An alternative architecture for a mission to Mars

Question: This image, which is supposed to represent the current architecture of the mission to Mars by NASA, raised a wave of emotions. People find it too long and complicated. But is it really possible to make it fundamentally simpler? I think that the idea of a single-launch Starship that will land on Mars, where it will use ISRU to produce fuel and return to Earth in 2030 is far from the truth.

https://twitter.com/KenKirtland17/status/1745931455199338512
Comment: @SaturnV But what's "better"? Cheaper? Faster? Safer? With fewer launches (and bigger rockets) or smaller rockets (and more launches)? Fewer orbital rendezvous? Fewer ground rendezvous? More astronaut-hours on the ground? Without knowing what parameter(s) you want to optimize, it's hard to say what a better approach would look like.
Comment: For context: The Apollo program took 8 years and 11 launches to put 3 men on the Moon ~350,000 km away, the missions lasted about a week, and the program cost a significant fraction of the US economy. Mars is 55,000,000 km away (about 150x further) and it will take over a year to get there and back. Considering NASA doesn't have anything like Moon landing money, and the problem is literally astronomically more difficult, I'd say their plan is pretty good!
Comment: "I think that the idea of a single-launch Starship that will land on Mars, where it will use ISRU to produce fuel and return to Earth in 2030 is far from the truth.": ...who has suggested such a thing? SpaceX certainly hasn't.
Comment: Yeah that's right. It's more of an exaggeration.
Comment: What exactly is your question?
Comment: The chart contains a copy/paste error. The top right text for the return-rendezvous of the ascended lander with the Deep Space Transport is copied from the similar arrival-rendezvous with the rover and the Transport upon arrival in orbit, to the left. It reads "Pressurized Rover & DST arrive in Mars Orbit and Rendezvous/2 crew members move into the Pressurized Rover". But there is no rover involved, and DST has not arrived but has been orbiting for a month by then. QA isn't any more what it used to be, is it now.
Comment: How to do it better than it is drawn in that picture
Answer: All manned Mars proposals that do not involve a nuclear launch from earth have a LOT of launches.
Pretty much every serious plan since Von Braun's have involved multiple launches assembled in earth orbit and look much the same over the years. His scaled down 12 person/two vehicle version needed 400 launches. Looking at the plan above you can consider the impacts of deleting things:
There are mass penalties with common transfer stage and landing system, a bespoke design might allow rover or power components to cut from three to two launches but increases the cost due to additional design and testing needs.
You can scale back or delete the power system, cutting three launches to one or zero, but compromise the rest of mission (eg do Landing with batteries and surface time in hours).
You can delete the rover and probably cut the landing component to a single launch, but that means your team must walk everywhere and MUST get down near the ascent vehicle. Surface time in hours, possibly crew size of one.
You can delete the ascent vehicle and make it a one way trip, saving three or more launches.
You can delete the landing, saving 9, possibly 10, launches and replace them with rovers operated in close to real time or a visit to the Martian moons. A pure free return flyby mission might be as low as two launches, especially if the crew is cut to one small person, though this leaves the question of 'why'.
Getting to Mars is hard, and if planning to do something actually useful there to justify the trip you need to take stuff with you. In practice, a sensible mission design probably has MORE launches in it since you want to provide redundancy to avoid a failure scrubbing the entire mission (eg two ascent vehicles and two landers).
Comment: Footfall: [Michael !!!!](https://wiki2.org/en/Footfall)
Answer: The infographic in your question references a Sept 28th, 2021 NASA document called the HEOMD Strategic Campaign Operations Plan for Exploration, where HEOMD stands for "Human Exploration and Operations Mission Directorate".
It is possible to propose a simpler plan. Mars Direct, and its revision, Mars Semi-Direct, are examples of mission plans that are arguably simpler than plan depicted in the above infographic.

(ref) Left panels say "Year 1", "Year 3", "Year 5". Right labels alternate between "Unmanned" and "Manned".
Of course, minimizing complexity isn't always the only objective. Other objectives include reaching a satisfactory political compromise, minimizing risk, increasing crew welfare, maximizing the utility of the mission as a learning experience, achieving certain science objectives, doing the most possible within a given budget, arriving first to score points for your ideology on the world stage, executing the mission in a way that best serves an even larger long-term goal (such as establishing a colony), etc.
The Starship Approach
Missions that land on Mars and missions that land on the Moon require imparting similar amounts of delta-v. So we can review what we know about Starship's lunar HLS mission plan to get a sense of the complexity of a Starship-based Mars mission. A plan involving sending Starship to land on the moon will involve refilling. According to this Space News article...

In a presentation at a meeting of the NASA Advisory Council's human exploration and operations committee Nov. 17, Lakiesha Hawkins, assistant deputy associate administrator in NASA's Moon to Mars Program Office, said...

SpaceX's concept of operations for the Starship lunar lander it is developing for the Human Landing System (HLS) program requires multiple launches of the Starship/Super Heavy system. One launch will place a propellant depot into orbit, followed by multiple other launches of tanker versions of Starship...

"It's in the high teens in the number of launches," Hawkins said. That's driven, she suggested, about concerns about boiloff, or loss of cryogenic liquid propellants, at the depot.

Earlier, in August, 2021, Blue Origin made an infographic for its lawsuit with NASA over funding a second HLS program. That infographic roughly illustrates what Hawkins explained during the meeting...

Blue Origin Lawsuit Infographic
Therefore, even if just a single Starship were sent to Mars, the overall mission complexity would still be high - likely involving on the order of 20 twenty launches from Earth.
Comment: I would argue that LEO refueling launches don't actually really increase the mission complexity that much. While it's yet to be demonstrated, I would actually argue that doing the same thing over and over actually reduces complexity in the system. Specifically, comparing two systems that have the same end capability: one requires many unique complex steps, while the other one requires many steps that, while complex, are not unique and have been done many times before.
Comment: Most of the criticisms about multiple Starship launches are similar to the "nine engines is crazy" argument, and later the "33 engines is crazy" argument. People are making comparisons assuming the complexity and cost of traditional hardware. Musk's goal is to simplify the processes so that multiple launches are not complicated or expensive. We won't know for a few years if Starship can meet these goals, but based on what we are seeing with Falcon 9s constantly increasing flight rate, it is quite possible that within a few years Starships will be able to fly relatively quickly and economically
Comment: @Dragongeek: And as Musk likes to point out, SpaceX has already demonstrated fully autonomous precision docking and proximity operations with Dragon many times, and orbital refilling should actually be easier, because SpaceX is in full control of the design of *both* vehicles and both vehicles can maneuver. So, the docking part should be easy, that leaves in-space cryogenic liquid transfer, which has already been demonstrated at small scale on the ISS as well with the robotic refueling experiments.
Comment: @StevePemberton and people are still thinking of launches as rare events, products of heroic effort planned years in advance with months of delays being routine, with vehicles like the SLS being designed with that being considered normal...52 months lead time on a fully expendable SLS core and a production pipeline that can't even put out a core a year. Falcon 9 does multiple launches a week and Starship is designed from the start to allow an even faster launch cadence.
Comment: I agree. I was thinking about getting into the topic of how one defines "complexity" but it seemed like too much of a tangent topic.
Comment: The tanker launches also have a form of serial, almost indefinitely extendable redundancy. If you lose a tanker or experience technical issues preventing it from transferring its propellant, you can send another, until you run out of tankers. Delays may require adding another tanker flight to account for boiloff, but that's just doing another routine tanker flight.
Answer: I think a lot of people are getting hung up on "complexity is bad" when the reality is that to solve complex challenges, we need complex solutions that can eventually be simplified once time and experience has been gained.
Specifically, there are plenty of "complex" systems that operate well and "seamlessly" today, to such a degree that most people don't even think about them.
An example:
Take something like the postal service. Explain to someone who has never heard of it before, that there is a system in place that enables anyone, regardless of how in-the-back-woods they live, to send letters and parcels to almost anywhere on Earth, across political and international borders, often in a matter of days. They would look at you like you've lost your mind. They could raise all sorts of questions about logistics, how it all works together, and generally just highlight how ridiculous this capability is and how monstrously complex it is.
Nevertheless, it works well. It works so well, that most people don't even think about it.
For this reason, while reducing complexity in a system is a nice thing to strive towards as an engineer, trying to jam simple solutions onto complex problems isn't always desirable.
NASA's Mars Plans
The plans, as outlined in the diagram, are knee-slapping, hilariously ludicrous. I would be mind-blow if Mars Sample Return managed to launch anything before 2030, and the idea that NASA will be launching components of a Mars base in Early 2030s is just not real. My bet is that this plan exists solely to sell the idea that SLS has plenty of work to do in the future, which is a debatable point.
Why? Multiple reasons:
NASA's focus is Luna
The Artemis program is just getting started. Currently, all the Artemis timelines are being pushed back, but, if I'm being optimistic, we will see boots-on-the-regolith before 2030. I suspect that this will result in the Moon capturing a large chunk of NASA's attention and budget over the following decade they will probably want to build out a Moon base so they can achieve the "sustainable" goal.
How exactly the ISS situation wraps up is unclear, but I could see a very realistic scenario where "moon base" becomes the type of budget line-item that the ISS is today: the premiere manned program, with widespread international cooperation, and with a dash of space tourism.
Supporting these Moon activities will eat up the SLS launches, and leave no budget for a flag-planting operation on Mars.
Travel times are too long, the stay on Mars is too short
There's just too little payoff. You've got astronauts crammed into a capsule for two years with a short, month-long surface jaunt in the middle. It's just stupid. Not only would we needlessly be psychologically damaging the astronauts, but there are all sorts of concerns associated with the short-stay mission structure.
For example, gravity and sickness. What happens if once our intrepid explorers arrive at the red planet, they are all so weak due to the sudden gravity that they can't perform mission tasks, or what happens if they fall ill (which they will) and this similarly degrades their performance? Even if the astronauts are just weakened for a week, that's already a third of the mission time.
I'm also skeptical of the scientific merit of a 30 day stay. As structured, this would essentially just be a flag-planting sample run. 30 days doesn't really leave enough time for actual "investigation". The hourly price of the astronauts there will be so extremely high in a dollars-per-minute way, that they won't have any time to do anything exploratory, and labs on Earth won't really have enough time to plan scientific activities. Beside the presumably larger volume of samples, there's little scientifically such a short stay could tell us that a completely robotic and significantly cheaper sample return mission couldn't.
Mass-is-expensive thinking paradigm
NASA and much of old-space is still stuck in a "mass-is-expensive" paradigm, meaning that one of the fundamental constraints is reducing mass down as much as possible. This is why our spacecraft have hulls thin enough that someone could poke a hole through with a moderately sharp screwdriver.
This will all (knock on wood) change when systems like Starship or New Glenn come online. The cost reduction that these will offer cannot be understated, and will require NASA to to scrap and remake basically all their plans once we cross this Rubicon where "kilotons to LEO" is no longer an unusual figure.
Comment: Mass will always be expensive. Without a space elevator or some other speculative technology, there's no escaping the tyranny of the rocket equation. New reusable launch vehicles can be more economical, but it will never be cheap climbing out of Earth's gravity well.
Comment: The short stay mission structure also increases the overall detrimental health effects. The astronauts are not only stuck in the interplanetary radiation environment for a longer period, but their trajectory takes them past Venus through a solar radiation environment twice as intense as that experienced at Earth and four times as intense as that experienced at Mars. It literally maximizes harm in order to minimize the benefits. It's an *idiotic* idea, but some people seem to be in love with it for some inexplicable reason.
Comment: @bjmc The point I'm trying to make is that most sacrifices made in NASA plans today are because mass is too expensive. This simple fact flows in from day one, and this is why we end up with ridiculously long transit times. With today's tech we could do a 100-ish-day transfer if we wanted to, but doing so is seen as a "waste" of fuel and budget: instead, the astronauts spend years aboard and we stomach the cost. With Starship-levels of lift, where we can send many, many kilotons of fuel to orbit for less than a single SLS launch, we can start being a bit "wasteful" with our mass priorities.
Comment: 180 days to Mars is like a normal stay on ISS. Most returning astronauts are pretty functional within a week, it will likely be no worse in the 2/5 gravity on Mars, maybe even a little better. Compared to a couple of days on the Moon three functional weeks on Mars will provide a lot of useful experience as well as scientific opportunities. Do I believe this powerpoint? No. I don't think the first Mars trips will occur until we have the propulsion technology to do short stay missions with return in just over a year, however many decades that takes to happen. Multi-year missions will then follow
Comment: @bjmc the "tyranny of the rocket equation" accounts for very little of the cost of launch, it's almost all operational complexity (which might not actually be any less for an elevator) and cost of expended hardware. If Starship gets anywhere close to its operating cost targets, it will be able to put payloads into orbit for far less than a space elevator. And Starship's cost estimates are far less speculative than those for such an elevator, considering partially-reusable rockets are already in use while a space elevator requires materials we can't even fabricate yet.
Comment: With Apollo, they found that the "flag-planting sample run" mission format gave the best science return.  On-site analysis has the problem that you might not have the right equipment -- for example, the Viking landers were confounded by the presence of perchlorates in the Martian soil.
Comment: @Mark Sure, but Luna and Mars are fundamentally different targets. Apollo missions only took 10 days, while any Mars mission will take years. We've advanced quite a bit since Apollo, and I think that with the advancement of small-scale manufacturing and faster comms any future manned deep-space mission will have a significant "improvisational" budget, where Earth creates and then uploads fixes that the astronauts can then implement in-situ. I just think that the cost-benefit of robotic missions beats short-stay manned Mars missions, only a long stay with human flexibility can flip this.


