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My 6 year old wants to know if infinity is an odd or even number. His 38 year old father is keen to know too.
In the context of transfinite ordinals, the usual definition is that an ordinal number $\alpha$ is even if it is a multiple of $2$, specifically: if there is another ordinal $\beta$ such that $2\cdot\beta=\alpha$. In other words, the order type $\alpha$ can be viewed as $\beta$ many pairs in sequence, or in other words, $\alpha$ is left-divisible by $2$. Otherwise, it is odd.
It is easy to prove from this definition by transfinite recursion that the ordinals come in an alternating even/odd pattern, and that every limit ordinal (and hence every infinite cardinal) is even. Many transfinite constructions proceed by doing something different on the even as opposed to the odd stages, just as with finite constructions.
The smallest infinite ordinal is $\omega$, which is even on this definition, since having $\omega$ many pairs in sequence is order-isomorphic to $\omega$, and so $2\cdot\omega=\omega$. Meanwhile, the next infinite ordinal is $\omega+1$, which is odd. The ordinal $\omega+2$ is even, since it is equal to $2\cdot(\omega+1)$, even though it is not $\beta+\beta$ for any $\beta$.
(Please note that $\alpha=2\cdot\beta$ is not at all the same as saying $\alpha=\beta+\beta$, since $\beta$ copies of $2$ is not the same order type as $2$ copies of $\beta$, a phenomenon at the heart of the non-commutativity of ordinal multiplication. )
To explain the idea to a child, I would focus on the principal idea: whether finite or infinite, a number is even when it can be divided into pairs. For finite sets, this is the same as the ability to divide the set into two sets of equal size, since one may consider the first element of each pair and the second element of each pair. In the infinite context, as others have noted, there are numerous concepts of infinity, each with its own concept of even and odd. In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite:
$$1,2,3,\cdots,\omega,\omega+1,\omega+2,\cdots,\omega+\omega=\omega\cdot2,\omega\cdot 2+1,\cdots,\omega\cdot 3,\cdots,\omega^2,\omega^2+1,\cdots,\omega^2+\omega,\cdots\cdots$$
This concept of infinity is attractive to children, because they can learn to count into the infinite this way. Also, this concept of infinity has one of the most successful parity concepts, since one maintains the even/odd pattern into the transfinite. The smallest infinity $\omega$ is even, $\omega+1$ is odd, $\omega+2$ is even and so on. Every limit ordinal is even, and then it repeats even/odd up to the next limit ordinal.
See the Wikipedia entries on transfinite ordinals and ordinal arithmetic for more information about the ordinals.
I suggest that you read the discussion at Is infinity a number? first (since of course you need to answer that question to answer this question). There are some senses in which infinity is a number, and there are some senses in which infinity is not a number, and it all depends on what exactly you mean by "number," which in turn depends on what applications you have in mind.
On the other hand, there is a useful sense in which infinity is even. To explain this we have to replace "numbers" with cardinalities of sets.
Definition: A set $S$ has even cardinality if it can be written as the disjoint union of two subsets $A, B$ which have the same cardinality.
In other words, we need to be able to divide $S$ into pairs. This definition reduces to the ordinary definition for finite sets, but an infinite set always has even cardinality. For example, the cardinality of the natural numbers $\mathbb{N}$ is even because we can pair up even numbers with odd numbers.
This definition of "even" came up in my answer to this question, where precisely the above property turned out to be relevant.
Be aware there are many different notions of infinity in mathematics, so the answer to your query will depend on the particular notion of infinity that you have in mind, and how it interacts with the operations and relations of the extended "number" system. For example, if your notion of $\infty$ satisfies $\:1 +\infty = \infty\:$ then this may yield an obstruction to extending parity arithmetic.
Here is a simple example that has some hope of being comprehensible to a 6-year-old. I will explain it in a language that is hopefully comprehensible to his 38-year-old father. Consider the ring of polynomial functions with integer coefficients, i.e $\rm\:\mathbb Z[x] = \{\: a_0 + a_1\ x\ +\:\cdots\: + a_n\: x^n\ :\ a_i \in \mathbb Z\:\}\:.\:$ If we consider these functions in a neighborhood of $\rm\:+\infty\:$ we obtain an ordered ring. Namely, define $\rm\ f(x) > g(x)\:$ if this holds true on some neighborhood $\rm\:(x_0,\:+\infty)\:$ of $\rm\:+\infty\:,\:$ i.e. if there is some $\rm\:x_0\:$ such that it holds true for all $\rm\:x > x_0\:,\:$ i.e. if it is "eventually" true. One easily checks that this is well-defined. Indeed, since polynomials have only a finite number of roots, they eventually have constant sign. Thus if $\rm\:f\ne g$ then eventually $\rm\:f-g > 0\:$ or $<0$ so eventually $\rm\:f>g\:$ or $\rm\:g>f\:$. In fact one easily deduces that this is equivalent to defining the sign of a polynomial to be the sign of its leading coefficient (the leading term eventually dominates lower-degree terms). This makes it clear that every polynomial is either positive, negative or zero, and the positive polynomials are closed under addition and multiplication (these are precisely the properties required in general to define a total order on a ring, compatible with the ring operations).
This ring $\rm\:\mathbb Z]x]\:$ has "infinite" elements, e.g. $\rm\:x > n\:$ for all integers $\rm\:n\:$ since $\rm\:x - n\:$ is eventually $> 0\:.\:$ Can we extend parity arithmetic from $\:\mathbb Z\:$ to such infinite elements? In fact we can, in two different ways. First, we can define $\rm\:x\:$ to be even. Since, by the Factor Theorem, $\rm\:f(x) = f(0) + x\ g(x)\:$ for some $\rm\:g(x)\in \mathbb Z[x]\:,\:$ this amounts to defining the parity of $\rm\:f(x)\:$ to be the parity of its constant coefficient $\rm\:f(0)\:.\:$ Alternatively we can define $\rm\:x\:$ to be odd. Again, by the Factor Theorem, we have $\rm\:f(x) = f(1) + (x-1)\ g(x)\:$ for some $\rm\:g(x)\in \mathbb Z[x]\:.\:$ Since $\rm\:x-1\:$ is even, this amounts to defining the parity of $\rm\:f(x)\:$ to be that of $\rm\:f(1)\:,\:$ i.e. the sum of its coefficients. Both definitions lead to a consistent parity arithmetic in the extension ring $\rm\:\mathbb Z[x]\:.\:$ But in general there is no compelling reason to decide which parity we should assign to the infinite element $\rm\:x\:.\:$
In contrast, there are "number" systems extending the integers where parity arithmetic has a unique extension. For example, the rational numbers (fractions) expressible with odd denominator have parity arithmetic given by defining the parity of $\rm\: m/(2\:n+1)\:$ to be the parity of $\rm\:m\:.\:$ Also the Gaussian integers $\ m + n\ i\:,\ m,n\in \mathbb Z\:,\ i = \sqrt{-1}\:,\: $ have parity arithmetic given by defining $\:i\:$ to be odd. On the other hand, there are also such number rings with no extension of parity, or with numerous possible extensions. For further discussion see my post here.
Also, as JDH mentioned, parity arithmetic extends in some sense to more exotic structures such as ordinals, which may or may not satisfy your definition of a "number". Based on a few decades teaching such concepts, I suspect that you'll have much more luck teaching a 6-year-old a concept of parity of polynomials vs. ordinals. Indeed, my experience is that many adult educated layfolks have difficulty comprehending ordinals (I've had hundreds of interactions with such adults based on my popular posts about Goodstein's Theorem, e.g. see my sci.math post of Dec 11 1995; update: now migrated here).
A nice introduction to the many different notions of infinity in mathematics is Rudy Rucker's book: Infinity and the Mind. Unlike many other popularizations, the author has expertise in the field, having completed a Ph.D. on a related topic. Moreover, Rucker has gone to great lengths to make the presentation faithful to the mathematics but still accessible to an educated layperson.
JH Conway's Surreal Numbers have a well-defined notion of Omnific Integer which extends the definition of integer from finite numbers. I believe this splits infinite integers between odd and even numbers according to whether they are twice an integer or not, and such that Omnific Integers which differ by 1 always have opposite parities.
I would not recommend the theory to a 6-year-old, but Knuth's "Surreal Numbers" would be a good introduction for his father, and might give some interesting ideas on how to explore the idea of numbers with a child who is asking interesting questions.
"Infinity" is not a number, but there are numbers that are infinite, including cardinals, ordinals, infinite nonstandard reals, and other things. Some of those can be considered even numbers.
The "infinity" you encounter in calculus would not normally be considered a number.
There are also other notions of "infinity", such as the ones involved in the Dirac delta function and its derivatives. But it's hard to see how to view those as being numbers.
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Does it build discipline to shower with cold water? Are there other benefits why you would recommend it? Are the disadvantages?
It gives you a rush of endorphins, wakes you up, desensitises you to the cold for the rest of the day, and makes you feel like a man for doing it (although the effect of cold water can temporarily make you look "less of a man"...ahem).
In other words it gives you SOME of the benefits of a work-out all for spending a few minutes in cold water. Do it.
According to Tim Ferris yes. Cold shower and ice baths burns more calories than anything you do.
I don't have time to exercise in the morning so I take a cold shower to get my blood flowing (because of the shiver and flexing to stay warm) and wake myself up.
I usually shower with hot water and then, the last minute or so, I turn off the hot water and stand under the cold shower. I occasionally grunt and make spastic movements, but it really helps me getting awake in the morning!
I'll address the "discipline" part, since it's the first question.
What does "building discipline" mean? If you're basically saying:
I suppose so, although whether or not it leads to generalized self-discipline, IMO, is a bit up-in-the-air.
In other words, will doing one specific thing you don't like to do make it easier to do other specific things you don't like to do? Self-discipline can be viewed as a muscle: in this sense, yes, practicing self-discipline in one area will build the an ability that may be transferable to other areas.
At the same time, it's one thing to take a cold shower--it's another to do you taxes, read that book, make that apology, wash those dishes, not eat that box of cookies, finish that project... whatever it is that requires self-discipline to get done.
Ultimately, to me, self-discipline has a lot to do with paying attention and remaining conscious of your goals (a subset of "paying attention"). Constancy of purpose, consistency of action.
For me, the answer is no--cold showers wouldn't help build discipline. There are other benefits, as the other answers show. The biggest disadvantage is that it's a cold shower.

