Does P≠NP over ℝ imply P≠NP ?
where ℝ is for Real number algorithms as described by Smale with a suitable formulation of P≠NP over ℝ.
Complexity Theory and Numerical Analysis, Steve Smale, 2000
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.4678&rep=rep1&type=pdf
The local-global principle you are citing comes from the fact that for any open subgroup $Hleq G$, $H^n(G,A)stackrel{text{Res}}{longrightarrow}H^n(H,A)stackrel{text{Cor}}{longrightarrow}H^n(G,A)$ is multiplication by $[G:H]$. So from that you can derive lots of local-global principles. E.g. as a generalisation of the one you cite, you can deduce that if $H_1$ and $H_2$ are two open subgroups of co-prime index such that $H^n(H_i,A)=0$ for $i=1,2$, then $H^n(G,A)=0$.
In the simply connected case, essentially everything is in principle computable, by some very early work of E.H. Brown:
bib{MR0083733}{article}{
author={Brown, Edgar H., Jr.},
title={Finite computability of Postnikov complexes},
journal={Ann. of Math. (2)},
volume={65},
date={1957},
pages={1--20},
issn={0003-486X},
review={MR{0083733 (18,753a)}},
}
In particular, if $X$ and $Y$ are finite simplicial complexes then $[Sigma^n X,Sigma^n Y]$ is computable for $ngeq 2$, and for large $n$ this gives the group of stable homotopy classes of maps. However, I do not think that there are practical algorithms for many such questions, although I am not up to date on this. Probably the simplest case that I do not know is as follows: is there a practical algorithm to compute the complex $K$-theory $K^0(X)$ for a finite simplicial complex $X$?
To add to what Charles wrote, another reference is Mac Lane and Moerdijk's Sheaves in Geometry and Logic. They prove something a bit more general, involving Lawvere-Tierney topologies on a topos. For the purposes of understanding what I'm about to write, it's not necessary to know what a Lawvere-Tierney topology is.
Mac Lane and Moerdijk's book contains the following two results:
Let $mathcal{E}$ be a topos. Then the subtoposes of $mathcal{E}$ (i.e. the reflective full subcategories with left exact reflectors) correspond canonically to the Lawvere-Tierney topologies on $mathcal{E}$.
Let $mathbf{C}$ be a small category. Then the Lawvere-Tierney topologies on $mathbf{Set}^{mathbf{C}^{mathrm{op}}}$ correspond canonically to the Grothendieck topologies on $mathbf{C}$.
Result 1 is almost part of Corollary VII.4.7. The "almost" is because they don't go the whole way in proving the one-to-one correspondence, but I guess it's not too hard to finish it off. (Edit: it also appears as Theorem A.4.4.8 of Johnstone's Sketches of an Elephant, where Lawvere-Tierney topologies are called local operators.) Result 2 is Theorem V.4.1.
I agree with the point of view that Charles advocates. When I started learning topos theory I got bogged down in detailed stuff about Grothendieck topologies, and it all seemed pretty technical and unappealing. It wasn't until years later that I learned the wonderful fact that Charles mentions: an elementary topos is Grothendieck iff it's a subtopos of some presheaf topos. I wish someone had told me that in the first place!
When Harry needed help escaping Malfoy Manor, Aberforth Dumbledore sent Dobby to apparate them out of there:
... the mirror fragment fell sparkling to the floor, and he saw a gleam of brightest blue -
Dumbledore’s eye was gazing at him out of the mirror.
“Help us!” he yelled at it in mad desperation. “We’re in the cellar of Malfoy Manor, help us!”
The eye blinked and was gone.
(Deathly Hallows, Chapter 23, "Malfoy Manor")
Dobby would never be able to tell them who had sent him to the cellar, but Harry knew what he had seen. A piercing blue eye had looked out of the mirror fragment, and then help had come.
Help will always be given at Hogwarts to those who ask for it.
(Deathly Hallows, Chapter 24, "The Wandmaker")
He wore spectacles. Behind the dirty lenses, the eyes were a piercing,
brilliant blue.
“It’s your eye I’ve been seeing in the mirror.”
There was a silence in the room. Harry and the barman looked
at each other.
“You sent Dobby.”
The barman nodded and looked around for the elf.
(Deathly Hallows, Chapter 28, "The Missing Mirror")
So, when Harry begged for help, how did he know to send a House-Elf?
How did he know that Malfoy Manor had anti-apparation set up?
OK, being an old-timey wizard he might have guessed that it'd be the case, but I'd like canon support for why he thought so.
How did Aberforth know that a House-Elf would be a correct solution to that problem?
The fact that house-elf magic is different and especially that they can apparate in anti-apparation jinx conditions doesn't seem to be a widely held knowledge in the series; and Aberforth isn't "learned" like Albus.
It is an example of chiasmus, which is
- Repetition of ideas in inverted order
- Repetition of grammatical structures in inverted order (not to be mistaken with antimetabole, in which identical words are repeated and inverted).
See here or any other reputable source. (One of my favorites, from which the above is drawn, is Silva Rhetoricae.
My interpretation is that the syntax is correct, and "termination" is necessary. The more common idiom "to come up" (to emerge, happen, arise, be noticed) is being combined with the prepositional phrase "for termination". The law regarding freedom from land obligations "came up" (in that it came to people's attention) in 1863, and specifically for the purpose of being terminated.
Semantically, it does seem rather confusing, I will admit. I think the author's intent was that the obligations themselves came up for termination, not the freedom from the obligations, but I don't know enough about Russian history to say which actually happened.
Star Trek is one of the few SF shows to have the distinction of running long enough to make some of their original situations outdated.
In the original Star Trek, the Eugenics wars took place between 1993-1996. Star Trek: The Next Generation was produced from 1987 until 1994, so it was being produced during that time period and Star Trek: Voyager started production after that, so those shows were actually produced during and after the time when Earth was supposedly going through a terrible war.
While the Eugenics Wars were not mentioned in The Next Generation or Deep Space Nine, and were never directly mentioned in Voyager. However, The Next Generation started with Q putting humanity on trial in a courtroom modeled after trials that took place after World War III, which is in the 21st century.
In Voyage there are at least two episodes that deal with the late 1990s or early 21st century, a time that was after the Eugenics wars were supposed to happen. In Future's End, the ship Voyager is in orbit around Earth in 1996 (current time for viewers when it was produced) and crew members spend time on Earth. Everything looks as we'd expect for people living in 1996. There's no trace of the Eugenics wars or any of the aftermath. In the episode 11:59 we see Janeway's ancestor in the year 1999 and there's no trace of any recent wars.
While this was necessary, since Trek had been around so long, at that time, that it had outdated itself, it does create problems in terms of internal continuity. I realize that the Voyager producers were more concerned about not confusing newer viewers than about maintaining continuity with a show that aired 20 years before then, but there are repeated references to Kirk later in the series that do keep some continuity between the shows.
Was there ever any on-screen or canon reference to this? Was the timing of the Eugenics wars moved forward to fit a new timetable? Were they just combined with World War III, sometime in the 21st century? Were retconned dates for the Eugenics wars ever given to go with a revised timeline?
If this was never addressed in canon, did any of the novels or games provide any explanation for the discontinuity between the 1990s as the time for the Eugenics Wars and the fact that we're still here, without such wars, in the 21st century?
Please understand: I know what the Eugenics Wars were and about them. What I'm focusing on, with this question, is what was done within the studio or the writer's meetings to handle the retconning when our world caught up to the time of the Eugenics Wars and Voyager was airing episodes of their characters visiting our non-wartorn planet instead of one decimated by those wars. Or did the writers in Voyager even realize that was an issue?
Quantum slipstream transcends the normal warp barrier by penetrating the quantum barrier with a focused quantum field. What is the quantum barrier you say? It's technobabble, and it's not explained in canon.
The net effect is that quantum slipstream technology far exceeds the speeds capable with a normal warp drive, and rivals the Borg transwarp technology. Transwarp isn't a specific type of drive, but a class of propulsion technologies that exceed the normal warp limits. In this sense, quantum slipstream would be a subset of transwarp technology.
In terms of speed comparisons, it's very hard to make a direct comparison because the writers played fast and loose with the velocities each warp factor corresponded to.
Let's start with a given: based on the episode "Hope and Fear", Voyager was able to travel 300 light years with one hour of use of the quantum slipstream drive it had.
Under the original series warp scale, traveling that distance at Warp 9 would take about 5 months.
They revised the scale for The Next Generation, and it's assumed that's what all subsequent series used. The new scale is discussed in the technical manual for The Next Generation, and is reportedly based on the formula:
On that scale, traveling that distance at Warp 9 would take about 2.3 months. This should be considered the "canon" answer, as the formula isn't explicitly contradicted by any later canon sources.