Where can you farm ore in Skyrim?

Question: I want to level up my blacksmithing, but I can't find enough ores to do it. I've farmed all dungeons, that I've farmed so far (I'm level 11) and bought all ores\ingots from NPCs. So are there respawn timers on ore sources, and what are the best places to farm it?
Answer: I've found that fast traveling between blacksmiths as they restock is much more efficient than mining as a method of leveling smithing.  Ore veins are few and far between and as far as I know, the respawn time is when the area resets. Furthermore, the act of smelting does not by itself give you experience.
For that reason, I found bouncing between War Maiden's in Whiterun, Alvor in Riverwood and Beirand in Solitude, buying their entire stock of usable ore, ingots and leather, turning it into weapons or armor then selling those back to them was the fastest method.
Since you gain experience in smithing proportional to the value of the items you create, there are a few items that can make the process more efficient.  Those are the Forgemaster Fingers and the Notched Pickaxe.  You can use the enchantments on these items to improve the items you create beyond you current skill level.
I also found that for each type of item you can create (Orcish, Elven, etc.) there is an item with the highest input to value ratio.  If you are going to grind smithing, it is best to grind whatever item this is for your level.  You can refer to the tables on the relevant type. For instance, for Dwarven smithing, the bow has by far the highest ratio as it requires only two dwarven ingots and an iron ingot.
Comment: Thats exactly method i started to use, after reading article on uesp
Comment: I would also recommend the Ars Metallica mod. It provides more smithing possibilities and will reward small amounts of skill advancement for mining and smelting. Mod link: http://www.nexusmods.com/skyrim/mods/16084/?
Comment: If you've done enough "small jobs" for the Thieves' Guild, there will be 3 ore selling vendors in the Ragged Flagon.  As an added bonus Tonilia will have more than enough cash to buy all the jewelery you make from the iron ore.  A nice Gold & Diamond Necklace can *really* boost your smithing skill
Answer: As ever with Skyrim, UESPWiki is your friend.
<code>Region          Location            Veins       Ores    Ingots
Whiterun Hold   Halted Stream Camp  16          4
Solitude        Solitude Blacksmith             5       42
Winterhold      Fort Fellhammer     10          10
Falkreath Hold  Embershard Mine     9           2       2
The Rift        Treva's Watch       1           3       18
Hjaalmarch      Sorli's House                   4       19
Haafingar       East Empire Company Warehouse           21
Falkreath Hold  Knifepoint Ridge    6           3
The Reach       Blind Cliff Cave    6
Eastmarch       Gloombound Mine     6
The Pale        Iron-Breaker Mine   6
Riften          Blacksmith                      2       15
The Reach       Left Hand Mine      5
The Reach       Nchuand-Zel         4
Hjaalmarch      Rockwallow Mine     4
The Pale        Forsaken Cave                           11
Haafingar       Haafingar Stormcloak Camp               10
The Pale        Nightgate Inn                           10
Hjaalmarch      Stonehills                              10
The Rift        Forelhost                       5       5
Haafingar       Jala's House                            9
Haafingar       Solitude Lighthouse             1       8
Eastmarch       Lost Knife Hideout  3
The Rift        Northwind Mine      3
Solitude        Proudspire Manor                        8
Solitude        Evette San's House                      5
Whiterun Hold   Riverwood                               5
The Reach       Understone Keep                 4       1
</code>
Comment: This would be more appropriate as a comment since it doesn't answer the question at all. At least quote the relevant section.
Comment: How about respawn? Are they respawn, or there are limited amount of  ores?
Comment: @Avdept They respawn after a while.
Comment: It helps a great deal to install one of the mods that make ore veins glow. There's a lot more of them than you might realize, since they blend in to the scenery so well.
Comment: @kotekzot The way i just did in this edit. Just takes a little effort but this is a Q&A site, not a link collection to wikis.
Comment: I nearly did a 'Let Me Google That For You' link.
Answer: The one that I've found more easy to farm is going to Halted Stream Camp, northeast of Witherun, there will be few guys to kill, go into the mine, kill everyone and in the table of the chief bandit will be a spell book, use it, it will transform iron ores to gold and etc, if you're low in magicka use the wait tool, and put in one hour every time your magicka is low, hope it helpd :D
Comment: thats actually good one, but it doesn't solve question where to get  other ore to transform it to gold
Answer: I've found that farming ore is too time consuming.
Find a vendor that sells it, buy them out, sell them something (if you have something) that will get your money back, then quick-save, attack them, quick-load and they have money and inventory back in full.
Rinse and repeat as long as you want to. Works great for grabbing ingredients too.
I use it for buying the following:

black soul gems (as well as the others) (Falion)
ingredients (anyone that is an alchemist)
ore/ingots/leather (any blacksmith)
building materials (any general sales vendor)
Answer: First off, go to Halted Stream camp. Mine all of the ore since you're there, but remember to pick up the spell tome on the table, Transmute, and process to turn your iron to silver and silver to gold. Go around to every blacksmith you can find and buy all their iron ore. (Also should be jotted that general traders also sell ore.)
Another mine you might try is Iron-Breaker Mine in Dawnstar. After you've turned all of that iron into gold, smelt it and make gold rings. (The gold rings sell for more than the Emulates and you don't have to waste precious gems on them. Also I would suggest having the warrior stone activated as well as having Lover's Comfort.)
Answer: Get the dwarven smith feat and raid dwarf fort/mines.
They are usually so loaded with scrap that you can't get enough of it.
If you cant get the feat then focus on raising money and buying smith materials.  Improve your speech feats until you are getting good deals on your stuff.
Enchanting and Smithing were the first skills I got to a hundred on, fairly rapidly. The better you get the more you can resell your products for and thus buy more crafting materials. Eventually you start clearing out smiths inventories.
Answer: You're going to want to go to Halted Steam Camp just like a bunch of other people said before me (gather ore, get the spell book, bla bla bla...), until this point it was rather self-explanatory, but now you're going to want to use for your best soul gems and enchant a helmet, armor, ring and amulet with fortify alteration. A good idea would be drinking an enchanters elixir first, And if you're enchanting Skill is good enough you can reduce the magica cost of your transmute spell to 0%. As for ore, there's the aforementioned Halted Steam Camp, Iron Breaker Mine, traveling between blacksmiths and general traders and there's even a Forsworn mine in the Reach that exclusively has gold ore (can't remember what it's called though). Rinse and repeat with the traders until the mines are replenished and you're golden [literaly].
Answer: Its better to buy from blacksmith in all town finding ore is much harder and need more time
funny thing the first and only time i found ore in the world i didnt have a pick axe to farm it with

Where can you farm ore in Skyrim?