subset: commoncrawl


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Fueguia 1833 Perfume Going Global
Fueguia 1833, whose inspirations include imagined smell of Darwin's cabin on his voyage to Patagonia, plans to place its perfumes in 25 stores across the U.S. and Europe by the end of the year.
FOR THE PAST three years, only those willing to trek to Fueguia 1833's tiny retail outposts in Buenos Aires were able to get their hands on the label's signature fragrances, whose poetic inspirations range from an Argentine song lyric to the imagined smell of Darwin's cabin on his voyage to Patagonia.
Now, the Argentine perfumery is going global. Its perfumes are available at Roman perfume shop Campomarzio 70; its candles and room fragrances will arrive this month at Lucky Scent in Los Angeles and New York's Aedes de Venustas. The company plans to place its products in 25 stores across the U.S. and Europe by the end of the year.
The brand—founded in 2010 by Julian Bedel and Amalia Amoedo—was named as a homage to Fuegia Basket, a 19th-century Patagonian girl who was captured by Captain Robert Fitzroy and taken, along with three other South American Indians, to England to be "civilized" as part of a bizarre and disturbing social experiment. After two years, Basket and the other surviving captives were repatriated. They returned home on the HMS Beagle, along with a traveler named Charles Darwin.
Fueguia's nearly 60 fragrances draw on happier inspirations, too, such as South America's rich tradition of cultivating fragrant herbs, plants, woods and grasses. Though Mr. Bedel sources many of the 800 ingredients in France, he has teamed up with small-scale farms in Argentina, Peru and Paraguay to grow some of the essential elements. With a dose of brash confidence, Mr. Bedel likes to call Fueguia the first South American luxury brand.
The company organizes its products into nature- and literature-inspired collections, such as the plant-based Linneo (named after Carl Linnaeus, the father of taxonomy) or South American cedar-heavy Borges, named after surrealist Argentine writer Jorge Luis Borges.
The fragrances are technically unisex, but scents such as the sweet myrrh-laced Homero skew male, while the magnolia-based Malena and jasmine-accented Amalia are more feminine. The goods come wrapped in historic maps of Patagonia and tucked into handmade boxes crafted from recycled locally sourced wood.
—David Kaufman