However, in "Caretaker", it's established Voyager would take 75 years at maximum speeds to reach Earth, which is 70,000 light years away. This would indicate, based on the scale for The Next Generation, Voyager's top speed to only be around Warp 7.78. This is contradicted over and over again throughout the series as Warp 9 is routinely mentioned in dialogue.
Indeed, as Memory Alpha notes, the unpublished (and consequently non-canon) technical manual for Voyager reportedly stated the "maximum speeds" talked about in "Caretaker" was actually Warp 9.6, which would indicate a different scale than that which is used in The Next Generation.
But let's discount the estimate in "Caretaker" as being too slow and continue to assume the warp scale factor hadn't changed in Voyager's time (a reasonable thing to assume since Voyager and the latter part of TNG's exploits occur simultaneously).
According to the technical manual for The Next Generation, Warp 9.6 was only sustainable on a Galaxy-class starship for no more than 12 hours. However, Voyager—an Intrepid-class starship—was designed and constructed several years after the Galaxy-class starships. We're also given every indication that Voyager is a marked improvement over previous ship designs, so it's reasonable to posit that Voyager might be indeed be able to sustain Warp 9.6 as a maximum speed, in the same vein that Janeway described it in "Caretaker".
Based on this, we can conclude that under maximum speeds, Voyager would take a little less than 2 months to reach the same distance it traveled with just one hour of quantum slipstream use.
Of course as you mentioned, in "Timeless", the claim is made that 10 years was shaved off the journey. This is where you just need to take a step back and just ignore the math. Assuming this is true, and assuming the figures for "Hope and Fear" are correct, it would mean Voyager traveled 18,900 light years.
But, wait a minute: this is crazy. "Caretaker" establishes Voyager was at most 70,000 light years from Earth, but Janeway claims they only took 10 years off their trip. Which would mean Earth was actually more than 142,000 light years away in "Caretaker".
To put that number into perspective: the diameter of the Milky Way is only 100,000 light years. Yeah, this is not going to add up.
So we're left with a paradox. To resolve it, either the numbers in "Hope and Fear" are wrong, the numbers in "Timeless" are wrong, or the quantum slipstream drive in "Timeless" is significantly slower than the one in "Hope and Fear".
For the sake of argument, let's say the one in "Timeless" is a "baby" quantum slipstream drive, and is just nowhere near the speed of the original version. Given it shaved 10 years off the trip, that means it traveled 9,333 light years. What would that tell us about Voyager's cruising speed?
Well, it tells us that it would take 10 years to travel 9,333 light years only if you were going warp 7.78, which is vastly lower than regular warp limits. I'm pretty sure they could've went faster if they got out and pushed.
And that's exactly the same estimate in "Caretaker", isn't it? Assuming Voyager's top speed isn't around warp 7 or 8, it seems Voyager is running off of a different warp scale from The Next Generation that's internally consistent, at least with these two data points. And if it is, it means Voyager was just way slower than earlier ships established in The Next Generation and Deep Space Nine.
My head's starting to hurt, but let's just continue to use The Next Generation's warp scale and compare this cruising speed to the distance mentioned in "Hope and Fear": 300 light years. To travel that distance at warp 7.78, it would take a little under 4 months.
The lesson to be learned from all of this is that the only concrete thing about quantum slipstream technology is that it's really fast and served as a fairly decent plot device to back out of a really huge and unreasonable time estimate established in the first episode.
As an aside, I point out the problems with the "Caretaker" estimate to illustrate the difficulties of direct speed comparisons, but as pointed out in the comments, it could be that Janeway really meant "maximum safe cruising speed" instead of "maximum speed", which would indicate she was unwilling to unreasonably tax Voyager's engines just to gun it back home.
In this case, the only discrepancy in warp scale factors would be the figure in the unpublished and non-canon technical manual for Voyager, and one starts to wonder if those sorts of technical discrepancies is why it was never published.
The Doctor is an attractive figure, not always only in the physical sense.
When things seem most hopeless, he bursts onto the scene in his time machine, and, with a few words and a wave of his screwdriver, dismantles the villains' carefully built plans.
He has done a lot of terrible things, but he has also achieved many incredible things. He is, though he does not recognize it, a hero. He has saved the entire human race hundreds of times, the universe several times, and the entire Doctor Who multiverse at least once.
He defeated the Master when he attempted to subjugate humanity with the Toclafane , and when he attempted to rule the universe by releasing the entropy wave from Logopolis, or when he tried to turn all humans on Earth into his clones, or when....
He stopped the Daleks in the xenocidal crusade again and again, even preventing them from destroying all universes at the Medusa Cascade.
He defeated the Cybermen, the Great Intelligence, the Memeovore, the Fendahl, the Silence, the Great Intelligence.
He has had to make some pretty difficult decisions, and sometimes made the wrong ones, but he always cares.
To his companions, the Doctor must be the very embodiment of adventure.
They all grow to admire him in some respect.
Indeed, Rose, Martha, Jack, and Amy (among others) fell in love with the Doctor.
And Clara travels with this person for years. Of course she will admire him. Of course she will want to be like him.
Even Moffat wants to be the Doctor:
"But when they made this particular hero, they didn't give him a
gun--they gave him a screwdriver to fix things. They didn't give him a
tank or a warship or an x-wing fighter--they gave him a box from which
you can call for help. And they didn't give him a superpower or pointy
ears or a heat-ray--they gave him an extra HEART. They gave him two
hearts! And that's an extraordinary thing. There will never come a
time when we don't need a hero like the Doctor.”
Far more than any other companion on the new series (well, except Jack), Clara has much less to tie her to Earth. Rose had her mother (and her alternate-universe father, and initially Mickey). Martha had her parents and siblings. Donna had her grandfather and her mother. Rory and Amy had each other. Clara had Danny Pink, and then he died. It is no coincidence that she threw herself into travelling with the Doctor after this loss.
When travelling, and adventuring, and heroism became all of Clara's life, it was the first step on the path to becoming like the Doctor. After all, his lifestyle became the very model for hers.
All the other companions experienced this, to some degree. Witness Martha taking up alien fighting with UNIT, or Jack working with Torchwood, or Sarah Jane Smith running her own outfit for managing extraterrestrial threats (and allies).
All of the Doctor's companions become more like the Doctor. It was strongest for Clara, because she had so few other ties.
Depending on what you mean, then no. Elliptic curves (abstractly) are in bijection with lattices modulo homothety (also, the upper half plane modulo SL(2,Z)). As for the Lie algebra of an elliptic curve, an elliptic curve is abelian, so the lie algebra is a one dimensional abelian complex Lie algebra, so it has trivial bracket.
There is also "The Wizards Of Pung's Corners" by Pohl, which considers adding in the effects of novelty, advertising, recycling and automated factories into this same situation. After a small-scale nuclear exchange, the automated bomb-proof factories of both the USSR and America produce goods non-stop as they can no longer be accessed; selling consumer goods becomes such an important part of the economy to prevent stockpiling, advertising companies become a wing of the US government and are housed in the Pentagon. The story focuses on a small town, Pung's Corners, and the attempts by the government to drag them into the never ending cycle of consumption and recycling of goods. It also satirizes over-support of field troops, and advertising in general.
They're interchangeable -- "can't hardly" is a regional/dialectical variant. The proscription against emphatic double negatives is purely artificial in English; they have been around as long as the English language itself.
Ne con ic noht singan; and ic for žon of þeossum gebeorscipe ut eode ond hider gewat, for þon ic naht singan ne cuðe.
Twice in that sentence (from the prologue to Cædmon's Poem from the Venerable Bede), Cædmon says the equivalent of "I can't sing nothing". Similar examples can be found in Chaucer, Shakespeare, the letters of Abigail Adams, and so on.
Double negatives used for emphasis are as idiomatic to English as split infinitives. Use whichever version you're comfortable with -- unless you're turning a composition in to be marked -- and realise that others do not need to be corrected out of it.
There are a couple of mathematical points to make which inform the English involved.
(1) 'Addition' (yes, simple addition!) covers two major operations:
(a) Combination of two elements from a set (a binary operation) (eg 3 marbles + 2 marbles = 5 marbles).
(b) Transformation of one element into another (a unary operation) (eg a 3cm-long worm grows by 2cm )
Both are modelled identically by 3 + 2 = 5, but a transformation arrow with '+2' over the top is fitting for the transformation.
In the first case, addend + addend = sum / total
In the second case, augend + addend = sum / total.
(2) We've had a thread discussing the fact that there is no agreed term for the result of a subtraction; 'directed difference' is used by some.
I'm pretty sure you're thinking of Theodore Sturgeon's 1940 novelette "It", a famous story which has been reprinted many times and has its own Wikipedia page. If so, you have misremembered a couple of details, or perhaps you read one of the comic book adaptations/ripoffs of Sturgeon's classic yarn. Sturgeon's creature formed in the woods, not the river:
It walked in the woods.
