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# Some lessons to learn from the 2017 elections

So, the election are over. Some statistics and factoids of interest.

1. From the election page:

22,919 voters were eligible, 9,261 visited the site during the election, 4,655 visited the election page, and 2,161 voted

This is quite a terrible statistics. Out of almost 10k users that could vote, and were online during this week, only half bothered to look at the election, and only about half of them bothered to even vote.

I am not someone who espouses "everyone should vote". In fact, I would limit voting rights to people who at least passively follow the meta site. And it is definitely the case that a lot of people have little interest in meta-matters, and they should avoid voting as they usually don't read the meta site, and aren't very well aware of the more or less pressing issues that are on the agenda often.

Nonetheless, I'd be happier if a higher percentage of people were more engaged to vote. At least of those who bothered to visit the election page.

2. Looking at the online statistics, one can open the ballots page. The first thing one notices, is that the first ballots have only one vote. In fact, the first ballot to even have a third vote is ballot number 77.

Using grep -c "2</div" and grep -c 3</div on the html page, shows that nearly 300 people didn't choose a third candidate; and out of these only a 100 had cast a second-choice vote (specifically, out of 2161 ballots there are 1985 ballots with at least two votes; and 1865 ballots with all three votes (it might interest someone to know that all ballots had a first choice)).

It is unclear, and probably impossible to know, if those partial ballots are due to lack of understanding the fact that one can vote for three candidates, or just people "gaming the election badges" and casting a vote for the first candidate on their page before moving on.

But it is best to cast three out of three votes. And so, I am not sure what to make out of this whole thing.

3. As I remarked before. The last election was a rage. We had many participants, many third-party-nominations of users nominating other users. There was a lot more debate going on, and a lot more energy poured into the meta site.

While I don't trust my memory to that degree, the election before that (2013) was also pretty active, even if not to the same degree. Or so I remember.

Long story short, I feel that perhaps this election came more as a surprise to many people here, and was somewhat hastily. In my opinion, at least, giving the community another week before starting the official nomination process might have been conducive to a more active election.

I would love to hear some input from the members of the community as to what do they think about the elections we just had, and what lessons can we learn from these—and other—things.

• Great question(s), @Asaf! I'm still trying to wrap my brain around the whole process, but this election is indeed different from the2014 election, in terms of the factors you mention: participation levels, 3rd party nominations, notice given that an election is coming up... etc. I tried to rally on a number of fronts, but to some extent, it seemed to fall on a lot of "dead/uninterested" ears. (That could of course be attributed to my failure as a rally-er!). I'll be considering this beyond my first impressions. Just know that this is a good question, and very relevant to this site. – Namaste Oct 17 '17 at 23:36
• Its not evident to see there was an election going on...I had the chance to see it on meta and could participate..I voted for three candidates... – Isham Oct 17 '17 at 23:36
• @Isham users are supposed to get a notification (like a comment notification) about the election. Maybe it did not work in your case (or you overlooked it). – quid Oct 17 '17 at 23:57
• I do agree with some of your points - the election was a complete surprise to me, and the participation rate was pretty terrible. As far as your point (2), I am one of the 300 who only cast two votes, since I only felt that two of the candidates were really supportable for me. I wonder how many people felt the same. – user296602 Oct 18 '17 at 0:03
• @Isham there was a message in the community bulletin (the box on the top right). – quid Oct 18 '17 at 0:12
• re 2, the ballots appear to be sorted by what is voted for. The first, or any segment, are thus an extremely biased sample. I would assume there were not few that just had a quick look and voted for somebody they recognized and found good. Which is maybe not optimal, but understandable. I doubt many voted just to get a batch. Anecdotally, it seems Jack has relatively many unique votes, which is compatible with the "recognized and find good" hypothesis, him being by far the most active answerer. – quid Oct 18 '17 at 0:20
• @quid If you are a user who primarily reads Math.SE on the app (as I am when school is in session...) an indication of a notification came through but there was no notification there when you clicked on it. Luckily I read the meta site so I was aware and went on my computer to vote - but it is still a potential issue. – emma Oct 18 '17 at 0:49
• Perhaps too many voted. As of now the candidate Q&A meta page has only 1153 views, I'm sure not all by unique users. math.meta.stackexchange.com/questions/27045/… I don't really think too many voted, but I don't second guess anyone who decides not to vote. I don't vote in elections when I'm not informed on the candidates or issues (except when someone is running unopposed, because I like to thank them for stepping up). – Jonas Meyer Oct 18 '17 at 2:02
• @Jonas: Yeah, that's probably right. See my repeated remarks that voting should be a privilege one earns by participating on meta. – Asaf Karagila Oct 18 '17 at 8:08
• @emma that's an interesting point. I do not use the app, and only rarely the mobile version. If there are issues with visibility in these it could make sense to record this as an answer. This is something that could be addressed. – quid Oct 18 '17 at 8:54
• In comparison, our stats aren't so terrible. – Daniel Fischer Oct 18 '17 at 12:56
• There was an awful lot of text on that survey page. I'm a fast reader. It was an overwhelming amount of text. And, it seemed extremely likely that the position would go to quid. I was quite surprised to see now that there are two new moderators; that wasn't clear to me at all. I did use at least two votes; I remember having trouble choosing a third and don't recall if I finally did or not. Thinking there was only one opening and seeing quid's excellent responses, it seemed silly even to use two votes. – Wildcard Oct 20 '17 at 16:01
• @Wildcard: Frankly, though, that's on you. It states very clearly on the side-bar that there will be two elected moderators. :) – Asaf Karagila Oct 20 '17 at 16:37
• I am one of the people who visited the election page but did not vote. And I don't follow meta (we're lucky that I even read this post), so in your opinion, I'm probably not informed enough to vote. So you should be happy that, when I looked at the election page, I came to that same conclusion! – Toby Bartels Oct 22 '17 at 7:27
• @Wildcard Just had to make sure. Thanks for the quick reply! – Simply Beautiful Art Oct 23 '17 at 20:52