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I noticed gobans are not square, but rectangular. Why is that, and what is the correct orientation of the board when playing?
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The design of Go components is all about symmetry. Because perspective shortens the vertical height of the board, the boards are made taller than they are wide. This way they appear to be square when you're playing. Another similar issue occurs with the stones. Black stones appear to be smaller than white stones, so the black stones are actually made slightly larger than the white stones to counter this effect.
Related and awesome: How many squares are there on a Go Board?
This is apparently to combat an optical illusion that "flattens" a board in front of you (as perspective narrows it towards the "horizon"). Therefore, the correct orientation is with the shorter edges in front of the players.
My japanese goban is exactly like that (45x42 cm²) and the effect it's actually noticeable after you have been playing for a while.
However, I also own a korean folding goban which is a bit smaller (understandably as it is supposed to be easier to carry around, with accordingly slightly smaller nice glass stones) which is exactly 38.5x38.5 cm², and although I cannot now find the reference (looked over the Internet and my books) I actually recall reading that Korean boards are usually squared instead of rectangular; maybe someone can find a source for this.
Anecdotically, our go club Sensei (a Japanese ex-insei) once really called us out in the middle of a game cause we had inadvertently put the goban the wrong way. It was amusing and embarrasing. So much, that in the end we called it a jigo, turned the board 90º and started a new game!
He actually nodded with his head and smiled the next time he came by to have a look.
Indeed it has to do something with perspective, but a full compensation for perpective would require a much more stretched board.
I believe the squares are stretched just enough so that vertically adjacent stones appear to be touching and not overlapping (consistent with horizontally adjacent stones). In that way, thicker stones require a deeper board than thinner stones.


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Obama's "grand" climate plan: reflections from a policy wonk
Jun. 25, 2013 / Posted by: Michelle Chan / Categories: Blog, Climate and Energy, Economics for the Earth
Today President Obama gave a much-anticipated climate change speech at Georgetown University. In true Obama fashion, the speech was pretty inspiring and sounded great; but dig a little deeper into the actual plan and you'll start uncovering ...Read More »


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When performing a FullTextSQLQuery against my SharePoint site's document library and retrieving field 'Path', I occasionally get the likes of "Forms/DispForm.aspx?ID=45" returned at the end of a record's Path field. Instead of this - I want the url of the file (deemac.pdf for example). What field do I instead to refer to?
SharePoint Search will return the url to the document in Path when it thinks a file is a document (isDocument == 1), but if the file isn't a recognized file type SharePoint will treat it as a list item and return the url of the display form in Path.
You can add support for more file types by adding IFilters (see here for PDF: How to configure PDF iFilter for SharePoint Server 2010 or Search Server 2010) or just add the file type as described in How to add a file type to the content index in SharePoint 2010
You should also consider using KeywordQuery instead of FullTextSQLQuery as this isn't supported when using FAST search or in SharePoint 2013
Try with FileName field as follow:
Hope it helps!! :)
It it's not then I believe, u have to go through the steps Per Jakobsen has mentioned above.
FileRef will give you the URL of file
FileDirRef will give you path of folder the file exists in
and FileLeafRef is the name of the file!
Hope this helps!
What you are looking at IS the URL needed. Forms/DispForm.aspx?ID=45 Let's break that URL down. "Forms/" It's a form. "DispForm.aspx" That's the form used to display results; which is what the search spider used. But with out an ID entry, you won't get any form results, just the form. "?ID=45" that's the particular form results to pull up and display.
So simply put, what you got IS the URL needed to display the results. What is being shown is the result of a form submission.