It was never born. It existed. Under the pine needles the fires burn, deep and smokeless in the mold. In heat and in darkness and decay there is growth. There is life and there is growth. It grew, but it was not alive. It walked unbreathing through the woods, and thought and saw and was hideous and strong, and it was not born and it did not live. It grew and moved about without living.
It crawled out of the darkness and hot damp mold into the cool of a morning. It was huge. It was lumped and crusted with its own hateful substances, and pieces of it dropped off as it went its way, dropped off and lay writhing, and stilled, and sank putrescent into the forest loam.
It had no mercy, no laughter, no beauty. It had strength and great intelligence. And—perhaps it could not be destroyed. It crawled out of its mound in the wood and lay pulsing in the sunlight for a long moment. Patches of it shone wetly in the golden glow, parts of it were nubbled and flaked. And whose dead bones had given it the form of a man?
There is no boy for it to dissect. Instead it dissects an unidentified field-creature, then a dog, and then the dog's owner (a young man probably in his twenties), all out of intellectual curiosity:
Kimbo slowed, then flipped himself through the air at the monster's throat. His jaws closed on it; his teeth clicked together through a mass of filth, and he fell choking and snarling at its feet. The thing leaned down and struck twice, and after the dog's back was broken, it sat beside him and began to tear him apart.
[. . .]
The thing in the woods looked curiously down at what it had done to Kimbo, and tried to moan the way Kimbo had before he died. It stood a minute storing away facts in its foul, unemotional mind. Blood was warm. The sunlight was warm. Things that moved and bore fur had a muscle to force the thick liquid through tiny tubes in their bodies. The liquid coagulated after a time. The liquid on rooted green things was thinner and the loss of a limb did not mean loss of life. It was very interesting, but the thing, the mold with a mind, was not pleased. Neither was it displeased. Its accidental urge was a thirst for knowledge, and it was only—interested.
Alton is the next victim. Kimbo was Alton's dog, and Cory is Alton's brother:
It was terrible that they died the same way. Cory Drew was a strong man, but he gasped and fainted dead away when he saw what the thing of the mold had done to his brother and his brother's dog.
[. . .]
It took Cory more than a moment to recover himself from what he had seen. He turned away from it and leaned weakly against a pine, panting. Alton. That was Alton, lying there, in—parts.
It caught Cory's little girl, and no doubt would have dissected her too, but she managed to get away:
Babe opened her eyes, saw that she was free, and just as the thing turned back to her she dove between its legs and out into the shallow pool in front of the rock, paddled across and hit the other bank screaming. A vicious little light of fury burned in her; she picked up a grapefruit-sized stone and hurled it with all her frenzied might. It flew low and fast, and struck squashily on the monster's ankle. The thing was just taking a step towards the water; the stone caught it off balance, and its unpracticed equilibrium could not save it. It tottered for a long, silent moment at the edge and then splashed into the stream. Without a second look Babe ran shrieking away.
It meets its end in the brook:
The monster lay in the water. It neither liked nor disliked this new element. It rested on the bottom, its massive head a foot beneath the surface, and it curiously considered the facts that it had garnered. [. . .] There was this new cold moving thing he had fallen into. It was washing his body away. That had never happened before. That was interesting. The monster decided to stay and observe this new thing. It felt no urge to save itself; it could only be curious.
[. . .]
"I am smaller," the thing thought. "That is interesting. I could not move now. And now this part of me which thinks is going, too. It will stop in just a moment, and drift away with the rest of the body. It will stop thinking and I will stop being, and that, too, is a very interesting thing."
So the monster melted and dirtied the water, and the water was clean again, washing and washing the skeleton that the monster had left. It was not very big, and there was a badly-healed knot on the left arm. The sunlight flickered on the triangular silver plate set into the pale skull, and the skeleton was very clean now. The brook laughed about it for an age.
I'm looking for a single word that describes a "legal ability to advertise" ("... to publish" and "... to communicate" are viable options too). I would like to use it in the following sentence:
You have 3 days until advertiseability of x.
I've considered communicability but I think it's related mostly to diseases.
The context is: I'm trying to find a name for a function in a programming language, so it should be short and concise. Something like: daysUntilAdvertiseabilityOf(x); Basically, you can publish an ad in three days, but not before.
Hi, I am reading an article and have encountered a remark in a proof which is not clear to me.
Maybe someone can help?
The proposition is:
Let X be a topological space without isolated points having countable $ pi $-weight and such that every nowhere dense subset in it is closed. Then it is a Pytkeev space.
Here is the begining of the proof:
Let $ x in Cl(A) setminus A$. Then $ x in Cl(Int(Cl(A))) $, because every nowhere dense set is closed (and hence discrete)...
The thing which is not clear to me:
Why can one conclude that every nowhere dense closed set is discrete? Suppose I take the set $ mathbb N$ with the cofinite topology. Then the finite sets are closed and nowhere dense. But as far as I undesrtand they are not discrete since every open set in the topology that contains a finit set also has to contain other points since it is infinite.
Can somone see what am I missing?
The definition of a Ptkeev space:
Let X be a topological space.
A point x is called a Pytkeev point if whenever $ x in overline {Asetminus{x}}$, there exists a countable $ pi $-net of infinite subsets of A. If every point of a space is a Pytkeev point then the space is called a Pytkeev space.
Thanks!
This question was studied in the early days of elementary topos theory, and the connection was worked out by Bill Mitchell and J.C. Cole (independently, as far as I know). The MathSciNet references are:
MR0319757 (47 #8299)
Mitchell, William,
Boolean topoi and the theory of sets.
J. Pure Appl. Algebra 2 (1972), 261--274.
MR0357116 (50 #9584)
Cole, J. C.,
Categories of sets and models of set theory. The Proceedings of the Bertrand Russell Memorial Conference (Uldum, 1971), pp. 351--399. Bertrand Russell Memorial Logic Conf., Leeds, 1973.
Essentially, they show that Boolean topos theory with a natural numbers object is equivalent to a version of Zermelo set theory (not ZF, i.e., without the replacement scheme) and with the separation scheme restricted to formulas with all quantifiers bounded (but the bounds can involve power sets, so quite a lot of separation is available). (I'm omitting some technicalities here, not because they're negligible but because I don't remember them.)
If you don't assume Boolean logic for your topos, I don't think it changes the consistency strength of the theory. In any nontrivial topos with a natural numbers object, the subtopos of double-negation sheaves will also be nontrivial and will have a natural numbers object (the associated sheaf of the original one). In other words, the double-negation translation of classical logic into intuitionistic logic works here.
The origin of the word quint is the late 17th century; it derives from French, which took the word from Latin quintus (fifth) from quinque (five). In Italian, quinto means fifth, and has the same origin.
Quintessential derives from quintessence (from Latin quinta essentia), which was considered thought to fill the Universe beyond Earth. In modern physics, quintessence is a hypothetical form of dark energy.
The NOAD reports that the origin of quintessence is late Middle English (as a term in philosophy), via French from medieval Latin quinta essentia ("fifth essence").
The first of your two examples is less clumsy than the second, but both are ambiguous or unclear. The examples in Shyam's answer remove the ambiguity by replacing it with the solution:
But when C happens, it depends only on Condition A.
→ But when C happens, the solution depends only on Condition A.
However, there is a problem with the first sentence when combined with the second, as the two contradict each other. The first sentence says the solution depends on Condition B and the second sentence says the solution does not depend on Condition B. Some possible re-wordings (sadly, convoluted or prolix) are shown below. It seems that while the dependencies among Conditions A, B, C are not particularly complex, they are difficult to state briefly, correctly, elegantly.
The solution depends on Conditions A and B, except only on A when C happens.
The solution depends on Condition A; solely on A when Condition C occurs, else on B as well.
If Condition C occurs, the solution depends only on Condition A; otherwise, it depends not only on A, but also on B.
I'm trying to describe, in one or two words, a system which is set up so that it cannot be long lasting; it is destined to collapse.
"Marx and Engels finish their overview of Marxist theory by arguing that the very nature of the bourgeoisie system makes it..."
I was going to use Sisyphean but that refers to a task that can never be finished rather than one that will end in disaster.
edit: currently using 'sisyphean and transient'
edit: the word doomed doesn't fit the sentence.
edit: to make it clear: im trying to find the word that best fits the sentence, im trying to convey the idea that the system cannot last, it is inherently self-destructive and will end sooner rather than later
Might be an episode of The Outer Limits, "Counterweight". Wikipedia description (spoilers):
Four scientists, a newspaper man and a construction tycoon agree to
spend 261 days in isolation in an interstellar flight simulation to
planet Antheon, a world that would be a potential target for future
human colonization. But the experiment is secretly infiltrated by an
extraterrestrial presence, who causes the subconscious mind of the
various passengers to go amok: one of the passengers finds the doll of
his deceased daughter on his bed, while another one is almost choked
in his sleep by invisible hands. As months pass onboard, relations
between passengers become increasingly tense and uneasy, each one
being faced with his own part of darkness. Horror eventually escalates
with the plants of one passenger coming to life and destroying one
another and the presence incarnating itself into one of the plants and
making it grow into a huge, hideous creature. The extraterrestrial
mind eventually reveals itself to the entire crew, claiming to be one
of Antheon's indigenous inhabitants. The Humans are accused of
planning to come to Antheon with intentions of aggressive
colonization, one thing the aliens cannot accept. In the end, the
simulation is interrupted.