1. Most people are here just for the mathematics and choosing moderators is a meta issue. Moderators are people who promise to help keep the site running, and even their very existence is somewhat irrelevant to many users. Perhaps the local soccer club needs to choose someone to take responsibility over finance, but most members of the club might have their sole interest in playing ball. And that's fine, the club exists for the purpose of facilitating the game, just like this site exists for facilitating certain mathematical exchanges.

Some people have interests in the inner workings of the site, but they are a minority. There are way more mathematicians than metamathicians. The percentage of people who chose to vote is actually higher than I expected.

2. I knowingly voted for exactly one candidate and left two blanks. I did not care much about the answers to the questionnaire. I required two things of a person I would vote for:

• Sufficient activity on meta, in review, and similar managerial aspects of the site.
• My personal experience of how the particular user approaches other users and problematic situations.

My votes are solely based on my personal experience with the candidates. I was mostly uninterested in their words in election discussions, but very interested in my memories of their past actions regarding my second point above. One could say that I will only vote for someone to become a moderator if I already think they are a good moderator and effectively act in that capacity. The line between moderators and some high reputation users is thin by design. Only one user passed my tests, so I only voted for them. I did not want to vote for anyone I don't have genuine support for.

3. Let me just point out that no matter how long the preparation stage is, most voters will presumably get to the election page when they get an announcement in their inbox and choose some candidates on a gut feeling. I don't think the amount of preparation or discussion has much effect on the majority's voting behavior. Granted, there are very active meta users and almost-moderators, but their weight in the overall voting is relatively small.

To me it seems that the key effect of sufficient discussion and visibility is getting good candidates to run for the job. Many will need some time to consider whether they want the burden on themselves with the moderator work. I'm not very enthusiastic about voting for someone who is willing to commit to moderatorship after two seconds of thought — I assume some of the best candidates (from my point of view) will need some time to consider their commitments. Perhaps some more time would have produced more candidates for me to vote on.

I don't see anything to be alarmed of about the election.

• I used to have a gut feeling that DC was to hold in a symmetric extension if and only if the forcing was sigma closed and the filter of subgroups was sigma complete. And I used to have the gut feeling that countable unions of countable sets are countable. And I used to have the gut feeling that maybe geometry is interesting (to me). All these things changed with experience. Interacting with, or passively observing interactions of, potential moderators will change your gut feeling about them. – Asaf Karagila Oct 20 '17 at 19:51
• If you're willing to spend the time, I have found going to a user's profile and looking through their activity, particularly comments, to be most edifying in choosing candidates to vote for. That gives you a sense of a user even when you don't have personal experience with them. – Todd Wilcox Oct 28 '17 at 20:14

re 2, as a non-regular occasional visitor, I struggled in choosing my 3rd vote, I think people who are not actively checking meta or other posts in the main site might have had similarly hard time in deciding who to vote for. Questionnaire is a useful thing but it is mostly the claims of users about themselves. If I haven't seen enough of their interactions with others on the site and their involvement on the meta discussions and how they approach policies I don't feel comfortable voting for them, I see the alternative as casting my vote randomly which is not a good thing in my opinion.

re 1, I personally don't think it is a really bad thing that only those who are actively involved in the site vote. In principle, moderator role should be an extension of what a user is already doing, right? Even if someone doesn't get elected as a moderator they should be actively involved in cleaning up junk, closing bad questions, editing to improving questions and answers, helping in building consensus on good policies and norms on meta, helping resolve disagreement and building a good environment for others to participate and feel good about the site, and do so by leading by example. Most of these do not require moderator privileges, a healthy established site like MSE should have enough active users with high enough rep that most of these are dealt with even without moderators.