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By Michael Springer Photos by dotfordot.com
Specs and Tester's Comments
Anatomy of a Winner
Detailed Tool Features
Dust Collection / Stock Removal Charts
The workhorse sander for most tradesmen is the 5-inch-diameter random-orbit sander. Thanks to its ability to hog off stock with a coarse grit disk and leave a smooth, finished surface with a fine grit, this single tool has replaced the old progression of belt sander to half-sheet finish sander for many. It doesn't replace all sanders for all applications – but truth be told, it has replaced a lot of them over the past few decades.
The random-orbit sander gets its wide range of capabilities from its action. The sanding pad is connected to a free spinning bearing, which is mounted off-center to a flywheel driven at full motor speed. This design gives the pad a full-diameter spinning motion along with a small wiggling action known as the orbit. The amount of orbital action is determined by how far off-center the pad is mounted and is called the orbit size.
Credit: Photo: dotfordot.com
Under no-load conditions, the combined motion is relatively uniform, and a dot marked on the sanding pad often traces what looks like a spirograph pattern. But once the pad touches the work the equilibrium is broken and the tool moves more randomly, changing rotation speed and orbit shape in response to varying pressure from the user. Random-orbit sanders can remove material quickly because a lot of area is covered by the sanding disk every second; and they can leave a nearly swirl-free finish with the finest grits because their eccentric rotation doesn't follow the same path, so the scratch pattern is truly random.
A mechanical pad brake built into each tool adds enough friction to keep the pad from free-spinning up to full motor rpm; the brake is a wear part that eventually needs to be replaced. Earlier electric random-orbit sanders were made without pad brakes, similar to pneumatic models, but they were tricky to handle when lifted off the work surface. At rpm of 10,000 or more, a sanding disk could land on the work as aggressively as a grinder, and a free spinning disk was apt to fly off the pad violently and could nearly jerk the tool out of your hand.
Of the many random-orbit sanders on the market, we narrowed our test selections down to the newest 5-inch electric models with variable-speed settings, hook-and-loop sanding pads, and on-board dust-collection containers. The variable-speed setting lets you fine-tune the sander's performance for different materials and abrasives.
Slower speeds, our testers noted, reduce heat when sanding plastics, decrease pitch buildup on disks when sanding knotty pine, and help the grit dig in better on oily woods like teak. For most sanding, though, our testers use the top of the speed range, occasionally making slight adjustments down from the maximum to improve troublesome vibration harmonics. All of our comparative testing was done at the highest speed setting for consistency, and as a result should be pretty accurate for the single-speed versions of these sanders too.
Hook-and-loop sanding disk attachment is the most common system for electric random-orbit sanders. The disks are reusable and easy to change, and are said to run cool because of the slight air space between the disk and the pad. Some of these sanders can be fitted with a smooth pad for use with pressure-sensitive adhesive (PSA) disks, which are typically thinner and less expensive.
When testing these tools side by side, we evaluated ergonomic concerns like switch access, grip comfort, and vibration, as well as control and performance factors like how gently a sander "landed" on the work, how smoothly it tracked on the work while sanding, and the relative effectiveness of its dust-collection features.
But the most important test result was sanding quality – how evenly and completely each pass of the tool actually sanded the wood. Evenness can be described as the density of the scratch pattern created by the sander, and completeness as how effectively that pattern was spread by the entire disk surface. When these two elements – evenness and completeness – are well coordinated, the sanding grit contacts every last bit of the work surface uniformly and blends its scratch pattern in fewer passes, making the work ready for the next-finer grit sooner and helping that finer grit cover and remove the previous coarser scratches completely. Yes, random disk movement is essential for a fine finish, but a more consistent scratch pattern is easier to blend and cover in fewer passes than one with wild looping arcs. Viewed this way, sanding quality equals sanding efficiency.
Porter-Cable turned in the best sanding results consistently, with the fastest and most uniform finishing. A strong new motor design gives the tool a body shape that took some getting used to, but the results cannot be denied.
Festool took second with very refined but slower performance in a comfortable lightweight tool. Bosch earned third place with all-around high-quality sanding, comfort, and features. Competent sanders by Makita, Milwaukee, and Hitachi occupy the middle tier, followed by the less preferred DeWalt and Ridgid models. And trailing them all is the Craftsman sander.
Karsten of Karsten Balsley Woodworking and Kerry Stoen of Westwoods of Boulder contributed to this test; both are career custom woodworkers in Boulder, Colo.
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Binocular Holder- Beckson
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Binocular Holder (Beckson Marine)
Will fit almost all binocular models. Also holds books, magazines, etc. White PVC.
Will fit almost all binocular models. Also holds books magazines etc. White PVC.
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Taxi Driver - Widescreen Collector's AC3 Dolby [Blu-ray] for $9.99 + free shipping
"All the animals come out at night" -- and one of them is a cabby about to snap. In Martin Scorsese's classic 1970s drama, insomniac ex-Marine Travis Bickle (Robert De Niro) works the nightshift, driving his cab throughout decaying mid-'70s New York City, wishing for a "real rain" to wash the "scum" off the neon-lit streets. Chronically alone, Travis cannot connect with anyone, not even with such other cabbies as blowhard Wizard (Peter Boyle). He becomes infatuated with vapid blonde presidential campaign worker Betsy (Cybill Shepherd), who agrees to a date and then spurns Travis when he cluelessly takes her to a porno movie. After an encounter with a malevolent fare (played by Scorsese), the increasingly paranoid Travis begins to condition (and arm) himself for his imagined destiny, a mission that mutates from assassinating Betsy's candidate, Charles Palatine (Leonard Harris), to violently "saving" teen hooker Iris (Jodie Foster) from her pimp, Sport (Harvey Keitel).
2 Comments add a comment
One of the most imitated lines/scenes in modern film...
Same price as on Amazon.
Which I am ordering now from AZ...haven't seen in years.
Thanks for the reminder.


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The skeleton variant bloody skeleton has the special quality Deathless:
Deathless (Su): A bloody skeleton is destroyed when reduced to 0 hit points, but it returns to unlife 1 hour later at 1 hit point, allowing its fast healing thereafter to resume healing it. A bloody skeleton can be permanently destroyed if it is destroyed by positive energy, if it is reduced to 0 hit points in the area of a bless or hallow spell, or if its remains are sprinkled with a vial of holy water.
The point here is the destruction, if it is reduced to 0 HP in the area of a Bless spell. That does not seem to make sense. Bless is a burst and every ally is affected that is in the burst, but not one that enters the area later (at least I think that works that way). Why should it have any effect on Bloody skeletons? Hallow makes sense, it affects an area. Consecrate would make more sense than bless in that case. Is that an error, or what is the idea behind this?