You can also watch it on archive.org:
http://archive.org/details/TheOuterLimits-Tos-2x14-Counterweight
Aragorn's people are Dúnedain [Men of the West, Númenórean in Quenya] which means they have different sinews than other men. They're stronger, taller, longer-lived, and hold onto their vitality late in life. Aragorn is directly descended from the male line through Isildur and from the female line from Anarion through Fíriel [who married Arvedui, last King of Arthedain], daughter of King Ondoher. Generally the line of Elros were the longer lived of the Dúnedain and during the final third of the 3rd Age Aragorn's descendants generally lived between 155-160 years of age. They held the title of Chieftains, but before their lands were overrun by Angmar his line ruled Arthedain and before that all of Arnor.
There was a time during the Rebellion on their homeland of Númenor that the King's Men who were made up of the majority of the Númenóreans rebelled against the Valar. The ruling Kings and Queens had a drastic drop in their lifespans and their other gifts so that there was no distinction between them and any other Dúnedain. This distinction is mentioned in Aldarion and Erendis as such:
this rule of "royal marriage" was never a matter of law, but it became
a custom of pride: "a symptom of the growth of the Shadow, since it
only became rigid when the distinction between the Line of Elros and
other families, in life-span, vigour, or ability, had diminished or
altogether disappeared."
However, other members of the Line of Elros, such as the Lords of Andúnië, did not have such a drastic drop in their lifespans even though the shadow touched their hearts as well. For example, Elendil, Isildur's father died when he was 322 at the hands of Sauron during the Siege of Mordor. The Last King of Númenor, who was his cousin, "felt the shadow of death approach" when he was "besotted, and walking under the shadow of death" [Akallabêth] when has was barely 200 years old. Ar-Pharazôn's father had died when he was 198.
In Middle-earth the diminishment of the Dúnedain continued. It
was not a normal tendency, shared by the peoples whose proper home was
Middle-earth, but due to the loss of their ancient land far in he
West, nearest of all mortal lands to the Undying Realm. [Disaster of
the Gladden Fields; Númenórean Linear Measures]
Most of the Dúnedain had a life expectancy of around 100 or so. For the royal line in the North it was 155-160. Aragorn lived for 210 years.
For any (connective) spectrum $E$ one may rationalise it to get a rational spectrum $E_mathbb{Q}$, and a map $E to E_mathbb{Q}$. Now rational spectra split as wedges of Eilenberg-Mac Lane spectra, so one may choose an isomorphism $E_mathbb{Q}^*(X) simeq H^*(X;pi_{-*}(E)otimes mathbb{Q})$, and the rationalisation gives a map
$$ch_E : E^*(X) longrightarrow H^*(X;pi_{-*}(E)otimes mathbb{Q}).$$
For complex K-theory this gives the Chern character, and for real K-theory it gives the Pontrjagin character.
Of course, if $E$ is a ring spectrum so is $E_mathbb{Q}$, and one must identify the induced ring structure on $H^*(X;pi_{-*}(E)otimes mathbb{Q})$.
Let E(S) be the category of Nisnevich sheaves on the site of smooth schemes over some base S. Then Morel and Voevosy's homotopy category H(S) is obtained as a localization of the category sE(S) of simplicial objects in E(S). The localization functor loc:sE(S)->H(S) can always by constructed in a way that it is the identity on objects, so that you can always think of the objects as genuine simplicial sheaves. A statement as above reads simply as: the object K(Z(0),0) is isomorphic to the image by loc of the constant sheaf Z. Now, if you want to use such a statement to compute something, you will need to know what are the maps in H(S). For this, you will need quite a few general homotopy theory (here the homotopy theory of simplicial sheaves as well as the theory of left Bousfield localization), and, of course, at some point, some geometry. However, the theory of Bousfield localization applies here in a rather gentle way, if you admit the homotopy theory of simplicial sheaves.
Let Ho(sE(s)) be the localization of sE(S) by the class of local weak equivalences (i.e. maps inducing weak equivalences of simplicial sets stackwise). Then, for any smooth S-scheme X, you have a derived global section functor RΓ(X,?) (with values in Kan complexes). Morel and Voevodsky's homotopy category H(S) is obtained by inverting some maps in Ho(sE(S)), so that we have a localization functor loc:Ho(sE(S))->H(S). As this comes from a left Bousfield localization at the level of the underlying model categories, this latter localization functor has a right adjoint i:H(S)->Ho(sE(S)) which is fully faithful (almost by construction/definiton). Hence, we can understand H(S) as the full subcategory of H(sE(S)). Moreover, we can understand the essential image of i in a rather simple way: it consists of the objects F such that, for any smooth S-scheme X, the map
RΓ(X,F)->RΓ(XxA^1,F)
is a weak equivalence of Kan complexes.
This means that, whenever you have your favourite cohomology theory F, if it satisfies Nisnevich descent (hence is representable in Ho(sE(S)), then it is representable in H(S) if and only if it is homotopy invariant. If it only satisfies Nisnevich descent, then you still have a universel way to force A^1-homotopy invariance (by applying the functor loc).
for instance, K(Z(0),O) is really the Nisnevich cohomology with ceofficients in Z.
However, in the latter case, you might have some trouble to compute what you get.
For the higher K(Z(n),2n), there is an explicit description in terms of complexes which is obtained as follows. Let F be a sheaf of abelian groups. Consider the cosimplicial scheme Δⁿ defined a the spectrum of the (sheaf of) ring(s) O[t_0,...,t_n] modulo the relation t_0+...+t_n=1 (O is the sheaf of functions on S). Taking the internal Hom's, you get a simplicial sheaf of abelian groups Hom(Δⁿ,F) (letting n vary; you can also play with the Dold-Kan correspondance to get a complex if you prefer a hypercohomology point of view). Applying this for the object which represents K(Z(n),2n) (as explained in there),
if S is smooth over a field, one of the deepest and less trivial result of Voevodsky is that we obtain an simplicial sheaf which satisfies Nisnevich descent and is A^1-homotopy invariant, so that it represents motivic cohomology both in H(S) and in Ho(sE(S)).
If I may suggest an exercise: apply Morel and Voevodsky's construction to describe usual algebraic topology: instead of the Nisnevich site of smooth S-scheme, consider the site of smooth analytic manifold on C (with the usual topology) (and replace the affine line by the disk D^1). Then Morel and Voevodsky theory gives a category which is canonically equivalent to the usual homotopy theory of topological spaces (this is due to the fact that any smooth complex manifold is locally constractible, so that after trivializing D^1, only locally constant invariants remain). Then, for instance, Poincaré lemma says that the de Rham complex is D^1-homotopy invariant. In this precise sense, this shows that complex de Rham cohomology is very well defined on any homotopy type.
If Tommen and Margaery both die, Stannis is the next in line for the throne (assuming he's also alive). If Stannis is also dead, then the answer depends on which medium you're talking about, (in the books, it's Shireen). Who's in line after Shireen is entirely unknown, because we don't know enough about Robert's family, but for practical purposes, it likely wouldn't matter.
Despite the fact that we know his real parents, Tommen is still legally a Baratheon. His position on the throne comes from his father Robert. As far as we can tell, the Seven Kingdoms use a typical male primogeniture system where the line of succession is basically:
Once you've followed the generations all the way down and run out of eldest male children, succession moves to that persons brothers, and then to that persons sisters. If there are none of those, you back up a generation and repeat the process.
So, Robert had two sons and a daughter. The line of succession was Joffrey, then Tommen, then Myrcella. (If Joffrey had given birth to a son, that boy would have been inserted before Tommen). If all three of those children are dead, you move up a generation, back to Robert, and go to the eldest brother.
This is exactly the reason that Eddard Stark claimed Stannis as the legitimate heir in the first place: if none of Robert's children are true-born, they don't count, and Stannis is next in line. If all of Robert's children are dead, then their legitimacy is irrelevant, and Stannis inherits anyway.
If Stannis is also dead, we repeat that process, starting from him as King; his only child is Shireen, who would become Queen.
Note that she's dead in the show but probably going to die in the books.
