutritional value. If anything, if it does not provide any nutritional value, a tasty treat might improve their happiness which is a roundabout way can improve the little guy or girl's well being. There are a lot of options on the market these days and some are less unhealthy than others. Most of them come in flashy packaging and contain a lot of sugar. Here is a list of some of the treats that are available: Avoid any treat that contains a high amount of sugar. This means no cakes, cookies, or chocolates. If you only spoil your hamster every so often and do not fall for their tricks that they just have to have a treat, then you are being a good pet hamster owner and providing them with the proper care they need.
Why Didn't Noah Have Any Grandchildren in the Ark?
Come on, having one of every animal is one thing, but now having grandchildren on the Ark? That would just be too hard to believe.the more disturbing question is eventually he would have had them. Exactly who is having sex to produce said child? Kind of like, how did Adam and Eve become grandparents?.1. Mothers: what would you do if some other child hit your child?Why do not you bring this up to the apartment complex manager? If parents are not out there watching their children then their children should not be out there either! I would have been tempted to swat the kids butt, but of course I would not have. I would take it to the manager.2. Easter baskets... How do you fill them?I feel the same way you do. I make it a point to not over do it. My family never over did it, but I remember my cousin's family thought it was normal to spend $300 per child for Easter. They would spend almost a $1000 in total on Easter 'gifts'. Gift certificates, you name it. I always thought it was crazy. I got some great ideas from a question I asked the other day. What I plan on doing for my kids Easter 'Buckets' is: Getting a couple plastic pales that have the shovels, rakes and what not in them (cost $1.50 each at Toys'R'Us right now). In them I am going to put a coloring book ($0.50 each) crayon pack ($0.50 each). Going to add one of their favorite fruit juices, couple Kinder Surprise eggs (got a package of 12 for $2) and a chocolate bunny ($1 each). Then on the side I have picked them up a movie (Go! Diego Go! Dinosaur Adventures for $5). My mom always got a 'family movie' as a gift to the family. It was usually a Disney movie of some sort. She did it because it kept us busy while she was cooking our big Easter Dinner.3. Is this art or child pornography?Defiantly Child Porn. Most art containing children are not nude4. How is child support calculated if the father is not in contact with the child?it is based on income of both parents. Child support amounts can always be changed based on income or other factors related to bring up the child.. It does not matter if you see your child or not you are still responsible to help support the child5. Is this normal? Is your child like this? ?Oh, that will change, just wait!6. parents: if your child was atheist?This is not about atheism vs. christianity - it's about respect and family. It's the holidays and whether you believe in God, Jesus or whatever you can still gather with your family and visit. Obviously exchanging gifts does not seem to offend you (funny how that works) so what is the worst that can happen? You just stand there and bow your head while everyone else is praying - I doubt they will be watching to make sure EVERYONE is praying along with them. Go and have fun visiting with your family and politely decline to exchange gifts with them - you do not want to go against your principles afterall7. Is this child abuse? And I so I it legally considered child abuse in Ohio?I am not from Ohio, and I have never lived there. BUT I would consider it to be child abuse. Be brave and consult a higher authority about it. It will be hard and scary, but your parents are the ones who are suppose to protect you. Not harm you. Would you rather live in pain and fear from your own parents, or potentially live in a safe and relaxed home?8. Is this considered child abuse?No this is not child abuse, if this was happening on a daily basis then yes. Sometimes parents flip out I know my mom has beat my *** like that when I did some bad stuff, but obviously she loves me because she feeds me and gives me shelter. Same with your parents, they may flip out for bullshit reasons sometimes but they still love ya.
Cheap but Fabulous Wedding Decoration Ideas
Wedding decorations are essential when planning a wedding. The chosen decors have the potential to make or break the atmosphere of the party, thus careful selection must be taken into serious consideration. It need not be expensive, actually. Price is not a determining factor in making your wedding decorations beautiful and elegant. Buy Cheap Wedding DecorationsFor a soon-to-be bride, planning a wedding usually goes way beyond choosing the most fitting bridal gown and accessories. More often than not, it involves almost every minute details of the occasion, from the wedding favors to the food at the reception. Because of the costs of all other aspects of the event, the prospect of saving some extra bucks on cheap wedding decorations is definitely welcome.In this times where the economy is not at its best, couples should pursue practical ways in making their wedding dreams come true. There are cheap wedding decorations out there that can give fabulous look to the wedding venue and reception. Whats the use of expensive wedding decors, when the decorator is not apt for the job? All you need is your sense of creativity. By being creative you can make each of the cheap wedding decoration shine in glamour and beauty. Affordable wedding decorationsBasically, wedding decorations are made up of flowers, ribbons and candles. Of all items, flowers are the most dominant. Now, to obtain dozens of flowers at the lowest price possible go to flower farms. Flower farms are indeed the cheapest place where you can buy them wholesale. As for the task of doing flower arrangements, you do not have to hire a florist when you can decorate it yourself. This way you can have a great deal of cutting the cost. Why not seek the helping hands of your family and friends to come with an amazing masterpiece? You can come up with different ideas from them. Also, this can be a good bonding time for you and your loved ones to enjoy with.The candles and the ribbon are like supporting artists that add more drama to your wedding decoration. Cheap candles are widely available. They jive perfectly with the flowers and with ribbons to accentuate them; you will certainly have an elegant wedding decoration. Sydney wedding decorationsTry to look around discount stores as well. Youll be surprised at the number of cute items youll find there. You can use these items to add more color to your decorations but dont overdo it. It should complement to your wedding colors and theme. Its safe to keep it simple but elegant.Again, make use of your imagination. The sky is the limit here! Be creative in coming up with a cheap but fabulous wedding decoration. However, this entails time. As with all subjects, you need to plan ahead. With a plan in hand, you can accomplish the task of designing the entire wedding decoration and the search for the cheapest materials. If everything is well-coordinated and well-planned you can rest assured that your cheap wedding decoration will turn out fabulous on your wedding day.Visit here Wedding Decoration Items for Sale·RELATED QUESTIONApartment, non-perm, cheap decor ideas?I have lived in some tiny temporary places with mis-matched furniture. The thing that I have done that has always had an absolutely HUGE impact in making everything come together and look alive and cozy is to incorporate as many plants as possible! The bigger, the better! You would not believe what a difference this makes. Try it! You wont believe your eyes!!