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The Melbourne Cup is tomorrow. Known as the race that stops the. Nation, it at the very least stops Melbourne (public holiday), but most people around Australia stop for the 3 minutes it takes the horses to run the course.
If I wasn't so busy with travel preparations right now, I would organize an ingame event, similar to the running of the Gnomes where everyone drops down to the Shmmering Flats Mirage Raceway and run a few laps.
Of course to be authentic there would need to be masses of toons in tuxedos and ball gowns in the "car park" downing brews until they chunder.
So if you are online tomorrow, and feel the urge, organize an Azeroth Cup and tell me the results.
So on the subject of the race track, I think it would be cool if you could go there and join a repeatable quest, or better yet some kind of public instance where you race and Blizzard keeps track old your racing achievement.
There could be a PvE version (no inter-faction combat allowed unless flagged) and the deathmatch/destruction version where it's last rider standing.
Consider it a mini game within WoW.
Anyway, I hope your horse comes in tomorrow!
Gnomer and Out!


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Buy Big Buck Bunny for a penny, get $1 MP3 credit for $0.01
Purchase or rent any paid movie or TV show from Amazon Instant Video and get a $1 MP3 credit. Prime instant video streaming is not eligible for this promotion. Limit one promotional credit per customer.
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The promotional credit must be used by January 31, 2013. This offer is subject to Terms and Conditions.
Find out more about Big Buck Bunny here.
It's a great short film that most people will enjoy. Not to mention support the Blender Foundation and this to help them gain exposure.
Song & a movie for $0.01? I'm in!
Can't upvote enough! Thanks!
Same deal on the HD version:
big buck bunny is now free so it's a no go
Yep, didn't work for me either.
Any other Movies for $.01? My account shows the Big Buck Bunny movie (and its HD version) as Free instead of .01, and when I buy it I can't get the $1 MP3 credit (presumably because I haven't made the requisite paid purchase).


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Caramelised onions seem easier to make in large batches, so could I make a big batch then freeze them in say, ice cube trays, for later use? Or would this have a detrimental effect on them?
I would say it depends. I find once you freeze an item the flavor/texture/propeties of the item is changed (for better or for worse) the next time you goto use it.
If your using caramelized onions in a soup, or stew, something where flavors blend together for a longer period of time, then yes go ahead.
however if your using the caramelized onions on top of a steak or something similar. Then my answer would be no.
They will keep reasonably well if you put them in a clean jar and cover in oil.
I've never done this myself, but my guess is that the primary negative effect is that they may become mushy; being as they're mushy already, I'm pretty sure you can go right ahead.
I agree with Tree77. Depends on what you plan on using them for. I've successfully frozen them and used them in risotto, but risotto simmers for quite some time so the onions are almost liquefied by the end anyway. I would say if you plan to try this as a garnish on something like meat, you should get a better then usual vacuum seal on them before freezing and even then it might not work out.


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Is $L^2(\mathbb{R})$ a Banach algebra, with convolution?
I am pretty sure the answer is no, because I think that $f,g \in L^2(\mathbb{R})$ does not imply that $f*g \in L^2(\mathbb{R})$. However, I can't seem to find a counterexample, or a proof that this is not the case, using Fourier Transform for example.
Can someone give a hint? Thank you


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Around the World
This printable will give your children practice with their map and Spanish skills.
Grade Levels: 0-12 months - 5
To view this printable you need Adobe Acrobat Reader. Click to download Acrobat Reader - it's free!
From The Everything Kids' Puzzle Book Copyright © 2000, F+W Publications, Inc. Used by permission of Adams Media, an F+W Publications Company. All rights reserved.
To order this book go to Amazon.


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6 Aug 2013 10:59 AM #61
Feel free to share your struggle ssamayoa
Couple things to try:
1. follow this guide
2. turn on the debug flag
3. only use "configuration": "Debug" unless you're submitting to app storePhil Strong
18 Aug 2013 2:07 PM #62
18 Aug 2013 6:40 PM #63
How do you account for dependencies that are resources in a SA project? When I try to execute sencha generate I get error: Unknown definition for dependency.
20 Aug 2013 7:41 AM #64
For now you need to add these files in your app.json both css and jsPhil Strong
21 Aug 2013 4:01 PM #65
Cannot call method 'substring' of undefined, how to debug (Namespace issue)
I am getting this error in my app after I built using "sencha app build testing" command.
My environment is ,
Sencha Architect Version: 2.2.2 Build: 991
Sencha Cmd v18.104.22.1682
Sencha SDK 2.2.0
Mac OsX
I created Architect project first, developed it completely (around 40 classes) and enabled it with Sencha CMD for building.
I read several blogs and posts and already corrected few crazy issues.
Other posts suggest that this error is because of class is not loaded but script trying to instantiate.
I want to dig down that class using stacktrace in Chrome developer, but there is so much stuff that I can not find which class is not getting loaded.
I am ready to attach/send my app.js and index.html
Error occurs here when name is undefined.
if (name === from || name.substring(0, from.length) === from) { name = name.substring(from.length); if (typeof to != 'string') { root = to; } else { parts = parts.concat(to.split('.')); } break; }
23 Aug 2013 10:58 AM #66
My problem got resolved by changing build.options.testing.debug to true. It showed me which class was missing in "requires" (it was pullrefresh plugin which was not added by architect+cmd automatically)
I already had this setting to true in build.xml of project directory. But when I changed this setting in .sencha/app/testing.properties , it showed me the problem like a good boy .
CMDs properties variable overriding is very confusing. Not sure if it is bug or .sencha/app/testing.properties has higher priority in chain of properties override.
Hope somebody saves days or weeks reading this.
10 Oct 2013 10:22 AM #67
After banging my head for a while trying to get the "generate" to work with an existing Architect project I'd like to point out one small piece of advise that might help others that I didn't find (so if it's mentioned elsewhere I missed it).
Make sure your project does not already have an "index.html" file. If you do delete or rename it otherwise you'll get error after error while trying to run the "generate" command.
Hope this helps.
14 May 2014 3:24 PM #68
Is this thread (changes necessary to build using both SA and Sencha Cmd) still relevant for SA 3.0 and Cmd 4?
15 May 2014 8:11 AM #69
Good question seade. I'm happy to report NO! All of these alterations now happen automatically by either Architect or Cmd.Phil Strong
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text:
The words of Proverbs, Chapter 31 describe the woman of noble character. So must be the characterization of the needle artists whose vintage embroidery appears in this book. "The vintage woman's hands were eager to stitch; she was skilled and worked hard; she had a green thumb; she was a steward and economist; and of course, she was creative". The gardner and stitcher alike will delight in this medley of over 35 embroidery projects.
Item : IJ1031