What type of screws should I use to attach a sign to fiber cement siding?

Question: My house has fiber cement siding and I want to attach a decorative sign to the siding. I'm told that I need a carbide tip drill bit to make a clean cut. But what type of screws should I use? And what length is recommended? (the house is wood framed).
Comment: I just mounted some objects to my house which is sided with Hardie Board (which is probably the same or similar product). I drilled through easily with a cheap Harbor Freight drill bit with no issues. I did screw through the siding into stud for security.
Answer: Just use ordinary wood screws.
Beneath the siding should be 3/8" or 1/2" sheathing. That is what the screws will really bite into.
Just make sure your screws are long enough to go through the sign and siding and have at least 1/2 of length beyond that. If you're concerned about water penetration squirt a little bit of caulk in the hole before placing the screw, but doing nothing is probably fine too
Comment: There's no indication of how big/heavy the sign is, but I'd suggest that the OP try to find studs, just to be sure. That also helps ensure that the screws holding the sign up don't accidentally hit wiring or plumbing behind the siding.


Should one introduce past work in PhD statement of interest?

Question: I wrote my statement of interests where one paragraph is dedicated to discuss my past works. But I wonder if that is necessary because it feels like repeating abstracts from the papers. And probably it will not make much sense to those who do not specialize in those topics. Should I just refer to the paper and make no formal introduction of what I did?  Since there is a word limit, it is really hard for me to explain all those ideas in just a few words without assuming any technical prerequisites, and I feel it is not really stating my interests and my visions of my doctoral studies anyways, because I'm open to other related topics as well and don't want people to think "oh, this is a XXX-guy and our faculties do not work on XXX so he is a mismatch".
Comment: Is there some theme to how you picked topics?
Comment: @PatriciaShanahan, that sounds like it could be developed into a proper answer.
Comment: @Buffy I don't have time at the moment, and you know more about how these statements are read.
Answer: I don't think Ben's answer says this strongly enough:
Your statement must include a description of your past work, if you have any.
The primary feature that PhD admissions committees looking for in applicants is evidence of potential for high-quality independent research.  The strongest possible evidence of your potential to do high-quality independent research is the fact that you have actually published high-quality independent research.
It doesn't matter whether your past research is on the same topics that you want to pursue in the future.  It's easy to communicate a change in interests in your statement with a single sentence: "More recently, however, my interests have shifted to quantum tropical M-theory."  (Obviously this sentence should be followed by a description of your specific interests in quantum tropical M-theory, written with enough maturity to convince experts in quantum tropical M-theory that you have the necessary knowledge and skills to be successful in quantum tropical M-theory, but that's what you were going to write anyway.)
Crucially, if your previous papers have coauthors, your statement (and your recommendation letters!) should focus on your specific technical contributions to those papers.  Remember that you are not trying to sell the work as good mathematics; you are trying to sell yourself as a good mathematician.
In particular, you are not trying to sell your past work to experts in your subsubfield of (past) interest, so you should not merely quote the abstracts.  You are trying to sell yourself to a general audience of trained mathematicians, some of whom are experts in your subsubfield of (past) interest.  So your description needs to be understandable to that broader audience, but still interesting enough to experts that they will want to read your papers for the actual technical details.
Obviously you should provide direct links to arXiv versions of your papers, in both your CV and your statement, so that interested committee members can read them without having to search.
[I'm an American theoretical computer scientist, which means I'm like a mathematician, except that I write less code.]
Answer:
I wrote my statement of interests where one paragraph is dedicated to discuss my past works. But I wonder if that is necessary because it feels like repeating abstracts from the papers.

If your past work relates to the research interests you are raising in your statement then it would not be out of place to mention these works.  Indeed, in many cases this will be useful context, since it sets out what you have already done, and frames your interests in the context of existing work.  Mentioning these works would not necessarily entail repeating information in the abstracts to those works.  Bear in mind that even if you do not mention your past papers, they will be present in your CV, so the academics reviewing your application will know that you have written previous papers.  Ultimately it is up to you to decide if these papers add useful context or information about your research interests.

...probably it will not make much sense to those who do not specialize in those topics.  ...

Then it is badly written and you need to write it better.  Your statement should be for a general audience of academics in your broad field, without necessarily having specialist knowledge in your particular topic.  These people are experienced researchers with PhDs and probably decades of experience in your degree area; if what you write does not make sense to them then you have written it badly, and you need to smack yourself on the wrists and try again.  Learning to write about technical research in a way that does not get bogged down in minutiae is an acquired skill, but it is one you need to practice for entry into a PhD program.  It should not be impossible to explain your past research in an way that makes sense to experienced researchers, even if your past research falls in an area that is not their particular specialty.  Keep trying to write out a good explanation, and explain the essence of the work while shedding any unnecessary technical information, until you have something that makes sense.

Should I just refer to the paper and make no formal introduction of what I did?

There would be no point to that, so no, you should not do that.  If you mention your past papers at all, it should be to provide context for your research interests and the present context of that research.

...I feel it is not really stating my interests and my visions of my doctoral studies anyways, because I'm open to other related topics as well...

That will take about one sentence in your application to explain.


Proof involving characters

Question: I'm self studying from a Classical Introduction to Modern Number Theory by Ireleand and Rosen. In the exercises for the chapter on Gauss and Jacobi sums I came across this question.
Let $\chi$ be a non-trivial multiplicative character of $F_p$ and let $\rho$ be the character of order 2 (the legendre symbol), then if $k \in F_p$ and $k \neq 0$, then $\sum_{t=0}^{p-1} \chi (t(k-t)) = \chi(k^2/4)J(\chi,\rho)$.
Now, $\sum_{t=0}^{p-1} \chi(t(k-t)) = \sum_{c=0}^{p-1}N(t(k-t)=c)\chi(c)$, where $N(t(k-t)=c)$ is the number of solutions to the equations $t(k-t) = c$. Now, $t(k-t) = c$ is solveable iff its discriminant is a quadratic residue and if its solveable there are two solutions. So $N(t(k-t) = c) = N(s^2 = k^2 - 4c) = 1 + \rho(k^2-4c)$
So, the sum becomes $\sum_{c=0}^{p-1}(1 + \rho(k^2-4c))\chi(c) = \sum_{c=0}^{p-1}\rho(4)\rho(k^2/4 -c)\chi(c) = \sum_{c=0}^{p-1}\rho(c)\chi(k^2/4 - c)$
Now, $\chi(k^2/4)J(\chi,\rho) = \chi(k^2/4)\sum_{t=0}^{p-1}\chi(t)\rho(1-t)$
And no matter how I try to manipulate it, I can't get the equations to equal each other. Did I do something wrong along the way?
Answer: In $\sum_{c=0}^{p-1}(1 + \rho(k^2-4c))\chi(c)$,
try replacing $c$ with $k^2/4c$ instead of $k^2/4-c$. (To get to the right hand side you want to be able to pull out a $\chi(k^2/4)$, so put yourself in a position to do this.) This should take you to
$\chi(k^2/4)\sum_{t=0}^{p-1}\chi(t)\rho(1-t)$.

Proof involving characters


Is elastomeric better with more polymer, or with added calcium carbonate?

Question: While comparing elastomeric roof coatings, I notice that one brand is 60% polymer, while the the other is 40% polymer along with 30% calcium carbonate.  Polymer is flexible.  Calcium carbonate is brittle.  With that consideration it would seem more polymer is better, since weather conditions challenge the membrane integrity for water resistance.  However, polymer degrades far more than calcium carbonate.  Perhaps inclusion of calcium carbonate provides some protection against degradation.  So is it better to have more polymer, or some of that replaced with calcium?  (Since polymer is more expensive than calcium carbonate, my instinct suggests there would be no reason to maximize polymer at its higher cost, if it did not improve performance.)
Answer: Stuff like calcium carbonate is generally used as a cost cutter, as it is far less expensive than even the cheapest elastomer (polymer). It allows the producer of the formulation to make a profit/make more profit, essentially.
Generally speaking, adding calcium carbonate to an elastomeric formulation will decrease the useful properties of said formulation, including its resistance to weathering. It's resistance to wear and tear (as represented by mechanical properties like tensile strength and abrasion resistance) will also suffer. Calcium carbonate containing formulations, all other things being equal, will also be less elastic and somewhat stiffer.
A polymer that has poor resistance to weathering (like SBR rubber) will generally also not benefit from calcium carbonate as a formulation ingredient. Instead, special anti-oxydant/anti-ozonants will improve this cheap polymer's fight against the elements.
But if a composition does contain significant amounts of calcium carbonate it is not automatically disqualified as suitable: that will largely depend on the end-user's expectations. In other words: cheap can work well too.


Not being prompted to "Erase Disk and Install eOS" during setup

Question: During installation from USB stick on W10 machine,
Rather, it skips right to the partition creation screen and clicking "change" or "+" or "add partition" just makes the installation hang. Any ideas?
Thanks!
Tony
Answer: If this happens, you can run the live version of elementary OS, delete partitions and format drives using gparted then try again. This worked for me.


Where I can download images of chess pieces for my chess app?