After that, things get very complicated. We would need to follow the family tree up to Robert's parents, who are obviously dead, and look for any uncles Robert might have had and track their children down. As far as I know, Robert's father and grandfather were both only children meaning it's going to take a lot of family-tree searching to find a legitimate heir. But at this point, if the line of succession gets this muddled, for all practical purposes it's basically ended.
People who are already close to the throne (particularly Cersei and Margaery's families) would probably begin to press claims for inheritance on their own. Normally a woman can't "marry into" the line of succession, Cersei can't be Queen on her own, but her daughter can, but when things get this murky, the rules tend to take a back seat to the people with the biggest armies.
In addition, this is the point where known bastard children would come into play. People like Edric, who is not in line for the throne legally but is Robert's child, become a huge political rallying point when the throne becomes heavily contested. They can make the argument that they're closer to the throne than anyone actually in the line of succession, and a lot of people would back them up.
So, if it happens that Tommen dies without producing an heir, the most likely outcome is various powerful houses (the Lannisters, Tyrells and the Baratheon's sworn houses w/ Edric Storm) going to war, again, until one of them has enough military and political support to simply declare themselves King and everyone will accept it and move on.
A similar scene does happen in the books, in the chapter The Field of Cormallen, where after Frodo recovers consciousness following his rescue from Mordor, we have a celebration:
As they came to the opening in the wood, they were surprised to see knights in bright mail and tall guards in silver and black standing there, who greeted them with honour and bowed before them ... And as the Hobbits approached swords were unsheathed, and spears were shaken, and horns and trumpets sang, and men cried with many voices and in many tongues:
'Long live the Halflings! Praise them with great praise!
Cuio i Pheriain anann! Aglar'ni Pheriannath!
Praise them with great praise, Frodo and Samwise!
Daur a Berhael, Conin en Annun! Eglerio!
(etc)
And so the red blood blushing in their faces and their eyes shining with wonder, Frodo and Sam went forward and saw that amidst the clamorous host were set three high-seats built of green turves ... On the throne sat a mail-clad man, a great sword was laid across his knees, but he wore no helm. As they drew near he rose. And then they knew him, changed as he was, so high and glad of face, kingly, lord of Men, dark-haired with eyes of grey.
...
And then to Sam's surprise and utter confusion he bowed his knee before them; and taking them by the hand, Frodo upon his right and Sam upon his left, he led them to the throne, and setting them upon it, he turned to the men and captains who stood by and spoke, so that his voice rang over all the host, crying:
'Praise them with great praise!'
It seems evident that Jackson worked elements from this scene into Aragorn's coronation scene for the movies, although the movie scene is considerably less grandiose than that from the book.
As for reasons why, they should be obvious:
In all of the other series besides "Enterprise" the transporter only works with the shields down. I'm not going to quote the multitudes of episodes but it's a given to any Star Trek fan that shields have to be lowered in order to transport in or out.
In the series "Enterprise" however often times in the middle of battle the transporter is used with both ships shields raised.
For example in Enterprise "Divergence":
PHLOX: Admiral Krell. Doctor Phlox again. By now you may have noticed
the
[Klingon Bridge]
PHLOX [OC]: Small package which we sent to your Bridge. What you may
not know is that it contains a potent sample of the metagenic virus.
Even as we speak it is dispersing throughout your ship, infecting you
and your crew.
KRELL: You're lying!
PHLOX [OC]: Check your internal sensors.
This was transported onto the bridge of the Klingon battle cruiser in the middle of a battle. During the same battle Reed says, "It's no use. I can't penetrate their shields." In the series "Enterprise" I can give many many examples of people or things being transported on and off ships in the middle of battle with the shields raised. For example Archer transports with a crew onto the device built to destroy the Earth. In that same battle the Xindi Lizards transport Nosho off the Enterprise bridge in the middle of the battle. In the episode where the Orion Syndicate takes 9 Enterprise crewmen to sell as slaves, the Syndicate ships simply transports the crewmen off the Enterprise including T'Pol off the bridge with the shields raised in the middle of a battle.
Almost without question in the other series there had to be a reason given and it was an exception that such a thing could be done. For example in TNG if they had the shield frequency, or shield modulation, or some other explanation it could be done from time to time, but it was infrequent and almost always the shields being raised was used as an excuse that the transporter couldn't be used.
In "Enterprise" I often wonder why they didn't simply transport armed photon torpedos inside of other people's ships. Or for example why didn't the Enterprise simply transport a small bomb onto the bridge of the Klingon Battle Cruiser's bridge or next to its warp drive.
In the Xindi storyline, there were many times the Enterprise could have simply transported a torpedo or bomb onto an enemy ship or the device that could destroy the Earth. And visa versa the Xindi also had transporter technology and they could have done the same.
There's been some discussion below about whether the NX class has shields or not. I looked at Wikia and it listed the NX, Constitution, and Galaxy classes as all having deflector shields for defensive purposes. It does not list any other kind of shielding by name(other than hull plating also listed for the NX which I assume the others have incorporated in all the time). The NX clearly had deflector shields by the fourth season after the retrofit. Either way, almost every other ship in the "Enterprise" series had shielding, and I can put a bunch of quotes in to make this a very long question, but suffice it to say in almost every episode of "Enterprise" where there is a battle they are talking about penetrating an enemy's shielding, shield generators, etc.
There has also been some discussion about whether shields prevent a transport.
TNG "The Wounded":
RIKER: He'd never drop his shields and allow you to transport on
board.
O'BRIEN: The Phoenix is using a high energy sensor system. It cycles
every five point five minutes. Between cycles there's a window of a
fiftieth of a second. Trust me, I can get through.
PICARD: Make it so.
[Phoenix Ready room]
MAXWELL: Not now! (O'Brien enters and Maxwell grabs a phaser)
O'BRIEN: I'm not armed.
MAXWELL: How the devil did you get over here?
So you see from this TNG episode that it's almost impossible, unless it's a transporter specialist, with the exact specifications of the other ships systems to transport through a ship's shields(there was no battle taking place and the Enterprise had its shields lowered at the time as well). Captain Maxwell was shocked since his shields were raised. This episode seemed a bit far fetched as it takes a full two seconds to complete the matter stream during a transport and a fiftieth of a second wouldn't give O'Brien enough time to get through, but that's a different question.
At what point and why does it become (almost) impossible to transport with the shields raised in the Star Trek Universe?
(If you feel like addressing my gleanings about why they didn't use this inability or ability however you view it, as a weapon more often, please feel free.)
We suppose that $K$ is a category defined by a "species of structures with morphisms" $Sigma$, the objects of $K$ are thus the sets endowed with structure of species $Sigma$ and the morphisms those of $Sigma$.
This is the language of Bourbaki. "Species of structures" are Bourbaki's version of categories. The analogue of an object is for example a set with some "structure", like a topology, or a group operation. Morphisms are functions that "preserve the structure". Rigorous definitions of these things and their morphisms, in full Bourbaki generality, can be found in Chapter IV: Structures of Theory of Sets.
Here first Grothendieck defines a solution to a universal problem in a category $K$. He's actually defining a limit, but for diagrams that look like a cover. He also defines a sheaf with values in an arbitrary category $K$, giving the extra condition on a presheaf. Then he restricts to the case where $K$ is made of objects with extra structures as above, and assumes that $K$ satisfies a further property: that a solution to a universal problem in $K$ remains a solution in the category of sets if we forget the structures. Then he says that in this case a sheaf with values in $K$ is also a sheaf of sets.
Having seen Correct placing and usage of "yet", it sounds like it may be correct to say either "You have not created any items yet." or "You have not yet created any items."
Is one more correct than the other, or is it a matter of preference? The first personally sounds more correct to me, but I wanted another opinion!
I am in search of word that exactly means 'a difficult person of my description'.
For example, I am on the look out for a heart specialist and ask my friend if he is familiar with any. However, he begins with the description of heart, its function, who can do without it, plausible threat from such doctors as are selective in their studies so as to skip 'heart' even and so on and so forth. I am lost in a maze, my head goes whirling and I fail to recollect what I was after.
Search among your acquaintances and you will find many similar examples. What I want is to give them an appropriate name–— preferably a single word.
The Original Poster's sentence is badly punctuated, but entirely grammatical.
Indeed this government - neither their great wealth nor their many supporters will benefit them on election day; they will fail.
This sentence looks very much as though it has this government for a subject. Beware! This is, in fact, not the case. Let's simplify the sentence, investigate it and put it all back together again.