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(273 Bytes)
Readd adlink.bat and adcomp.bat and other fixes.
Readd adlink and adcomp.
Add qoutes to fix broken build.
Get colfill tests working.
AMD builds should be -O2.
Build files should work with system variables CXXFLAGS and LDFLAGS.
Change order of linking libraries for mingw and cygwin.
Added contrib/lib and contrib/include.
Catch errors.
Remove more unneeded scripts.
Merge CC scripts to main admb scripts.
Start combining scripts.
Change order object files in adlink.
Fix admb scripts to build with$ admb ad2csv.cpp
Major changes to the gmake build files to simplify and improve.To use just type
$ make
Or for Visual C++
$ nmake
in the main source directory.
Allow admb and admb.bat scripts to do the following$ admb simple additional.cpp another.cpp
$ admb simple.tpl add.cpp
Merge changes from admb-11 branch.
Fixed linking for contributed libraries
dos2unix it.
fix contrib link problem
Add contrib library path.
Added support for linking user contributed libraries.
Minor improvements in adcomp/adlink/admb for Linux
Simplify and comment CXXFLAGS and LDFLAGS in adcomp, adlink, and admb
Fix scripts to pass CXXFLAGS and LDFLAGS to adcomp and adlink.
Copied revision 1006 from shibi to nceas. Old version control will now be only read only. This will be the primary version control.


text:
NUMBERS: Opponents of a more robust H-1B program declare that immigrant workers, particularly high skill workers, displace U.S. workers and drive down the wages of those workers. In many areas of the country, however, businesses are encountering something quite different: that there simply are not enough qualified, high skill U.S. workers to fill the needs of U.S. employers. High skill foreign professionals are therefore essential in filling these needs and complementing the native born workforce.
- U.S. professionals in information technology (IT) are doing well economically and are among the best-compensated workers in the world. "Software engineers have the best jobs in America," according to a 2006 Money magazine survey. American professionals in "computer and mathematical" occupations are at virtual full employment, with a low annual unemployment rate of 2.4 percent in 2006.
- Research by Paul E. Harrington, associate director of the Center for Labor Market Studies at Northeastern University, shows foreign-born and native professionals earn virtually identical salaries in math and science fields.
- Between 2003 and 2006, salaries in math and computer occupations increased by 9.5%, slightly more than the 8.2% for all occupations. Salaries for computer and information scientists increased 14.1% over the same 3 years.
- 57 percent of new H-1B professionals have earned a master's degree or higher. Companies find that foreign nationals account for 50 to 80 percent of advanced degree candidates in science and engineering disciplines at leading American universities.
- In an apparent effort to discredit the use of visas to hire foreign nationals in general, in 2007 critics started arguing that most H-1B visas are used by companies headquartered in India and that this deprives U.S. companies of the visas. However, USCIS data indicates that the 10 "outsourcing" companies cited most by critics used less than 14 percent of new H-1B petitions approved in 2006 for initial employment.
- Moreover, the new H-1B professionals hired in 2006 by these global companies totaled fewer than 15,000, representing 0.01 percent of the U.S. labor force and less than 4 percent of the approximately 440,000 people employed by these 10 companies worldwide. Given this relatively small number and proportion of employees, it is hard to argue that they are leading to a loss of large numbers of American jobs, particularly within the context of a U.S. economy producing employment for over 145 million people.
IMPACT: Studies show that high skill immigrants exact a positive net effect on native workers.
- Companies generally pay approximately $6,000 in legal and government-imposed fees when hiring an H-1B visa holder (and up to $10,000 more to sponsor an individual for permanent residence). Even among the relatively small number of employers where suspicion of abuse has been present the average underpayments owed to H-1B workers have turned out to be relatively small. In examining all DOL final agency actions between 1992 and 2004, one finds the average amount of back wages owed to an H-1B employee was $5,919.
- The unemployment rate for those in math and computer occupations is at 2.8 percent, compared to 4.7 percent nationally. This is virtually full employment, with those seeking work primarily between jobs, located in the wrong geographic region, or possessing the wrong skill set. This low unemployment rate is indicative, along with the demand for H-1B visas, of the demand for technology professionals in non-IT businesses that need to utilize information technology (IT), as well as in more traditional technology firms.
- A recent study by Madeline Zavodny, a research economist at the Federal Reserve Bank of Atlanta, concluded, "None of the results suggest that an influx of H-1Bs . . . lower contemporaneous average earnings."
- According to Zavodny's study, in fact, many of the results indicate a positive, statistically significant relationship." This would mean H-1B employment is actually associated with better job conditions for natives because H-1B professionals are complementary to native professionals.
NECESSITY: While high skill professionals—teachers, doctors, engineers, professors, lawyers, physical therapists, and computer professionals, among others—comprise less than one-tenth of one percent of the U.S. workforce, they are necessary, irreplaceable components of our country's preeminence in a variety of scientific and technical fields, competitiveness in the global market, and overall prosperity.
- For 12 months at a time during each of the past four fiscal years, no new H-1Bs could enter the U.S. labor market because the annual quota had been reached before the year started.
- Employers snapped up all H-1B visas the first day applications were submitted for FY 2008, turning foreign professionals away and leaving U.S. employers without the talent they need to fill jobs.
- If the arbitrary cap continues to prevent U.S. employers from hiring H-1Bs, we will see a disturbing trend continue—foreign professionals turned away from here and going abroad to work for our competitors, often taking with them knowledge, experience and expertise gained while studying or training in the U.S.
- The end result—an undesirable result that is fast approaching—is that U.S. preeminence in a variety of scientific and technical fields, competitiveness in the global market, and overall prosperity will suffer.
Published On: Tue, Jan 01, 2008 | Download File [1]