Question: I am developing an Android app and I need chess pieces images for my it. I am concerned about copyright issues as well. I can copy images from other chess apps on GitHub projects, but I am not sure if that is legal. Is there any free source to get images of chess pieces?
Comment: [This](https://chess.stackexchange.com/q/6272/21604) might help you.
Comment: @wimi hey, Thanks for that link, very useful!
Answer: Check out the licenses of the piece sets that lichess uses: https://github.com/ornicar/lila/blob/master/COPYING.md#exceptions-free
Personally I am using the cburnett piece set for my project.
Comment: Hi, Thanks for that link but I am still concerned about the license, for example `cburnett` pieces have  `Apache License 2.0` .https://github.com/LexLuengas/chessnut-pieces/blob/master/LICENSE.txt  it says
`A permissive license whose main conditions require preservation of copyright and license notices..`  does that mean I have to add some kind of license file in my app?
Comment: @beginner yes, you would have to include in your app a copy of the Apache 2.0 license text (i.e., the file LICENSE.txt in that repository) AND also a copy of the copyright notice (which is in file COPYRIGHT.txt). You would also have to state it if you change the piece sets. You can do all this in an "About" screen that can be accessed through the "Settings" button in your app. If you write "about:licensing" on Firefox, you can see an example of such a screen. You can ask questions about licensing on https://opensource.stackexchange.com/ .
Comment: @wimi thank you so much for your help, but actually I was looking for a free and standard version of pieces, those pieces are a bit too fancy for my app and tey also require adding copyright and license text, anyway thanks for your help:)


formation of σ molecular orbital in H2

Question:
In the picture, graphs show the constructive interference of two 1s atomic orbitals. My question is, what does the horizontal axis in wavefunction graph represent, does It represent the distance from the nucleus? We see the pick point of wavefunction on H atom, does It mean that highest probability of electron density is on the nucleus, which is impossible.  I am quite confused about the meaning of a wavefunction, can anyone help me?
Comment: We should also keep in mind that nuclei are usually described as point charges in quantum chemistry.
Answer: You are mostly right. The horizontal axis represents the distance from the nucleus. The maximum of the electron density of 1s orbitals is in fact at the nucleus. This is not impossible, remember that electron density can be interpreted as the probability that an appropriate experiment will detect the electron there. In fact, electron density "at" the nucleus is one of the major ways NMR spectroscopy works.
Comment: Thank you for the answers,  everything is more clear now.  As far as I understand since the size of nucleus is extremely small,  Its considered as a point and electrons can be assumed to have the highest probability on that point.  Even though they are not exactly inside the nucleus It can be assumed that they share same location.

formation of σ molecular orbital in H2


New document version and old document version

Question: I have a form that I had to create a new version of. I don't want anyone to be able to use the old form, but we need to be able to access, modify the entries in the old version of the document.
Answer: I'm a developer with Cognito Forms.
As long as you are only modifying the entries of the old form on the Entries page you can set up the Limited Availability feature on the Build page. By setting an end date you can then show an unavailable message for the form, that will prevent your end users form filling it out.


Local Storage Database size

Question: I am creating an application which runs on Safari/Chrome and iPad. I am using an HTML 5 database to store the data with a library which decides itself whether to use an indexed db or websql as per the browser. Since each browser has its own storage limit, I want to know is there any way to find out how much space is left in the database so that I can display a message to the user to clear the local database before allowing data to store.
Answer: By default in Firefox 4, a site can use up to 50MB of IndexedDB storage. If it tries to use more than 50MB, Firefox will ask the user for permission
In Firefox for mobile devices (Google Android and Nokia Maemo), Firefox will ask for permission if a site tries to use more than 5MB
For Chrome browser you can see here: https://developers.google.com/chrome/whitepapers/storage

Local Storage Database size


Do Fire Walkers damage enemies?

Question: The new Fire Walkers leave a trail of fire behind you.

Does this fire damages enemies it touches?  If so, how much?
Answer: Yes it does damage enemies! There's some information on the forum about this. Here is someone who knows a bit more. Look at post #2
He says the damage ticks at around 2500-5500. He also mentions it can hit objects such as barrels to open them. I have no idea if the damage is based off weapon damage or if it is fixed.
Answer: According to the 1.0.4 Legendary Items preview, the caption below these boots say:

Aside from looking really cool as it leaves a trail of fire behind you, this lets you create some interesting traps.

That implies that yes, the fire trail does do damage, and the mechanics behind it are probably exactly the same as the elite Molten affix.
As for the amount of damage these provide, I can find no information on that, but if this works just like Molten (which I believe is based on monster level), then it's going to provide a set amount of damage at level 60.  Paragon levels will almost certainly not affect it.
As an additional note, there are now affixes that increase fire damage by X%.  I do not believe the damage from the fire trail will benefit from these affixes.
Answer: My boots definitely do damage from the trail. can't say the amount but it looks like its about half of what my normal attacks do, so im guess about 7000-8000. Who knows if its linked to weapon damage; level, crit, fire res, monster level, or just a flat rate but i promise you... monsters walk into my trail and they flash. health drops some even though no damage numbers appear. unless im witnessing thorn damage without the monster attacking.
Answer: Fire walkers do NO damage from the fire left behind. The trail is PURELY COSMETIC. However it can trigger destructibles such as barrels. I am testifying from in-game experience using them.
Now that said, I expected fire walkers to do damage as well. So I sold mine immediately before people start catching on to the fact that they do no damage.
Comment: This video clearly shows that you are incorrect.  http://da.twitch.tv/eightkilo/b/329519860

Do Fire Walkers damage enemies?


Why is "a" in "What is a desperate humanity to do?"

Question: I heard this sentence in the TV show Severance: "What is a desperate humanity to do?" Isn't "humanity" an uncountable noun? Why is "a" in front of it? Thank you.
Comment: **Comments have been [moved to chat](https://chat.stackexchange.com/rooms/143075/discussion-on-question-by-abcd-why-is-a-in-what-is-a-desperate-humanity-to-do); please do not continue the discussion here.** Before posting a comment below this one, please review the [purposes of comments](/help/privileges/comment). Comments that do not request clarification or suggest improvements usually belong as an [answer](/help/how-to-answer), on [meta], or in [chat]. Comments continuing discussion may be removed.
Answer: In his Comprehensive Grammar of the English Language, Randolph Quirk says:

Some noncount nouns accept the indefinite article when they are modified .  eg:

They are doing a brisk business. (NOT *a business)

In some cases no modification seems to be required. In the following example, however, modification is in fact implied:

She has had an education. ['a good education']

The same author argues that

The conditions under which a/an occurs in such cases are unclear, but appear to include the following:

(i) the noun refers to a quality or other abstraction which is attributed to a person;
(ii) the noun is premodified and/or postmodified; and, generally speaking, the greater the amount of modification, the greater the acceptability of a/an. (see ch 5.9, p. 252 and ch. 5.59, p. 287)
Comment: "What's an X to do?" is something of a fixed phrase, likely contributing to this sentence's acceptability.
Answer: Several dictionaries do not recognize that "humanity" can be countable, but apparently that does not corresponds to usage (page of results for following ngram).

Cambridge,  Collins OALD, Longman
This is also true to a certain extent, for instance, of a common word such as "paint" (OALD); yet you can say "some paints are more lasting than others". The fact that an indefinite article is used results from a general process called conversion, the particular sort involved here being "change of secondary word class for nouns" (A comprehensive grammar of the English language, Quirk et al.,  I 53).  This is a process that is not fully productive [and not easily acknowledged]. It is recorded in dictionaries for certain nouns that are so often used this way, so that their conversion has been "completed", so to speak";  for others it is not  convincing enough. There are three sorts of secondary word conversion for nouns.

CoGEL
[i] A unit of < noun > a beer, a coffee, a cheese, … (examples given shown as [U,C] in dictionaries)
[ii]  A kind of < noun > bread  — (not in Cambridge, OALD, Longman)
[iii]  An instance of < noun > difficulty, frailty (examples given shown as [U,C] in dictionaries)

This is what happens to the word "humanity", which when used with "a" in this case means "a sort of humanity" (conversion of type 2). The reason for not finding a definition in dictionaries could be that saying "a sort of humanity" in the way of a definition would be saying something too general and having a meaning that is too vague; the meaning in the text is not vague because it is made precise by the context, this latter providing the clues that allow to determine what is that portion of humanity at a given place and time and what is its plight (or success, or something else). However it is not so easy  to recognize that, and this usage is anyway literary in my opinion.
In the context of the dialogue in Severance it means something like Humanity such as found at a particular point of its evolution [that the context explains] (paraphrase of above definition) and that was also desperate"; humanity is not generally reckoned with as being desperate in all the periods of its known existence.

Complement aiming at clarifying comments made by user Mari Lou A and adding a precision highlighted by that user
First of all, it should be well understood that this conversion is a conversion from noun to noun, not a de-adjectival conversion to nouns ("final race, the final"); so as "desperate" is not a noun but only an adjective, the remark about this word is not relevant. It is however a good remark to say that you can't say "two desperate humanities". Secondly, the conversion being examined concerns that of uncount nouns, but I suppose rather that the countable nouns "kind" and "instance" where used in your comment to show the full range of possibilities that presents a truly countable noun.
The process of conversion is not a fully productive one; for certain nouns, in particular because of the nature of these nouns, it does not even occur at all. For instance  you'll find that nouns such as

"leniency", "heredity", "censure", "impiety", "religiosity", "permanence", etc. (You might plot the ngrams "< N >,a/an < N >"  and verify the nouns in the dictionaries that provide a label of countability.)

are fundamentally uncount nouns as recorded in dictionaries but that nevertheless they appear in text preceded by the indefinite article. This is true for a great number of uncount nouns. Even if  "a/an < N >" is included in "< N >", in most cases if not nearly all, it can be seen that conversion results in a lot less occurrences.
You will also find that there are nouns such as "indefensibility"  (basically noncount) for which connversion does not occur at all.

The explanation for this is to be sought in the nature of the word: "indefensibility" is of such a nature that we are not inclined to classify it into categories or singularize it into instances,  except perhaps in a philosophical treatise. Conversion does occur for "defensibility" probably because in reference to this concept a particular scheme of defensibility raises much more interest. There are more common nouns with no conversion, as, for example "money".