The string of words running neither their great .... election day is parenthetical. This means that it is not integrated into the grammar of the main clause. It is like an aside by the author. The fact that it is parenthetical is shown by the fact that we could literally put it in brackets or dashes:
Or we could even leave this whole section out altogether:
Now, the sentence above is a bit easier to get to grips with. Notice that that word indeed is an adjunct. It links back to something that was said in a previous sentence and emphasises that what is coming up next is emphatically true. Being an adjunct this word is not integrated into the main clause either. This leaves us with:
Now, this sentence has the same kind of structure as:
As mentioned above, it's tempting to think that This government or Bob are the subjects of these sentences -but they aren't. Notice that these phrases can come at the end of the sentence as easily as the beginning:
We can also turn these sentences into yes/no questions. The phrases that invert with the auxiliary verbs will be the subjects:
Notice as well that both sentences are well-formed without the phrases this government or Bob. This shows, firstly, that they and not this government is the subject of the Original Poster's question. Secondly, it also shows that this government is also an Adjunct in the sentence. It doesn't form part of its essential structure.
The sentence therefore has a subject they, whose predicate is ostensibly will fail. It has three parenthetical elements which are not integrated into the clause structure:
This last element has the structure of a complete sentence which has been interpolated into the main one. It, too, is well formed. It has a co-ordinated subject neither their great wealth nor their many supporters and a predicate will benefit them on election day.
Note: Notice that it would be easy to confuse this sentence with one such as:
In the sentence above, which seeks to differentiate the government from their supporters or their financial reserves, the phrase the government would be the subject and the string beginning is neither would be the predicate.
You seem to be confused both about terminology and tenses, so let's try to get this straight:
For present hypotheticals we use a form that is technically referred to as the subjunctive. The subjunctive is identical to the simple past in most forms, but you'll notice that it differs for the first-person singular:
If they were here, I would be happy.
If I were rich, I would be happy. (Not: If I was rich.)
(Just to make things complicated, this form of the subjunctive is disappearing and many people do, in fact, say If I was rich. But for the purposes of illumination, let's treat this as a separate way of inflecting the verb.)
For past hypotheticals we use the past perfect (or pluperfect), not the "present past" that you referred to. (I've never heard the term "present past" before, and in any case I would interpret it as a reference to the present perfect, which is incorrect.) The reason for this is that the simple past is the same in almost all cases as the subjunctive, which is used for the present hypothetical.
If they had been there, I would have been happy.
If I had stayed, I would have met her.
For future hypotheticals we use the simple present. This is not actually surprising, since the simple present is used for near-future events in a variety of contexts in English.
If they come, I'll be happy.
Note, however, that it's actually possible to use both the modal will and other future constructions such as going to in this construction, depending on context.
If they will reduce the price, I'll buy.
Here will retains some of its historical sense of willingness as opposed to indicating mere futurity.
If they are going to leave, then I am, too.
This is a pure future conditional. You can use going to for the future hypothetical in almost any case where you would otherwise use the simple present with no change in meaning.
Idiot-savant comes to mind, but that's neither accurate nor indeed specific enough. I've looked up some synonyms: no cigar. The problem with defining such people is there's more to their patterns of behavior than meets the eye. They're whimsical. One never knows when they're:
Pretending to be absentminded just to spite everybody
Also, you never know how much of it is deliberate, and how much instinctive. Like that sleepy Texas sheriff. You know:
He's parked behind a tree, with the radar pointed in the right direction. He's dozing off. Cars keep zooming by on the highway. He couldn't care less. A whole bunch of cars rolls by, all of them most definitely over the speed limit. 80 mph. 85. 90. 85 again. 80. 92. 93. 85. And so forth. Nothing: no reaction from the sheriff. All of a sudden this souped-up Porsche flies by, doing 140! The sheriff opens one eye, looks at the radar, and goes, "Wow, I'll be f***!" The next moment, the engine is running, the lights and siren are on, and he swings onto the highway in pursuit of the offending Porsche.
He wasn't pretending to be absentminded. He was actually being absentminded. Which didn't stop him from acting quickly when it became really necessary to do his duty.
Something like that.
The first let's consider when we can and cannot do this shifting at all. Our hypothetical "he" is going to take the toy away, look at it, and then look it up (in a catalogue of toys or similar). Then he's going to look up toward it (perhaps the toy is a helicopter):
He took away my toy.
He looked at my toy.
He looked up my toy.
He looked up toward my toy.
Consider if the word with the verb is acting as a preposition. This is perhaps easier with away (not generally considered a preposition in any case) than up (which can also be a preposition).
The at is a preposition with the classic school-learning explanation that it is about the relationship between his looking and the toy. up toward is also serving this rôle, though it's two prepositions together.
The away and up are not prepositions in this sense, (despite up generally being considered a preposition and serving as such in other expressions*) because it doesn't describe a relation between the taking and the toy. Instead it's a particle that is giving us a new verb "take away" that names a different action than just "take".
In the preposition (at) case we can't shift the noun because then we change what elements the preposition is describing a relationship between (if any), but we can with the other case (away):
He took my toy away.
*He looked my toy at.
He looked my toy up.
*He looked my toy up toward.
Indeed, it's perhaps easiest to see that away and up are not prepositions in the first set of sentences is by considering that very fact that it still works here, while the preposition at and up toward do not. (Again, despite the fact that up is a preposition in other uses.
Now, of those case where we can shift (away and up) when the object is a pronoun we always shift:
*He took away it.
He took it away.
He looked it up.
*He looked up it.
Notably, while the first here seems just plain wrong, the last seems to have a different meaning; because up can also be a preposition, and because we would always shift it with a phrasal verb of this sort it seems that it must be acting as a preposition in this case and so we are led to wonder what shape this toy must be that "looking up it" makes sense.
While always done with pronouns, the freedom with other noun phrases to shift or not shift and the likelihood that we would, is reduced with the length of the phrase:
He took away my really cool remote control helicopter that I got for Christmas and had been playing with every day since.
?He took my really cool remote control helicopter that I got for Christmas and had been playing with every day since away.
Here the second sentence isn't wrong, but it is unusual and unlikely to be used.
*Which can lead to ambiguity: "He looked up my skirt" differs considerably between a sense that can be rewritten as "he looked my skirt up" and a sense that cannot.
Unofficially the Starship class is due to certain specifications and qualities of a particular starship.
According to The Star Trek Wikia.
http://en.memory-alpha.org/wiki/Category:Starship_classes
A class of starship is a term referring to the design of a group of
vessels built to the specifications, capabilities, modification or
type arrangement and outfitting. Many cultures name separate series or
classes based on these qualities. A starship classification is usually
used to refer to the general abilities of a vessel, but a specific
class designation refers to its shape or layout in differing degrees,
according to how specific species and cultures use the term.
Here is an example of what the Intrepid-class Starship was.
http://en.memory-alpha.org/wiki/Intrepid_class
The Intrepid-class starship was a Federation design that entered
service in the later half of the 24th century. The Intrepid-class was
designed for long-term exploration missions. At less than half the
size of a Galaxy-class starship, it was considered "quick and smart."
Another example would be the Galaxy-class Starship.
http://en.memory-alpha.org/wiki/Galaxy_class
The Galaxy Class Starship Development Project began in the 2350s at
Utopia Planitia Fleet Yards. (TNG: "Booby Trap", "Eye of the
Beholder") Numerous technologies implemented on Galaxy-class starships
were tested aboard earlier prototype vessels, including the
Oberth-class USS Pegasus in the 2350s. (TNG: "The Pegasus")
The warp core was designed at Outpost Seran-T-one on stardate 40052 by
some of the most brilliant engineering minds in the Federation,
including Leah Brahms of the Theoretical Propulsion Group. (TNG:
"Booby Trap")
http://en.memory-alpha.org/wiki/Starship_classification
Unofficially, many starships are classified by their design type. Although Starfleet tries not to classify their vessels in any such categorization, there have been numerous occasions where a Starfleet officer referred to Starfleet or enemy vessels by type during a fleet engagement, such as in Operation Return when Captain Sisko calls upon Galaxy wings to engage Galor-class destroyers. (DS9: "Sacrifice of Angels")
For reasons unknown, I am unable to access the reference link provided by you.
Nonetheless, I can infer that the article is about how to write e-mails to customers.
You seem to have problems in interpreting the expression - "to chirp back".
As you've pointed out, the ODO defines chirp as
(Of a person) say something in a lively and cheerful way
In this context, it simply refers to a response. Whether it was cheerful or lively, as readers, we are not concerned.
Taking the sentence in question,
But I slowly started to notice a change. Clients were increasingly respondent to my emails. Even prospects were beginning to chirp back more times than not.
The author is probably giving out e-mail etiquette/ writing tips when sending mails to customers. By following those, the author noticed that customers, who generally don't respond to e-mails soliciting their feedback or product promotions (e-mail of any kind, for that fact!), start to respond to them and even "prospects"(potential customers of a business) were starting to reply to messages and perhaps reacting to promotional campaigns("chirping back"). More times than not means "often" or "frequently".
I think "condescending" would be an apt description.
Or really, "unfair" might work too, as it is pretty unfair he'd give you so much trouble over one mistake, when I assume your advice is typically helpful.