text:
The method of stationary phase is very well-known and employed in many areas of physics and mathematics, and, of course, included in various versions as theorem in textbooks, especially on pseudors and microlocal analysis.
However, it always is somewhat dependent on local coordinates and the Fourier transform, despite being a quite invariant problem. To be precise, the question would be the following.
Let $M$ be a manifold and $\phi: M \longrightarrow \mathbb{C}$ be a smooth function with values in the closed right half plane. Let $u$ be an volume density on $M$ with compact support in $M$. Determine an asymptotic expansion as $t \rightarrow \infty$ of the integral $$ I(\phi, u, t) = \int_M e^{-\phi t} u$$ under some nondegeneracy conditions on $\phi$.
(For example, one could require $\phi$ to be Morse or, more general, require that the set where it vanishes is a submanifold $C$ of $M$ and that at a point $p \in C$, the Hessian of $\phi$ is non-degenerate on the space $T_pM/T_pC$.)
It is well-known that in these cases $I(\phi, u, t)$ has an asymptotic expansion of the form $$ I(\phi, u, t) = (t/\pi)^{-(n-k)/2}\sum_{j=0}^\infty t^{-j} \int_C s_j,$$ where $k$ is the dimension of $C$ and the $s_j$ are certain volume densities on $C$. In fact, they have to be certain universal terms, depending only on the $2j$-th jets of $\phi$ and $u$ at $C$. This is not stated in most textbooks.
I wonder if it is possible to find these terms $s_j$ using Invariance theory alone. I would like if someone ever thought about this and knows a reference to this more invariant, geometric approach.
/Edit: To clarify my question: I was wondering if it is possible to determine the constants by invariance theory, i.e. some argument like "there is only one polynomial on the $2j$-jets of $u$ and $\phi$ that is invariant under coordinate transformation" or so. For the first term, this goes like this, supposed that $\phi$ is purely real:
Define the $n-k$-density $\mathrm{H}\phi$ on $C$ by setting $$\mathrm{H}\phi[X_1, \dots, X_{n-k}] := \sqrt{\left|\det \bigl( D^2\phi[X_i, X_j] \bigr)_{ij}\right|},$$ where $D^2\phi$ is the (on $C$ well-defined) Hessian of $\phi$. Now $u/\mathrm{H}\phi$ is a $k$-density on $C$ -- this is $s_0$.
Now there should be similar characterizations of the higher $s_j$ (which obviously can get arbitrarily complicated).