An enormous majority of the cases concern premodification and a few are cases when money means "currency" (a money).
This is the first phenomenon, I believe, that accounts for calling the productiveness partial; the second is the generally incomplete  process of conversion that a noun undergoes; whereas a countable noun and an uncountable one present the following possibilities.

det/number
count
noncount
dual membership

zero

furniture
brick

the
the book
the furniture
the brick

a
a book

a brick

some

some furniture
some brick

plural
books

bricks

A conversion does not show a perfect reversal;  this is the reason why those nouns are not recognized in dictionaries as countable.

det/number
noncount
count by conversion

zero
humanity

the
_________
the humanity

a

a humanity

some
_________

plural

________

Here are cases of the use of "the".
(ref.  1875) Ah , Sappho , you are a close little reader of the humanity you are afraid of.
(ref. 2008) Be an excellent observer of the humanity you are a part of.
(ref.  1902) You are a formal pedantic, heartless, professional sociologist, with no more real knowledge of the humanity you are writing about, than a mummy, but I'll forgive all that, for what you have just said.
Notice that the usual form "some N" (some bread, some furniture, etc.) does not exist for "humanity": in "some humanity" "humanity" means "quality of being kind to people", and the true partitive construction is "some of humanity"; nor does that of using "the"; so nouns that are called uncountable in the dictionaries do not necessarily have themselves all the characteristics of uncountable nouns.
Let's now take up the second one of your questions.
This first example shows the notion very well (Fabric of Humanity).

Naskar the person died long ago, now what lives in front of you, and indeed within you, is Naskar the idea—the idea of one humanity—the idea of a harmonious humanity—a humanity that places the benfit of the neighbor above the benfit of the self—a humanity that places the significance of shared joy above the joy of the individual—a humanity that lives not in a chaotic planet, but in a truly intertwined conscientious society.

It is clear that what is presented is an idealized picture of humanity, a picture that we do not know as that of  humanity such as we experienced it to the present day: it has its own characteristics which are not those of real humanity. It is therefore a fictitious humanity, a sort that could take the place of humanity as we experience it. There is no doubt that the idea of kind or sort is central in this text. However, we must concede that it is a fictitious sort and perhaps that beyond the sphere of fiction another reality could have to be contended with.
Concerning the ngram
common
ex. 1
In the case of "common humanity" the meaning is "the state of being a person rather than a god or an animal or a machine";  I believe that "common" means "well known, accepted by all". (Mad Or Bad?)

The psychopath shares with us a common humanity ; he remains a person.

The behaviour that results from being sick in the mind is part of the humanity of someone; as well, that which results along the lines of accepted norms is part of someone's humanity; the common humanity shared by the psychopath is that of a normal person; but the humanity of the normal person cannot include all the patterns of behaviour of the psychopath; in that respect it is a different sort of humanity.
ex. 2
(
Hearing Before the Committee on Immigration and )

It is only through treaty or through residence here, that such rights accrue. But we should not, however, be forgetful of the obligations of a common humanity." Having the words of the President in mind, let us ask the question. "Are we not 'forgetful of the obligations of a common humanity' in depriving those citizens of our country  whose wives are of a race ineligible to citizenship of the confort and society of their wives—in forgetting the family tie and decreeing by law the wives of such citizens shall be debarred from […]

new — I assume that in this next example "humanity" means "people in general" (
Search for a New Humanity: A Dialogue Between Josef Derbolav, The dialogue concludes with a reflection on the future for the human race, looking to an inner revolution - a radical alteration in our way of thinking - which will conquer the daunting problems currently facing the planet and its people.)

In conclusion, I should like to pose this question: In the light of the jeopardy in which our future stands, is there any point in discussing the chances for a new humanity? The kind of humanity that is meant here is not to be found in horizons of a […]

The idea of sort is explicited in the text itself.
little This result does not apply: "little" is part of the quantifier "a little" (some)
suffering
This adjective implies something new, at least in certain cases (in particular in religious contexts): it is not possible to conclude that a kind is implied; the whole of humanity is understood by this phrase. The use of "a" is not usual, perhaps to be assimilated to the usage of "a" in "She plays the oboe with (a) charming sensibility."; in the words of CoGEL, "the conditions under which "a/an" occur in such cases are unclear".
Wholeness in Hope Care: On Nurturing the Beauty of the Human ...) The suffering on the cross becomes a source of hope for a suffering humanity only when it is seen in the light of Jesus' resurrection.
Therefore, this usage which seems to defy explanation is also found, but I think it might be found much less often than the usage explained through conversion.
Comment: This answer doesn't convince me. The words *instance* and *kind* are nouns and are both countable; I can talk about "different kind**s** of bread " and "three instance**s** of despair/joy" I cannot say "two desperate**s** nor "two desperate humanitie**s**" It seems unlikely that the expression is talking about "a sort of humanity" (ii) but rather it refers to all humans. Can you please explain what you meant by *sort*? Personally, I think that speakers use the term humanity as a synonym for *world* (C) and *people* (C) i.e. *a desperate people/world* which follows the conventions of grammar.
Comment: But when we speak of humanity meaning caring, sharing, and being compassionate, then adding the "a" before an adjective sounds idiomatic, e.g "a common humanity". See results of the [ngram](https://books.google.com/ngrams/graph?content=a+*+humanity&year_start=1900&year_end=2019&case_insensitive=on&corpus=en-2019&smoothing=7)
Comment: @Mari-LouA I found that your interpretation is correct, but not that it should be the only one. You'll find  in my post what  details I could still add.
Answer: Most English abstract nouns like humanity can have an a + adjective or just a appended to them. Abstract nouns are uncountable, yes.
"A humanity of the kind he displays is unusual".
"Only an unreasonable curiosity would make that claim".
examples of abstract nouns
Love, curiosity, grief, chaos, and friendship
From that same site, here are two examples of abstract nouns used by famous people:

"We must
accept finite disappointment, but never lose infinite hope." - Martin
Luther King, Jr. "Overcoming poverty is not a gesture of charity. It
is an act of justice." - Nelson Mandela

You can see that when talking about notion of the noun, no determiner is used.
However, a determiner, an a can be used and is perfectly acceptable.
For example:
"A humanity of the kind he displays is unusual".
"Only an unreasonable definition of humanity would contain that claim".
So, as regards the question about this: "What is a desperate humanity to do?"
It is perfectly in keeping with characterizing humanity. And its meaning is not exactly the same as:
What is desperate humanity to do?
That would be interpreted as humanity overall being desperate.
Here is a definition of this usage:

used before some uncountable nouns when you want to limit their meaning in some way, such as when describing them more completely or
referring to one example of them:
I only have a limited knowledge of
Spanish.
He has a great love of music.
There was a fierceness in her
voice.

Cambridge Dictionary
Answer:
"What is a desperate humanity to do?"

(Absent context or clarification, I am going to assume that the meaning of "humanity" is "humankind" and the words are interchangeable.)
We should consider what "a/an" means. "A noun" means one example of that noun, taken at random, from that class of noun.
Thus "Here is a cat" = Here is one example of a cat that was taken, at random, from the class of animal known as "cat".
For convenience, we can reduce that to "a/an noun" ~ one example of the noun.
Next:
Humanity is weakly uncountable. It accepts the indefinite article when modified by an adjective, a relative, or adjectival phrase.
Compare another weakly uncountable noun:
This is coffee - This is a good coffee - This is a coffee that is good - This is a coffee for the connoisseur.
(Strongly uncountable nouns, e.g. guidance, weather do not do this:
That is good guidance. We are having bad weather.
*That is a good guidance. *We are having a bad weather.")
With weakly uncountable nouns, the adjective/relative/adjunct has a partitive effect. The adjectival separates the class of the uncountable noun (humanity) into examples of subcategories of the uncountable noun (humanity).
This happens as
"What is a desperate humanity to do?" = "What is an example of desperate humanity to do?" = "What is an example of humanity that is desperate to do?" = "What is an example of humanity in desperation to do?"
Does that make "humanity" countable? "No".
Humanity needs to progress
*Two humanities need to progress
*Many humanities need to progress
Answer: The original sentence is "What is a girl to do?" It's a common phrase in English. Sometimes we just use common grammar forms like this and replace the noun, in this case "What is a ______ to do?", and just sub "girl" for "desperate humanity".

Why is “a” in “What is a desperate humanity to do?”