EDIT: Also, I think the word you used yourself, "sarcastic", is an equally good word, if not better! Because that's exactly what his remarks are. Keep in mind to be careful he isn't just joking; there may be no bad intentions, and it's entirely possible he doesn't understand his teasing is bothering you. :)
One vivid way to describe the act of moving one's forefinger toward the other person's face is "jabbing [one's] finger." A Google search turns up multiple examples of this usage. From Laura Simon, Dreams of Paradise (1991):
"It's a legitimate business from which I fully expect to realize a profit. I wouldn't have started it otherwise. I would have sent you anonymous envelopes full of money instead. God knows, it would have been easier. Given that fact," he went on, jabbing his finger in front of her face, "I can't comprehend why you should find it less objectionable to sell your designs to some cigar-chomping stranger than to me."
Hazel swatted his finger away.
From Diana Dempsey, Falling Star (2002) [combined snippets]:
Then his eyes got all wild and he started screaming and jabbing his finger in her face, as if he was going out of control. He looked like a lunatic. But she didn't budge. She just waited for it to be over.
From Atwater v. City of Lago Vista (2001), quoted in Andrew Taslitz, Reconstructing the Fourth Amendment: A History of Search and Seizure, 1789–1868 (2006):
Turek was loud and accusatory from the moment he approached Atwater's car. Atwater's young children were terrified and hysterical. Yet when Atwater asked Turek to lower his voice because he was scaring the children, he responded by jabbing his finger in Atwater's face and saying, “You're going to jail.”
From Mileikowsky v. Tenet HealthSystem, California Court of Appeal, Second District (April 18, 2005):
The second stated basis for the suspension was a December 1999 incident where Dr. Mileikowsky was informed, during performance of a surgery, that his assistant did not have surgical privileges. Dr. Mileikowsky allegedly backed the operating room manager against a wall while screaming at her and jabbing his finger in her face.
From Walter Sorrels, Fake ID (2005) [combined snippets]:
Two minutes later I was sitting in his office while he stood over me, jabbing his finger in my face. "Where were you yesterday afternoon?" he shouted.
From Jeffrey Feldman, Outright Barbarous: How the Violent Language of the Right Poisons American Democracy (2008) [combined snippets]:
In this case, the exclamation points in the transcript indicate moments where O'Reilly barked loudly and jabbed his finger towards Rivera's face. In fact, a video clip of O'Reilly shouting and jabbing his finger at a stunned Rivera circulated on the Internet and was discussed on political talk shows for the next week.
The Cassell Guide to Common Errors in English (p251) would agree with you. It states:
There is a tendency to combine 'more' (or some other comparative) with
'rather than' in such a way as to upset the grammar.
Among the examples the CGCEE lists is this one:
'The German appeal for an armistice was put to President Woodrow
Wilson in the hope it would get a better deal from him rather than
from Britain or France' (The Times). Here again the word 'rather' should
be omitted.
The same advice is given by The Right Word at the Right Time (p513):
Take care not to use rather than in place of than after more, simpler,
harder, and so on.
*He finds it simpler doing the sums in his head rather than looking for a paper and pencil. Either omit the rather here, or say simply He
does the sums in his head rather than looking for a pencil and paper.
The more recent Garner's Modern American Usage (p694) concurs:
*More...rather than. It's poor syntax to write more...rather than-e.g.: "His ideological convictions...were defined more by
present-day concerns rather [delete 'rather'] than by thirteenth-century
conditions," Robert E. Norton, Secret Germany 667 (2002).
Merriam Webster's Dictionary of English Usage (p798) lists various commentators who "notice a curious construction in which a comparative that you would expect to be followed by 'than' takes 'rather than' instead". The MWDEU gives a couple of examples of this usage and continues:
The reason for the awkwardness of the sentences is that the more in
each sentence leads the reader to expect the usual than, but rather
than turns up in its place. The existence of such sentences (which we
advise you to avoid) is good evidence that rather than is perceived as
a unit by many writers. We lexicographers will, in time, have to
recognise its existence.
So the usage guides are fairly unanimous that this is a construction to be avoided. And, as the OP suggests, a careful writer might not only omit the rather in New Yorker sentence but also insert a to for sake of parallelism:
I find it easier to use the serial comma consistently than to stop
every time I come to a series ... .
I myself, however, do not find the rather than usage particularly problematic.
I'm looking for an old SciFi movie I'd seen as a child (a long time ago). I just remember, the earth is colliding with another planet (and it's not "When Worlds collide") and the atmospheres of the 2 planets merge or exchange. Somehow men get to the primordial planet or dinosaurs walk earth, I don't remember which was the case. Maybe men flew by plane... Anybody know the movie and the name or can give me a hint, where to look for. Oh, and by the way, I'm in Germany, just in case you like to show me the way to an allknowing wise man somewhere far beyond ;-)
Here's what we know about House-elves:
I believe, if a house-elf could be made into a Secret Keeper, it would not be a good idea for the elf to be its master's Secret-Keeper, as its master could order the elf to divulge the secret and I don't think the house-elf could refuse.
The Fidelius Charm is complex:
‘An immensely complex spell,’ he said squeakily, ‘involving the magical concealment of a secret inside a single, living soul. The information is hidden inside the chosen person, or Secret-Keeper, and is henceforth impossible to find – unless, of course, the Secret-Keeper chooses to divulge it. As long as the Secret-Keeper refused to speak, You-Know-Who could search the village where Lily and James were staying for years and never find them, not even if he had his nose pressed against their sitting-room window!’
Prisoner of Azkaban - page 153 - Bloomsbury - chapter 10, The Marauder's Map
A single, living soul suggests just a soul; it doesn't say the soul has to be human. Conversely, inside the chosen person suggests that being a Secret-Keeper is specifically a human ability.
House-elf magic is different than wizarding magic. For example, house-elves can Apparate within Hogwarts; human witches and wizards cannot. We don't know enough about house-elf magic to adequately assess a house-elf's ability to be a Secret-Keeper; however, their profound loyalty toward their master, whether voluntary or indentured, does demonstrate a characteristic that would be conducive to being a good and strong Secret-Keeper.
However, what I noted above shows why we don't have enough canon information to say yes or no to this question; there is no information in canon that, when put together in good faith or the spirit of canon, suggests a definitive answer.
I don't think that "always" matters. I can't imagine a situation in which it would change anything. For example:
Bob cries at funerals.
This is in the gnomic aspect without "always." In as much as funerals don't happen habitually for Bob, Bob's crying at them is habitual. If there's a funeral, Bob has a habit of crying at it. Adding "always" doesn't change the aspect.
The same goes for generics:
Twenty-year-olds become twenty-one-year-olds.
You may be thinking that this can't be generic because all 20-year-olds don't turn 21, some die. You may be thinking it's not habitual because 20-year-olds only become 21 once, hardly a habit. But it is generic because it is being applied to a class or group, and it is habitual because it is what 21 year-olds do. "Always" doesn't change that.
Basically, in English, the gnomic aspect is created by the subject, particularly its number, and the verb, particularly its tense. Given a subject with the correct singularity or plurality coordinating with specific verb tenses, things gain the gnomic aspect. Adjectives can't eek sentences into a gnomic aspect.
I would like to add to the list my favorite book on Classical Functional Analysis:
Dunford, Nelson; Schwartz, Jacob T. Linear operators. Part I. General theory. With the assistance of William G. Bade and Robert G. Bartle. Reprint of the 1958 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1988. xiv+858 pp. ISBN: 0-471-60848-3
This book contains a plenty of exercises, which allow to check understanding and much more.
I don't know any number theory, so excuse me if the following notions have names that I'm not using.
For a positive natural number $nin{mathbb N}_{geq 1}$, define $Log(n)in{mathbb N}$ to be the ``total exponent" of $n$. That is, in the prime factorization of $n$ it is the total number of primes being multiplied together (counted with multiplicity); for example $Log(20)=3.$ I'll define $log_2(n)in{mathbb R}$ to be the usual log-base-2 of $n$, so $log_2(20)approx 4.32$.
One can think of $log_2(n)$ as "the most factors that $n$ could have" and think of $Log(n)$ as the number of factors it actually has. Define $D(n)$ to be the ratio of those quantities $$D(n)=frac{Log(n)}{log_2(n)}in(0,1],$$ and call it the divisibility of $n$. Hence, powers of 2 are maximally divisible, and large primes have divisibility close to 0. Another example: $D(5040)=frac{8}{12.3}approx 0.65$, whereas $D(5041)approxfrac{2}{12.3}approx 0.16$.
Question: What is the expected divisibility $D(n)$ for a positive integer $n$? That is, if we define $$E(p):=frac{sum_{n=1}^p D(n)}{p},$$ the expected divisibility for integers between 1 and $p$, I want to know the value of $$E:=lim_{prightarrowinfty}E(p),$$ the expected divisibility for positive integers.