Children
ChildrenImage quality checkingReliability of measurements increases if indicators of pelvic alignment are taken into account: Obturator foramen diameter ratio (of Tnnis): A quotient of pelvic rotation by dividing the horizontal diameter of the obturator foramen of the right side and that of the left. In neutral rotation the ratio is 1 but is considered to be acceptable when it is between 0.56 and 1.8. Symphysis os-ischium angle (of Tnnis): This evaluates the pelvic position in the sagittal plane. Lines are drawn from the highest point of the ischium to the most prominent point of the symphysis, joining at the inside of the pelvis. The range of normal values is from 90 to 135 and is related to the infant's age.MeasurementsThe most useful lines and angles that can be drawn in the pediatric pelvis assessing hip dysplasia are as follows: Normal hip. Hip dysplasia. (A) Hilgenreiner line, connects the inferior tips of the iliac bones, at the triradiate cartilage. This line is used to measure the acetabular angle and as a reference for Perkin line. (B) Perkin line is perpendicular to Hilgenreiner line, touching the lateral margin of the acetabular roof. This leads to four quadrants and a normal femoral head has to be located in the inferomedial quadrant. We can measure the lateral displacement of the femoral head with regard to the Perkin line by dividing the width of the head that crosses the Perkin line by the diameter of the head. The value for patients under 3 years must be 0 and in older children this ranges from 0 to 22%. (C) Shenton line is a continuous arc drawn from the inner edge of the femoral neck to the superior margin of the obturator foramen. In children over about 3 to 4 years of age, this line should be smooth and undisrupted, otherwise it may indicate a fracture or hip dysplasia. However, in infants this line can be unreliable as it depends on the rotation of the hip when the image is taken. (D) The acetabular index measures the acetabular roof slope. It is the most useful measure of acetabular dysplasia until 6 years of age. It is formed between Hilgenreiner line and the acetabular roof. In newborns, values of in males and in females are considered normal. It normally decreases with age: Acetabular index by age in males. Acetabular index by age in females. (E) The medial articular joint space is measured between the medial border of the femoral head or neck (when epiphysis is not ossified) and the acetabular platform. Normal values range between 5 and 12 mm. Differences greater than 1.5 mm between the two sides are considered abnormal.Reimer's migration index (MI), also called the femoral extrusion index, is calculated if hip dysplasia is detected. It can be used to indicate hip dislocation. It is the horizontal distance (parallel to the Hilgenreiner Line) between the Perkin line and the lateral border of the ossification center of the femoral head, divided by the horizontal width of the ossification center. The migration index is normally less than 33% by most sources, but 25% and 30% has also been suggested.— — — — — —What would you think if?I had the same thing, only I had no children from my first marriage. My second, my husband's first. I wore white, I do not think anyone really cares anymore. Hell, let's face it, there are not that many virginal brides ANYWAYS right. It's your wedding, your choice. I see wearing white as a fresh start. .you can think of it that way too.— — — — — —Wife and childrenOn 29 April 1858, Ainslie married Eliza Anne Sawer, daughter of Thomas Sawer of Ickham, Kent, and they had ten children, William Langstaff, Lylie Sophia, Francis Sawer, Mary Isobel, Montague, Rose, Beatrice, George Robert, Thomas Oswald, and Charles Bernard Ainslie (1879-1937), the last of whom became the father of the Liberal politician Jack Ainslie. Ainslie's widow outlived him by six years, dying on 27 December 1899.— — — — — —Do you think there is a problem with Illegal Aliens in the LGBT community?I do agree that people should be able to choose a place to live that is safe and offers more oppotunities for them. Unfortunately, we as U.S. citizens do not fully understand what hell people have to go through just to come to America. My husband of 6yrs. came here illegally simply because when he tried to it the right way the Embassy denied him simply because he was single, educated, and had no children. Therefore, they believed if they granted him a visa he would have no reason to come back to Nigeria. His living conditions in Africa were horrible and he had no reason to stay. I am grateful that he found a way to better his situation, even if it was not "Legal." Everyone has the right to choose to be happy. Why do we give the government so much authority over that? Why should the government get to decide who should and should not be happy? By the way, since my husband has been in the US, he's held a legal job for over 6yrs., pays taxes, and has been a terrific father to 3 beautiful children he helped create....not many American men can even do that!!!!
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