What vampires get from blood

Question: My vampires eat normal food too, but if they don't drink blood they get really hungry for it. If their hunger goes on for too long they become unhealthy and weak.
I figure that blood of mammals contains a chemical or compound that their body is unable to create on its own. They crave the blood because they need the chemical, doesn't mean they aren't gluttonous for blood or peruse it even when they're not hungry.
I'm just having a hard time researching what they need from human blood.
Comment: ??? Every substance which is made by the human body is transported from the place of manufacture to the place of use by the blood stream. There is no other transportation network in the human body. So that I don't get what you mean by having a hard time researching what they need from human blood; obviously, sugar and spice and all things nice -- insulin, adrenaline, noradrenaline, dopamine, melatonin, etc. etc. etc.
Comment: In the original concept, they weren't sparkly and driven by the need to survive, but diabolical and driven by the lust to destroy the living and spread despair to those they could not send to hell immediately. Why? That devolves into the silly and unanswerable theological question of "what is evil, truly?". If Stoker focused on blood-sucking, it might have been because of a then-new medical science of hematology, or maybe he was just a kinky freak. The Eastern European mythology doesn't make it so explicit, just that this predatory consumption didn't cause immediate death.
Comment: Perhaps hemoglobin iron?
Answer: Iron: Blood is rich in iron, an essential mineral that plays a crucial role in many bodily functions, including the production of red blood cells. If a vampire's body cannot synthesize iron, they may crave blood to obtain it. Iron deficiency can lead to weakness, fatigue, and anemia, which could explain why a vampire becomes unhealthy and weak without blood.
Proteins and amino acids: Blood contains many proteins and amino acids that are important for building and repairing tissues, transporting molecules, and regulating bodily functions. If a vampire's body cannot synthesize these molecules, they may crave blood to obtain them.
Vitamins and minerals: Blood also contains many vitamins and minerals that are essential for health, such as vitamin B12, vitamin D, calcium, and potassium. If a vampire's body cannot synthesize these nutrients, they may crave blood to obtain them.
Neurotransmitters: Blood contains several neurotransmitters, including dopamine, serotonin, and norepinephrine, which play a critical role in regulating mood, behavior, and other bodily functions. If a vampire's body cannot synthesize these molecules, they may crave blood to obtain them.
Comment: Other than the neurotrans, regular food is easier to get all that. Iron, for example, can be obtained by eating red meat, or even by using a cast iron frying pan. Neurotransmitters are complicated molecules. If the vamp's digestive system passes them into its blood then they will get other complex molecules and have a blood reaction from the wrong blood type.
Answer: Vitamin D
The vampires have a skin allergy to sunlight, and so can't get vitamin d the usual way. As such, they drink blood to get all their nutritional needs.
Comment: Could you define what different thing you are thinking of?
Comment: There is precious little vitamin D in human blood; the human body cannot store it efficiently, so all that's made is either used or pissed out. If they need vitamin D supplements they need to eat fatty fish such as salmon (80 grams per day), or take cod liver oil (half a teaspoon per day). Human blood won't help.
Comment: Vitamin d is definitely a bonus but I'm th8nking of something different
Comment: Lots of vitamin D in beef liver. Don't need to get the humans pissed off for that. If they need just huge amounts of it they can go for carnivore liver (bear, wolf, shark, etc.) but be mighty careful of the dose. Carnivore liver contains high amounts of vitamin A, which can be a big problem.
Answer: Live Red Blood Cells
As other answers have pointed out, all the same basic chemicals and elements present in human blood can also be found in equal or greater quantities somewhere else in nature.  But maybe it's not a thing in human blood that vampires need so much as the blood itself.
Vampire biology is physically incapable of producing its own red blood cells; so, they need to intake live red blood cells from humans to fill this need.  Any other blood will not be compatible and initiate an immune response; so, it has to be human, and old, cooked, or frozen* cells don't count because the vampire needs live cells to replace his own dying cells.
The vampires can't actually drink the blood because that would would destroy the cells in the digestive tract, instead the fangs are hollow or have adjacent sphincters somewhere in the mouth that allows the vampire to directly transfuse the human blood with his own. This said, nearly all vampires will have an AB+ immune system allowing them to receive and use blood safely from virtually all human donors.  A vampire without AB+ blood would be "allergic" to certain humans, and could get very sick if they tried drinking the wrong blood.
* The blood donation industry sometimes freezes cells with cryoprotectants,  allowing them to be thawed and still alive, but these need to be properly filtered of the cryoprotectants before being transfused.  So, if your vampire steals frozen blood, and does not have the proper equipment to prepare it, then it could be mildly toxic for him.
How often do they need to feed
The average red blood cell lives about 120 days meaning that when a vampire feeds it will get an equal distribution of cells with 0-120 days left in them. A person generally starts to notice the signs of blood lose at about 100 ml which is about 2% of your total blood volume.  If vampires are similarly effected, then they should start to get hungry about every 2-3 days. Since significant dizziness and fatigue set in at about 14% blood lose, a vampire should start to feel significantly impaired after not feeding for about 2-3 weeks.  And, since 40% blood lose is fatal, a Vampire should "starve" to death after about 7 weeks without blood.
If your vampire is consuming donor blood, count how long your vampire has eaten as equivalent to when the blood was harvested.  So, if you have a vampire who raids a blood bank, the blood should range from about 1-35 days old.  So, even if he drinks it all, he may still feel like it's been 18 days since he's feed.  A smart vampire will only steal and drink blood that was harvested within the past couple of days, but even that could leave him feeling hungry.
Answer: amino acids
your vampire's digestive system is a mess and they have trouble extracting any amino acids from most proteins so they require hemoglobin to get them iron would be the second best answer, their bodies may only be able to absorb iron from organometallic sources so if they don't drink blood or eat raw meat they get anemia.
Comment: Okay your comment helped me figure it out, vampires constantly feel like they're starving. Even if they eat food they still feel hungry, but blood lets them feel full somehow. This ties into vampire folklore as it's said they love a good meal and that's one way to get them to leave you alone.
Answer: You would need to invent something, or make it spiritual. There's no chemical in human blood which you cannot get from a butcher's shop.
I suppose you could say they need to get the blood itself. Like the plasma and blood cells specifically. that it's absorbed directly into their bloodstream, and it needs to be human because pig or sheep's blood isn't compatible, but frankly that seems less likely to me than that they just need soul juice.

What vampires get from blood


Admin sidebar customization

Question: My new clients wordpress site does not have plugins, appearance or any of the other default items in the admin sidebar. Can anyone tell me how I get those to appear. The site is being run in a sub-directory of the main site. It has it's own wordpress installation. The theme is rttheme16 from themeforest. Thanks in advance.
Comment: [Troubleshoot](http://wordpress.org/support/topic/troubleshooting-wordpress-34-master-list?replies=5) your WordPress installation. Unless you detect what piece of code in the theme has a problem, there's nothing we can do. That's a *premium* theme, with closed code, and that does have its own support channels. ..... Oh, and welcome to WPSE!
Answer: This may sound silly but are you sure you have administrator permissions? (Logged in with an account with Administrator privileges.)
If you are sure you have the correct permissions, you may also want to check with the original theme developer to see if there are white label admin features enabled within the theme.  You will need your client's login to communicate with the developer of a purchased theme on ThemeForest.
White label options would be most commonly located in the theme's functions.php file (or a similar named file - so check your includes) and would look similar to the example in the below link:
http://www.wprecipes.com/how-to-remove-menus-in-wordpress-dashboard
Comment: I agree with Christi. At least that would be the first place that I would check. It sounds like the user account that you are using to log in to admin panel is less than an administrator, such as an editor or author. The theme or the fact that its located in a sub directory of the main site should have no bearing on the admin menu structure.

Admin sidebar customization


Refresh rate drops significantly after connecting external monitor to laptop

Question: I have a Lenovo Gaming i3 with a GTX 1650 and am running Ubuntu 20.04 latest. The laptop's screen is 1080p 120Hz and I connect an external 1080p 60Hz monitor. When the monitor is connected my laptop's 120Hz screen drops to about 60Hz and it experiences some vertical tearing. xrandr reports the laptop screen as 120Hz the entire time, even though it's clearly not.
How can I run my laptop's screen at 120Hz and the external monitor at 60Hz in the same time?
Changing the PRIME profile in Nvidia X Server settings to Preformace Mode only makes the problem worse. When I do that, I get a lot of vertical tearing and it does nothing to the refresh rates. In fact, changing to Preformance Mode makes the screen tear even without an external monitor. Changing to On Demand makes the tearing stop, but that's because it's using the AMDGPU from the processor and not Nvidia. On Demand does not fix the refresh rate issue.
I've also tried toggling vsync, but it made no difference to refresh rates or tearing. I've tried downgrading nvidia-driver, but it also made no difference. Enabling Force composition pipeline also did nothing. Reinstalled the driver multiple times at this point. Still nothing. The problem happens on all monitors that I've tested. And I know it's not a hardware limitation because Windows 10 on the same laptop works out of the box with both monitors at the correct refresh rate and without any tearing.
This is my xrandr with both displays:
$ xrandr
Screen 0: minimum 320 x 200, current 3840 x 1080, maximum 16384 x 16384
eDP connected primary 1920x1080+0+0 (normal left inverted right x axis y axis) 344mm x 193mm
   1920x1080    120.21*+
   1680x1050    120.21
   1280x1024    120.21
   1440x900     120.21
   1280x800     120.21
   1280x720     120.21
   1024x768     120.21
   800x600      120.21
   640x480      120.21
HDMI-1-0 connected 1920x1080+1920+0 (normal left inverted right x axis y axis) 521mm x 293mm
   1920x1080     60.00*+  59.94    50.00
   1680x1050     59.95
   1440x900      59.89
   1280x1024     75.02    60.02
   1280x960      60.00
   1280x720      60.00    59.94    50.00
   1024x768      75.03    70.07    60.00
   800x600       75.00    72.19    60.32    56.25
   720x576       50.00
   720x480       59.94
   640x480       75.00    72.81    59.94    59.93

Answer: I solved this problem and it is the only way:
steps (google each step please):

Use Ubuntu 21.04 (not working in ubuntu 21.10)
Install Nvidia driver 470 (maybe higher version)
blacklist nouveau
Comment: I assume you meant to post a link? There is no link in your post
Comment: @Ciprum can you google the step?  it would be a really long answer to write the detail.


Are there some libraries with C API to draw pictures?

Question: Are there some libraries with C API to draw pictures? Just like the library matplotlib in python. I will use it to draw lines, dots, circles and I hope it has detailed documentation and opensource. My platform is gentoo.
Answer: The most comprehensive one is probably ImageMagick. They suggest using the MagickWand API.
Other options are cairo, with a image buffer output device, or maybe libgd.
Answer: There's no such functionality in the C standard library.
Comment: You said, and I quote, "Does C have some libraries to draw pictures?" C does not. Here's why. Per the C standard, the C language only includes the standard library and per that same standard the standard library doesn't have anything for drawing pictures. All other libraries are out of the scope of the language, although they can be implemented in it or for it. In other words, they may exist, but, unlike things like `printf()`, they aren't guaranteed to be available for every OS and every compiler.
Comment: My question doesn't limit to standard library.
Comment: And besides after 40 years, I would think they would have created a properitery library for this task. So a question should rather be, what API can I use with C for graphics?
Answer: Depends on your needs. Maybe you can use

SDL
SFML also has C bindings

These are game engines (full list of them here - check with C bindings), but you can also use them for drawing plots and etc too.
Also you can check - maybe you can include Python bindings in C, and after that - run Python code (matplotLib) from C ?
Answer: One popular choice is SDL. I'm not familiar with matplotlob, it's possible that SDL is (quite a bit) more low-level than you expect.
Answer: If you running linux and compiling with gcc, the most obvious choice would be plotutils. It has both a C and a C++ API.


Our company needs to perform automation testing for charts like pie chart, bar chart, which testing tool I should go with?