Hints:
I once wrote and ran a program to determine $E(p)$ for input $p$. My recollection is a bit faint, but I believe it calculated $E(10^9)$ to be about $0.19.$
A friend of mine who is a professor in number theory at a university once guessed that $E$ should be 0. I never understood why that would be.
There is a large body of work studying ill-founded models of set theory. The goal is to provide a robust model theory for models of set theory, usually focussing on the countable models. Much of this theory grows out of the study of nonstandard models of arithmetic,
and many tools and theorems from models of arithmetic generalize to the study of models of ZFC.
Let me give a few examples. If M is a model of ZF, one can form the standard system of M by looking at the trace on the standard ω of all the reals of M. It is easy to see that Ssy(M) is a Boolean algebra, closed under Turing reducibility and if T is an infinite binary tree coded in Ssy(M), then there is a path through T coded in Ssy(M). Any set of reals with those three properties is called a Scott set, in honor of Dana Scott, who proved the following amazing characterization:
Theorem.(Scott) If ZFC is consistent, then every countable Scott set arises as the standard system of a model of ZFC.
Scott's theorem is usually stated for models of PA, but the proof for ZFC is identical. It remains a big open question whether Scott's theorem holds for all uncountable Scott sets. The answer is known for Scott sets of size ω1, and so under CH the problem is solved, but it remains open when CH fails.
A key definition is that a model M of ZFC is computably saturated if it realizes every finitely consistent computable type over M. All such models are ω-nonstandard. It turns out that M is computably saturated if and only if it is (isomorphic to) a model that is an element of an ω-nonstandard model of ZFC. Furthermore, these models have interesting closure properties.
Theorem. Any two countable computably saturated models of ZFC with the same standard system and same theory are isomorphic.
Theorem. Every countable computably saturated model M of ZFC is isomorphic to a rank initial segment Vα of itself.
Much of the analysis of models of PA, such as that in the book by Jim Schmerl (UConn) and Roman Kossak (CUNY) extends to models of ZFC. Ali Enayat has also done a lot of interesting work along these lines.
Here is another interesting theorem having to do with nonstandard ZFC models. Let ZFC* be any finite fragment of ZFC. If there is a (very small) large cardinal, then one can use full ZFC in this theorem (e.g. it suffices is there some uncountable θ with Lθ satisfying ZFC). The theorem is interesting in the case that there are nonconstructible reals.
Theorem. Every real x is an element of a model of ZFC*+V=L. Furtheremore, one can find such a model whose ordinals are well-founded at least to α, for any desired countable ordinal α.
Proof. First, the statement of the theorem is definitely true in L, since every real in L is in some large Lθ. Second, the complexity of the statement is Σ11 in x and a real coding α. Thus, by Shoenfield's Absoluteness theorem, it is true in V. QED
Thus, even when x is non-constructible, it can still exist in a model of V=L! This is quite remarkable. (This theorem was shown to me by Adrian Mathias, but I'm not sure to whom it is originally due.)
Worked for about five years at accompany that rented these out in the USA, and they were called jumping castles (when they resembled castles, and were for jumping in) and inflatables the rest of the time. This includes slides, Velcro walls, or obstacle courses as your picture indicates. The company has them listed generally as 'inflatables' on their site.
Note that jumping castles or bouncy houses are simply a more specific for of inflatable. The following photos are all from their website.
Jumping Castle, Bouncy House, or simply Bounce
45 foot obstacle course Inflatable
27 foot dual-lane Inflatable slide
I would add that there may also be regional differences. My experience was all in the southwestern USA.
How about:
"He was a boy who was beaten often."
EDIT
Based on Jim's point that beaten is ambiguous and John Lawler's comment about the requirement for slang usage, consider:
"He was a boy who was beaten up often."
If the requirements of slang mandate that got must be used in place of was, then so be it.
I'm trying to find the right word to describe someone who wants to voice their opinion about subjects (especially controversial ones or ones where the speaker is going against easily-provided facts) but who doesn't want those opinions challenged directly and gets angry if they are.
I'm looking for words with a negative connotation. I'm aware of the word "obstinate", but it doesn't really feel like it does the concept justice, perhaps because it can also be used to mean "not easily controlled" and can be interpreted as a positive. Also, obstinate seems to mean that someone won't change their mind in response to an argument and leaves out that the person explicitly forbids an argument from being presented in the first place. It also leaves out that the person not only won't change their mind about a subject but also wants to make sure others know what their opinion is.
Either a word or a phrase is fine. I'm just having difficulty finding the right words that fully capture the idea.
Edit
I don't feel like the question at Word for someone that always has to be right quite captures what I'm getting at here, though some of those answers might apply.
The need to be right isn't so much the important part as much as the unwillingness to discuss at all. The type of person I want a phrase to describe is the one who says, "Here is my opinion. I'm not looking for a debate." This type of person doesn't just say this about one issue, but about all issues, especially ones that are likely to entice others to discussion and debate.
It helps if the word or phrase describes someone who holds opinions that fly in the face of facts, but it's not strictly necessary. The cutting discussion off at the pass is more important than the ignorance.
This answer is not exactly an answer to the original question, but this is for the benefit of MO user vonjd who wanted to know more details about the similarities between solving differential equations through Laplace transforms and solving recurrence relations using generating functions.
Since I was going to write it anyway, I figured I might as well post it here for anyone interested.
I will do an example of each, and this should be enough to show the similarities. In each case, we have a linear equation with constant coefficients; this is where both methods really shine, although they both can handle some variable coefficients more or less gracefully. Ultimately, the biggest challenge is to apply the inverse transform: always possible in the linear case, not so easy otherwise.
Take the function $y(t)=2e^{3t}-5e^{2t}$. It is a solution of the IVP:
begin{equation}
y''-5y'+6y=0; qquad y(0)=-3, y'(0)=-4.
end{equation}
If we apply the Laplace transform to the equation, letting $Y(s)$ denote the transform of $y(t)$,
we get
$$ s^2Y(s)-sy(0)-y'(0)-5[sY(s)-y(0)]+6Y(s)=0.$$
Substitute the values of $y(0)$ and $y'(0)$, and solve to obtain:
$$ Y(s)=frac{11-3 s}{s^2-5s+6};$$
and apply partial fractions to get:
$$ Y(s)= frac{2}{s-3}+frac{-5}{s-2}.$$
This is where you exclaim: "Wait a second! I recognize this, since it's well known that
$$mathcal{L}[e^{at}]= frac{1}{s-a}$$
for all $a$, then by linearity we recognize the function that I started from.
Let $(a_n)$ be the sequence defined for all $ngeq 0$ by $a_n=2(3^n)-5(2^n)$.
It is a solution of the IVP:
begin{equation}
a_{n+2}-5a_{n+1}+6a_n=0 qquad a_0=-3, a_1=-4.
end{equation}
Define the generating function $A(x)$ to be:
$$ A(x)=sum_{n=0}^{infty} a_n; x^n. $$
Multiplying each line of the recurrence by $x^{n+2}$ gives:
$$ a_{n+2}; x^{n+2}-5a_{n+1}; x^{n+2}+6a_n; x^{n+2}=0 $$
You can sum those lines for all $ngeq 0$, do a small change of index in each sum, and factor out relevant powers of $x$ to get
$$ sum_{n=2}^{infty} a_n; x^n-5x sum_{n=1}^{infty} a_n; x^n+6x^2 sum_{n=0}^{infty} a_n; x^n=0.$$
Or in other terms:
$$ A(x)-a_1x-a_0-5x[A(x)-a_0]+6x^2A(x)=0.$$
Substituting $a_0$ and $a_1$ and solving for $A(x)$ then gives, with partial fractions:
$$ A(x)=frac{11 x-3}{6 x^2-5 x+1}=frac{2}{1-3 x}+frac{-5}{1-2 x}$$
Looks familiar? It should! If you substitute $x=1/s$, you will recover $sY(s)$ from the differential example.
For generating functions, the key fact we need here is the sum of geometric series:
$$ sum_{n=0}^{infty} (ax)^n=frac{1}{1-ax}.$$
Thus, by linearity again, we recognize the sequence we started from in the expression for $A(x)$.
In both theories, there is the notion of characteristic polynomial of a linear equation with constant coefficients. This polynomial ends up being the denominator of the Laplace transform, and the reversed polynomial $x^dp(1/x)$ is the denominator of the generating function. In both cases, multiple roots are very well managed by the theories and explain very naturally the appearances of otherwise "magical" solutions of the type $te^{lambda t}$ or $n(r^n)$.
The biggest mystery to me is the historical perspective: did one technique pre-date the other, and were the connections actively exploited, or did both techniques develop independently for a while before the similarities were noticed?