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text:
I mostly use Java and generics are relatively new. I keep reading that Java made the wrong decision or that .NET has better implementations etc. etc.
So, what are the main differences between C++, C#, Java in generics? Pros/cons of each?
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closed as too broad by animuson♦ Dec 5 '13 at 17:10
There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.
I'll add my voice to the noise and take a stab at making things clear:
C# Generics allow you to declare something like this.
and then the compiler will prevent you from putting things that aren't
The benefit of this is that it makes it really fast. There's no casting or any other stuff, and because the dll contains the information that this is a List of
The downside of this is that old C# 1.0 and 1.1 code (before they added generics) doesn't understand these new
Java Generics allow you to declare something like this.
On the surface it looks the same, and it sort-of is. The compiler will also prevent you from putting things that aren't
The difference is what happens behind the scenes. Unlike C#, Java does not go and build a special
The benefit of this approach is that old code which doesn't understand generics doesn't have to care. It's still dealing with the same old
The downside is the speed hit I mentioned previously, and also because there is no
C++ Templates allow you to declare something like this
It looks like C# and Java generics, and it will do what you think it should do, but behind the scenes different things are happening.
It has the most in common with C# generics in that it builds special
Both C# and Java produce output which is designed for virtual machines. If you write some code which has a
C++ produces raw x86 binary code. Everything is not an object, and there's no underlying virtual machine which needs to know about a
Because of this, the C++ compiler places no restrictions on what you can do with templates - basically any code you could write manually, you can get templates to write for you.
In C# and Java, the generics system needs to know what methods are available for a class, and it needs to pass this down to the virtual machine. The only way to tell it this is by either hard-coding the actual class in, or using interfaces. For example:
That code won't compile in C# or Java, because it doesn't know that the type
And then you have to make sure the things you pass to addNames implement the IHasName interface and so on. The java syntax is different (
The 'classic' case for this problem is trying to write a function which does this
You can't actually write this code because there are no ways to declare an interface with the
C++ suffers from none of these problems. The compiler doesn't care about passing types down to any VM's - if both your objects have a .Name() function, it will compile. If they don't, it won't. Simple.
So, there you have it :-)
C++ rarely uses the "generics" terminology. Instead, the word "templates" is used and is more accurate. Templates describes one technique to achieve a generic design.
C++ templates is very different from what both C# and Java implement for two main reasons. The first reason is that C++ templates don't only allow compile-time type arguments but also compile-time const-value arguments: templates can be given as integers or even function signatures. This means that you can do some quite funky stuff at compile time, e.g. calculations:
This code also uses the other distinguished feature of C++ templates, namely template specialization. The code defines one class template,
Template specialization is important for C++ because it allows for structural differences in data structures. Templates as a whole is a means of unifying an interface across types. However, although this is desirable, all types cannot be treated equally inside the implementation. C++ templates takes this into account. This is very much the same difference that OOP makes between interface and implementation with the overriding of virtual methods.
C++ templates are essential for its algorithmic programming paradigm. For example, almost all algorithms for containers are defined as functions that accept the container type as a template type and treat them uniformly. Actually, that's not quite right: C++ doesn't work on containers but rather on ranges that are defined by two iterators, pointing to the beginning and behind the end of the container. Thus, the whole content is circumscribed by the iterators: begin <= elements < end.
Using iterators instead of containers is useful because it allows to operate on parts of a container instead of on the whole.
Another distinguishing feature of C++ is the possibility of partial specialization for class templates. This is somewhat related to pattern matching on arguments in Haskell and other functional languages. For example, let's consider a class that stores elements:
This works for any element type. But let's say that we can store pointers more effciently than other types by applying some special trick. We can do this by partially specializing for all pointer types:
Now, whenever we instance a container template for one type, the appropriate definition is used:
Anders Hejlsberg himself described the differences here "Generics in C#, Java, and C++".
There are already a lot of good answers on what the differences are, so let me give a slightly different perspective and add the why.
As was already explained, the main difference is type erasure, i.e. the fact that the Java compiler erases the generic types and they don't end up in the generated bytecode. However, the question is: why would anyone do that? It doesn't make sense! Or does it?
Well, what's the alternative? If you don't implement generics in the language, where do you implement them? And the answer is: in the Virtual Machine. Which breaks backwards compatibility.
Type erasure, on the other hand, allows you to mix generic clients with non-generic libraries. In other words: code that was compiled on Java 5 can still be deployed to Java 1.4.
Microsoft, however, decided to break backwards compatibility for generics. That's why .NET Generics are "better" than Java Generics.
Of course, Sun aren't idiots or cowards. The reason why they "chickened out", was that Java was significantly older and more widespread than .NET when they introduced generics. (They were introduced roughly at the same time in both worlds.) Breaking backwards compatibility would have been a huge pain.
Put yet another way: in Java, Generics are a part of the Language (which means they apply only to Java, not to other languages), in .NET they are part of the Virtual Machine (which means they apply to all languages, not just C# and Visual Basic.NET).
Compare this with .NET features like LINQ, lambda expressions, local variable type inference, anonymous types and expression trees: these are all language features. That's why there are subtle differences between VB.NET and C#: if those features were part of the VM, they would be the same in all languages. But the CLR hasn't changed: it's still the same in .NET 3.5 SP1 as it was in .NET 2.0. You can compile a C# program that uses LINQ with the .NET 3.5 compiler and still run it on .NET 2.0, provided that you don't use any .NET 3.5 libraries. That would not work with generics and .NET 1.1, but it would work with Java and Java 1.4.
Follow-up to my previous posting.
Templates are one of the main reasons why C++ fails so abysmally at intellisense, regardless of the IDE used. Because of template specialization, the IDE can never be really sure if a given member exists or not. Consider:
Now, the cursor is at the indicated position and it's damn hard for the IDE to say at that point if, and what, members
It gets worse. What if
After a bit of thinking, a programmer would conclude that this code is the same as the above:
Wrong. At the point where the compiler tries to resolve this statement, it doesn't actually know
Now, the code compiles. To see how ambiguities arise from this situation, consider the following code:
This code statement is perfectly valid and tells C++ to execute the function call to
Both Java and C# introduced generics after their first language release. However, there are differences in how the core libraries changed when generics was introduced. C#'s generics are not just compiler magic and so it was not possible to generify existing library classes without breaking backwards compatibility.
For example, in Java the existing Collections Framework was completely genericised. Java does not have both a generic and legacy non-generic version of the collections classes. In some ways this is much cleaner - if you need to use a collection in C# there is really very little reason to go with the non-generic version, but those legacy classes remain in place, cluttering up the landscape.
Another notable difference is the Enum classes in Java and C#. Java's Enum has this somewhat tortuous looking definition:
(see Angelika Langer's very clear explanation of exactly why this is so. Essentially, this means Java can give type safe access from a string to its Enum value:
Compare this to C#'s version:
As Enum already existed in C# before generics was introduced to the language, the definition could not change without breaking existing code. So, like collections, it remains in the core libraries in this legacy state.
11 months late, but I think this question is ready for some Java Wildcard stuff.
This is a syntactical feature of Java. Suppose you have a method:
And suppose you don't need to refer to the type T in the method body. You're declaring a name T and then only using it once, so why should you have to think of a name for it? Instead, you can write:
The question-mark asks the the compiler to pretend that you declared a normal named type parameter that only needs to appear once in that spot.
There's nothing you can do with wildcards that you can't also do with a named type parameter (which is how these things are always done in C++ and C#).
Wikipedia has great write-ups comparing both Java/C# generics and Java generics/C++ templates. The main article on Generics seems a bit cluttered but it does have some good info in it.
The biggest complaint is type erasure. In that, generics are not enforced at runtime. Here's a link to some Sun docs on the subject.
C++ templates are actually much more powerful than their C# and Java counterparts as they are evaluated at compile time and support specialization. This allows for Template Meta-Programming and makes the C++ compiler equivalent to a Turing machine (i.e. during the compilation process you can compute anything that is computable with a Turing machine).
In Java, generics are compiler level only, so you get:
Note that the type of 'a' is an array list, not a list of strings. So the type of a list of bananas would equal() a list of monkeys.
So to speak.
Looks like, among other very interesting proposals, there is one about refining generics and breaking backwards compatibility:
NB: I don't have enough point to comment, so feel free to move this as a comment to appropriate answer.
Contrary to popular believe, which I never understand where it came from, .net implemented true generics without breaking backward compatibility, and they spent explicit effort for that. You don't have to change your non-generic .net 1.0 code into generics just to be used in .net 2.0. Both the generic and non-generic lists are still available in .Net framework 2.0 even until 4.0, exactly for nothing else but backward compatibility reason. Therefore old codes that still used non-generic ArrayList will still work, and use the same ArrayList class as before. Backward code compatibility is always maintained since 1.0 till now... So even in .net 4.0, you still have to option to use any non-generics class from 1.0 BCL if you choose to do so.
So I don't think java has to break backward compatibility to support true generics.