Question: My company designed dashboard for database data, I need to find best tool who will automate company's website
This dashboard contains all types of charts like pie chart, bar chart, line chart etc and I need to automate this chart to find whether all charts are working fine or not
How could I achieve this?
Comment: The technology your company is using based on javascript, flash, html5 or WPF, or Swing, or etc.? Automation is technology dependent in many cases.
Comment: Then you can use the tools which deal with DOM tree. Selenium, WebDriver, CodedUI, etc. I don't know all of them. I think you should do a few POCs to figure out which one is proper for your company and the cases you have to face.
Comment: Javascript and I guess using third party library for showing charts like D2Charts,HighCharts
Answer: If what you care is the visual aspect of your charts, a tool like Selenium might not be enough. You should take a look to "visual tests" tools like Sikuli, PDIFF, PhantomCSS, Huxley. And maybe you could end up using both type of tools: Selenium to navigate in your app/site and visual-tool to check that the visual aspect of your graph is correct.
Answer: I think you should try Ranorex 5.0 it's a great took to work with pie charts and bar graphs. It is based on dot net framework hence uses c# language, I am saying this because I have worked on this tool and work with bar graphs and pie charts. There are various cases in which we have to validate the tool tip on a bar graph and with the help of this tool it worked seamlessly
Comment: Have you been able to use it to validate more than just the tool tip; for example the shapes, colours, sizes of the data displayed in the graph?
Comment: Well i have not tried it for shape but you can work with color and the size of data. With whole .net functionality at your finger tips the quality of scripts just depends upon your imagination and more over the tool support is just incredible and your queries are always herd with priority and the license cost is also minimal
Answer: Selenium + Ocular
Maven dependency
<dependency>
    <groupId>com.testautomationguru.ocular</groupId>
    <artifactId>ocular</artifactId>
    <version>1.0.0.Alpha</version>
</dependency>

You can compare specific WebElement
Ocular.snapshot()
      .from(this)
      .sample()
      .using(driver)
      .element(element)
      .compare();


Why is current non-zero when applied potential is still below E$^0$ in cyclic voltammetry?

Question: In this diagram (Evans et al., J. Chem. Edu.) the current is non-zero, but the potential is still below the normal potential. How can the compound become oxidized at the working electrode, when the applied potential is still below the normal potential of the compound?
Answer: I think you may be coming at this question from the wrong angle. Since I'm not entirely knowledgeable about electrochemistry, I'll give a somewhat qualitative answer, the general idea of which I hope to be understandable.
Fundamentally, what you are doing is taking a system containing a species, say $\ce{A}$, and its oxidized form $\ce{A+}$ (of course this same argument applies for the reduced form $\ce{A-}$ if you sweep in the other direction of voltage). In the absence of an applied voltage, the system is at equilibrium with a certain concentration of $\ce{A}$ and $\ce{A+}$. Let us consider that $\ce{[A]}$ $\gg $ $\ce{[A+]}$. This implies that the equilibrium constant for $\ce{A <=> A+ + e-}$ is much smaller than 1, and therefore that the oxidation reaction has a high positive standard reaction free energy change $\Delta _r G^{o} \gg 0$ (loosely speaking, the reaction is "not spontaneous" in standard conditions, though this sort of thinking is misleading, as I explain later).
As you start to sweep the voltage, you begin adding electrical free energy into the system, such that the reaction free energy (in non-standard conditions) now becomes a sum of the initial chemical free energy change and the electrical free energy $\Delta _r G = \Delta _r G^{o} + G_{electrical} = \Delta _r G^{o} + nFE$ (I think that you can argue that by altering the voltage, you are altering the free energy of the electron in the equilibrium). If you sweep in the right direction, then the electrical free energy term can contribute to decrease the reaction free energy. At some defined voltage, the two factors cancel out, giving $\Delta _r G = 0\ \ \rightarrow \ \ \ \Delta _r G^{o} = -nFE^*$, where to $E^*$ we give the special name "oxidation potential", $E^{ox}$.
The important thing to notice is that all this time, the potential sweep is altering the reaction free energy incrementally. Since the free energy is shifting, the associated equilibrium constant is also changing. At voltages much than lower $E^{ox}$,  $\Delta _r G = \Delta _r G^{o} + nFE \gg 0$, and so even though the reaction free energy is lowering, it is still quite positive and the associated equilibrium constant is still much smaller than 1. Thus the reaction is only slowly shifting towards products, and therefore there are few electrons being passed into the circuit, and the current is close to zero. However, when the voltage applied starts to get close to the oxidation potential, even if $\Delta _r G < 0$, the equilibrium constant will be smaller than but somewhat close to 1, and there is some conversion of $\ce{A}$ into $\ce{A+}$, creating a current below the formal oxidation potential.
The whole problem comes from thinking that as long as $\Delta _r G < 0$, a reaction "happens", while for $\Delta _r G > 0$, the reaction "doesn't happen". In truth, there is a gradual change of equilibrium concentrations as a reaction goes from one regime to the other. Even if $\Delta _r G > 0$, if it sufficiently close to zero then the equilibrium constant is only a bit smaller than 1, and you can expect appreciable amounts of products. Notice that in the voltammogram, the current is practically zero until about 0.1 V away from the oxidation potential, and it only really starts to pick up around a mere 0.05 V away. Even though these values mean $\Delta _r G > 0$, they are sufficiently close to the oxidation potential that the equilibrium constants aren't so small, and so you can actually measure a significant amount of species being oxidized.
Answer: I'm having a hard time understanding fully what the question is asking.
I think the answer to the question is that there is an energy associated with the full oxidation of whatever chemical you are working with. So basically, the more you oxidize the working electrode the easier it becomes.
In situations I'm familiar with, you form a layer on the working electrode. This layer has Van der Waals forces associated with it, so the more molecules that participate, the stronger the interaction. This makes it easier/less negative to form a skin/oxide on the working electrode.
This also makes the reduction harder. If the skin/oxide you have on the working electrode has Van der Waals forces associated with it, it's not going to be as easy as just applying the normal potential to remove/reduce the oxide; you have to apply a little bit more negative potential.
If I completely misunderstood the question, just let me know; I'm pretty familiar with CVs.


Sharepoint MOSS 2007 advanced search customization

Question: In my sharepoint site, the master page template is chagned and we moved the search box into the site which showed as a web part, When the user enters a search string in that box, it should search whatever the materials available in the site itself, document library, blogs in the web, forums and wikis. Therefore, I think I need a way to figure out how these types of searches are done using sharepoint as well as how programmatically provide a search string to advanced search and receive search results. Any Idea how to do this? my code behinds are in C#
Comment: What do you mean by *we moved the search box into the site which showed as a web part*? Did you create a custom search box Web Part?
Answer: I don't think that should be any issue as sharepoint search is based upon the query string K parameter stands for Keyword, s parameter stands for scope, cs stands for contextual scope So use these parameters in query string to your results page having the core results webpart.
eg.
http:// <>/ <>/ results.aspx?k="Test Keyowrd"&s="All Sites"


E-mail regular expression

Question: I'm trying to make a regular expression that will match an e-mail address.
The address must start and end with a letter, and a period must have two letters before and after it.
Here is a part of my expression so far before the @ symbol:
<code>^[A-Za-z0-9]+[A-Za-z0-9\'\-\_]*(([A-Za-z]{2})+(\.([A-Za-z]){2})+)*[A-Za-z0-9]+
</code>
The problem I'm having is if a user enters simply two letters, a period, and another two letters; ab.cd, it validates as false since it's still looking for that starting letter.
abc.def validates just fine for example.
So my question is, is there any way to have it match the starting letter only if it is not followed by another letter? And vice-versa for the ending letter.
Thanks guys.
Comment: http://stackoverflow.com/questions/201323/how-to-use-a-regular-expression-to-validate-an-email-addresses
Answer: See http://www.ex-parrot.com/pdw/Mail-RFC822-Address.html

E-mail regular expression


$\alpha$-particle decay in Heavy nuclei

Question: Can someone explain why heavy nuclei prefer to go through $\alpha$-particle decay instead of nucleon decay?
Answer: Nuclei are quantum mechanical "particles" composed out of protons and neutrons, which themselves are composed out of quarks and a sea of gluons and antiquarks. The basic holding "force" of this is the strong interaction force, modeled with QCD for the protons and neutrons, and  a spill over force from the protons and neutrons called the strong nuclear force.
Quantum mechanical models have been developed which explain the decay and fission behavior of nuclei.
Hand waving: the alpha particle is very tightly bound, as seen in this binding energy curve, and in addition, it is stable. Thus within the "bag" containing the nucleons a stable configuration of alphas can exist in unstable nuclei, and the fission  or decay into alphas may be  energetically favored over the emission of a single nucleon, for a particular nucleus.
The models fit this behavior and can predict how other nuclei will fission or decay.

$\alpha$-particle decay in Heavy nuclei


Query Notification setup

Question: I am relatively new at playing around with this and have been trying to follow a tutorial on setting up in the section named "Prerequisites to Create SQL Notification Requests" within this site http://www.codeproject.com/Articles/144344/Query-Notification-using-SqlDependency-and-SqlCach However I am not sure what I should be putting in :://the service and there were no instructions or information on the site regarding this.  I was wondering what I should do or what other information I need to complete this section.
Answer: The service specification is the name of the service used for query notifications.  The tutorial is focused on SqlDependency, which creates dynamically-named services (GUID appended).  No need to explicitly grant SEND permissions on the service in that case because the creator of the service will have CONTROL permissions on the service anyway.
If you were to use the lower-level SqlNotificationRequest object, then you would need to grant SEND on the service, REFERENCES on the contracts, and RECEIVE on the queues.  That allows a less privileged account to subscribe to query notifications.

Query Notification setup


How do I add Yahoo contacts to Google Chat?

Question: I have several people who don't have Gmail accounts and I'd like to be able to chat with them via Google Chat in my Gmail inbox.
Answer: I'm pretty sure it's not possible to do it using the native Gmail client. You could achieve this using a third party client like Adium (on Mac) or Pidgin (on Mac or Windows).
There is also this tutorial that explains how to import your contacts via PSI messenger, but I find it rather cumbersome.
Comment: Is it possible with iChat?
Comment: I don't know, I never used iChat.


What is the origin of the phrase "from your lips to God's ears?"

Question: I used this phrase in a conversation with my wife yesterday and was surprised to learn that she had never heard of it.  This led me to wonder where it came from.
Comment: I think [this](http://itre.cis.upenn.edu/~myl/languagelog/archives/005226.html) is the best you're going to get.
Comment: @Kris I did.  Couldn't find much.
Comment: Have you googled it?
Comment: On the Web there are a lot of site on idiom. Try with 'americanidiom.com'.
Comment: @AngloSaxon, that site is no longer functioning
Comment: Isn't this expression too easily not understood or worse, misunderstood, and perhaps better not used?
Comment: @ElberichSchneider, Ha, *a lot of site on idiom* and you suggest only for American, when the phrase origin seems to be Yiddish
Answer: By request from the comments: here is a link to a Language Log post that, among other things, explains the origin of the phrase.

from your mouth to God's ear (or ... to the Gates of Heaven).  May God hear what I/you say and act upon it.  Or, as defined in The Taste of Yiddish by Lillian Merwin Feinsilver (1970): 'Fun zayn moyl, in Gots oyer.  Lit, From his mouth into God's ear.  May God hear what he has said (and fulfil it)!'  The 'Gates of Heaven' may be an Arab version. ...  The first expression my stem from Psalm 130:2: 'Lord, hear my voice: let thine ears be attentive to the voice of my supplications'.  The phrase also appears in the orthodox Jewish prayer book.

The explanation above taken from
Nigel Rees, Cassell's Dictionary of Word and Phrase Origins (2002), p. 90
Comment: @AngloSaxon - it's when a link that I write on this page points to an address, but the page at that address gets moved or deleted, thereby making my link point to nowhere.
Comment: A link alone isn't much use in case of linkrot. Please provide a summary.
Comment: @Hugo that's why I made it a comment, but I'll edit in a summary.
Comment: @Hugo - what does it mean 'linkrot'?
Answer: "From your lips to God's ear" appears in Arabic (من فمك لباب السما ياختي) about as much as in Hebrew (מפיך לאוזני אלוהים). The expression does not appear in
Hebrew literature before the rebirth of modern Hebrew in the last century. In modern Hebrew it is commonly used in contexts such as ynet.co.il blogs that indicate that the writer believes the origin of the phrase is Arabic. I venture to guess that the expression migrated from the Arabic to the Jewish colloquial in Andalusia and from there to the Yiddish. A quote from Arabic literature of the period might answer the question more conclusively. In any event, the expression is loaned in English. The expression can be used to indicate true heartfelt agreement and can also be used sarcastically or wryly as in "would that it were so", or "insha'alah".
Answer: There's a similar proverb in the Apochrypha, Sirach 21:5

The prayer of the poor goes from their lips to the ears of God, and His judgment comes speedily.
Comment: Welcome to ELU, your contribution is worthy and quite interesting but not an answer to the OP's question. As such it risks deletion unless your source predates the *"Psalm 130:2:'Lord, hear my voice: let thine ears be attentive to the voice of my supplications'* Of which I confess, I have no idea.
Comment: @Kris I took it from Cameron's awarded answer. i took it to mean that was the earliest recorded source of the saying.
Comment: Now now, surely you mean the Deuterocanonicals. :)
Comment: @Mari-LouA What has Psalm 130:2 got to do with this?
Comment: @Mari-LouA Let there be no hasty comments, anyway.
Answer: The phrase "From your mouth to God's ears" appears in Bandit, a short story written in Yiddish by Sholem Aleichem (better know as the author of Fiddler on the Roof), who lived from 1859 to 1916. The version "From your lips to God's ears appears in the novel The Devil's Arithmetic, written by Jane Yolen about a Jewish girl in New York who is transported back in time to a Nazi death camp. And the phrase is something I hear often from Jewish friends. (I'm Jewish but was brought up outside the community.) When my friends use it, it takes on the meaning of "You said it! You hit the nail on the head!" In other words, what you've said so perfectly explains something that it can be heard by God. It's not hard to conclude that the phrase is one of the Yiddishisms that has entered mainstream American culture. I've seen it described as a "Jewish proverb," which seems likely.
Answer: There are two forms of this idiom.  The first which you identify:
Idiom expressing a wish that the desires of the person to whom the saying is spoken will come true.  The original, literal meaning of the saying indicates that the speaker wishes that whatever the addressee has just said will be heard by God and answered.
May be used sarcastically, in which case it is roughly equivalent to "good luck with that."
Eg.
J: "Hopefully, my investments are going to return 400%!"
M: "From your lips to God's ears."
The second form is less common and reversed.  It is from God's lips to your ears.
It simply means the instruction came from on high and was passed to you directly (no one else heard/knows).  It conveys a high level of confidence/knowledge in the information passed.
Eg.
J: "John was fired by Tom"
M: "How do you know?"
J: "All I can say is that this is from God's lips to your ears".
Comment: The OP is not asking for the meaning of the idiom. He's interested in its origin.

What is the origin of the phrase "from your lips to God’s ears?"


Local inertial coordinates/Fermi normal coordinates

Question: It is said that we can introduce local inertial coordinates/Fermi normal coordinates for any timelike geodesic. But why only for timelike geodesics? What about null geodesics? Perhaps it has to do with invertibility or something?
Answer: We assume OP's question (v2) is the following:

Given a null geodesic on a Lorentzian manifold, do there locally exist Fermi normal coordinates along the null geodesic? (Here the word 'locally' means in some tubular neighborhood.)

The answer is Yes, see. e.g. Ref. 1. (As OP correctly notes, most textbooks deal only with Fermi normal coordinates for timelike geodesics, cf. e.g. Ref. 2 and Ref. 3.)
References:

M. Blau, D. Frank, and S. Weiss, Fermi Coordinates and Penrose Limits, Class. Quant. Grav 23 (2006) 3993, http://arxiv.org/abs/hep-th/0603109
MTW.
E. Poisson, The Motion of Point Particles in Curved Spacetime, (2004),   http://www.livingreviews.org/lrr-2004-6
Comment: Note for later: A version of Fermi normal coordinates for Riemannian manifolds is proven in Section 3 of http://dx.doi.org/10.2991/jnmp.2007.14.1.8
Answer:
But why only for timelike geodesics? What about null geodesics? Perhaps it has to do with invertibility or something?

Physically, Fermi normal coordinates represent the frame of reference of an inertial observer. Relativity doesn't allow observers with lightlike motion, and, yes, one way to understand why they're not allowed is that if you try to extend the Lorentz transformation to $v=c$, it's not one-to-one.
Another way of saying this is that in Fermi normal coordinates, we're trying to get the metric to look like a diagonal matrix with elements $(1,-1,-1,-1)$. This requires that three coordinates be spacelike and one timelike. It's not going to work if one coordinate is lightlike.


How were unit labor costs estimated by Gali and Gertler (1999)?

Question: I am trying to estimate a NKPC like the one
Gali & Gerter, 1999 and Gali &Gerter, 2001 estimated. I am having trouble with understangind how they calculated the marginal cost, i.e., which time series they actually used. I tried consulting '''Sbordone, 2002, who estimates the same model using the same (or at the very least a similar) proxy for the marginal costs. As far as I could understand MC = C/Y where MC is the marginal cost, Y is GDP and C are the total compensations given to workers, i.e., the sum of all real wages paid to workers. I would like to know if that is correct and, if it isnt, how Gali & Gertler calculated the marginal costs. In the specific interpretation I have described I dont know if one must use real or nominal GDP. If I use real GDP, it seems to me, that when dividing real salaries by the real GDP the deflators dividing both nominal salaries and nominal GDP will "cancel" each other and I would only get the ratio between nominal salaries and nominal GDP, which does not seem useful given the fact that in the price formation model firms are considered not to suffer money ilussion. I apologize in advance in case my words have not been precise enough and thank you all for your answers. Any help and references to articles or textbooks is greatly appreciated.
Answer: In Galı́ & Gertler (1999) the authors state that marginal costs is given by:
$$MC_t = \frac{S_t}{\alpha}$$ where $\alpha$ is the labor elasticity (from the Cobb-Douglas prod. function), and $S_t$ is the labor share of income (i.e. what portion of output GDP goes to labor). Next they actually get around estimating $\alpha$ by expressing everything in percentage changes so they actually use:
$$mc_t = \frac{MC_t - MC_{t-1}}{MC_{t-1}}= \frac{\frac{S_t}{\alpha} - \frac{S_{t-1}}{\alpha}}{\frac{S_{t-1}}{\alpha}}$$
where alpha cancels out so you are left with just  change in the labor share of income $\Delta S_t = s_t$.
They even state in the paper:

The data we use is quarterly for US over the period 1960:1}1997:4. We use the
(log) labor income share in the non-farm business sector for $s_t$

So in this case they just seem to have directly taken the labor share of income, which is plausible data for labor shares of income exist without any 'assembly' required (e.g. see this Fred dataset as an example).
Comment: Thank you for your answer. I read again the article published in 1999. Gali and Gertler state that $mc_t$ is the  marginal cost deviation from its steady state level. I was wondering if actually, $mc_t = \dfrac{\dfrac{S_t}{\alpha}-\dfrac{S^*_t}{\alpha}}{\dfrac{S^*_t}{\alpha}}$ where $S^*_t$ is the marginal cost steady state for period $t$. The steady state marginal cost is estimated, I supose, using the HP filter, as they did with the potential GDP.
Comment: @DanielJoséAguilar You are welcome. Also, no in 1999 paper they show no indication of estimating the S (that is what they do in 2001 paper). They mention HP-detrending it but that is not the same as estimating it. Also, they even specifically use words like "we use a measure of real marginal cost" instead of we estimated mc. When they refer to steady state that does not mean they are referring to some empirical model, theoretical models have steady state as well.
Comment: Thanks. What I meant is that perhaps they used the deviation of the labour income share from its steady state level as a proxy for $mc_t$.  Then, as a proxy for the "steady state labour income share" they just used the labour income share trend  which one can obtain by applying the HP filter to the labour income share "original" time series. It seems that I used the word "estimate" incorrectly. One can proxy the steady state GDP as the GDP trend obtained with the HP filter. Similarly perhaps one can proxy the labour income share steady state level  as its trend as obtained with the HP filter.