As I see it moderator privileges are to deal with infrequent exceptions that normal users cannot deal with, e.g. users trying to game the voting system, dealing with problematic users that create toxic environment for others, users persistently and consciously violating agreed upon policies, quickly deleting occasional spam posts, calming down and resolving heated discussions that lead to "requires moderator attention" flags, and a bit more authority in explaining what the policies and norms of the site are to new users. And as far as I understand these are the reason why moderators exists, the things in the previous paragraph do not need moderator privileges really. To perform these duties requires giving moderators access to non-public information and unilateral actions and requires establishment of some level of trust over time. Can I really cast a meaningful vote if I have not interacted with a candidate directly nor observed their interactions with others? I don't feel so. My vote would be either a random one or based on how others think (in which case I am just amplifying their vote).

By the way, for future elections, I think it would be rather helpful (at least to me) to ask candidates to provide some examples of how they have behaved in those exceptional situations on the site and also their contributions to meta discussions.

• Admittedly, as one of the more active users, I was struggling with finding all three suitable candidates. – Asaf Karagila Oct 18 '17 at 8:01
• Tbh, I also struggled a bit with choosing all 3 candidates. But it wasn't due to lack of knowledge, I just thought there were more than 3 good candidates this year. – Simply Beautiful Art Oct 18 '17 at 14:23
• I was sorely tempted for quite a while to leave my vote at just two candidates. – J. M. is a poor mathematician Oct 20 '17 at 2:43
• Me too, wrt to really only endorsing two candidates. I did include a third vote, but it was more a "lesser of evils" vote, not an endorsement. – Namaste Jul 10 '18 at 18:42

Thanks for collecting these pieces of data. Digesting it all, and its relation with the outcome of the election, will take a while. As I spent one bike ride to work thinking about this I share my impressions with you all.

1. I am against limiting the right to vote. We have come a long way since that privilege was limited to men owning land worth 40 shillings or more. Even in modern times there have been attempts to limit the right to vote by various political entities, but I don't recall much good having come from such attempts. Ideally we would like the voters to be informed, and educate them about why it is a good idea to be informed, but even many modern societies continue to fail in that task. And continue to disagree about what being informed means. If it cannot be done here in a community of educated people, then...
2. But, I also agree that voters should make a serious effort to learn about the issues and the candidates. Not mentioning the fact that an election is going on. May be most of the voters actually felt that they are not sufficiently informed, and hence abstained from voting? A very disciplined decision, if you ask me. Anyway, I don't have much sympathy for the users who said they didn't notice that an election is coming. I mean, it's not like the notice to demolish your planet was posted only in the Proxima Centauri office. Pay attention to those local affairs (or forfeit your right to complain)!
3. The discussion preceding this election was possibly less heated than what we had prior to couple earlier ones. Or was it? Here our personal perception will necessarily be colored by how high a stake we held in the key issues (if any). The previous election was held shortly after we had discussed the issues with PSQs/homework and "the massive campaign" lead by Normal Human to delete unworthy threads. May be we have since converged towards a more universally accepted policy? I'm not sure, but may be this time such divisive issues were absent simply because no new important ones emerged? I'm not saying that the PSQ problem would now be solved, you all know that it isn't. But, now we collectively understand the matter a lot better (and hopefully also where the other side stands). No surprise changes in site dynamics - just the same old grumble, grumble.
4. You pay particular attention to meta participation. While I largely agree, I have some nagging doubts revolving around the questions 1) Does the meta discussion actually fairly represent the views of our user base? 2) Does it matter if the answer to the preceding question is "No"? Ideally I like to think that meta is a home to all the letters-to-the-editor, but I'm not sure it works that way as well as it should. I'm somewhat worried about the possibility that meta has become not unlike an official newsletter of a single party. A prominent (but recently silenced) dissenting voice may have done a disservice to all opposition by alienating the regulars with their rhetoric, but surely we don't want to shun all differences of opinions. I don't have a huge problem with this, because I apparently support that meta party. OTOH it is my job to take care of the entire user base. Early in my tenure, after yet another meta-quarrel with Bill, a more experienced moderator gave me the piece of advice. Don't feel too good about it (=the support from other meta regulars). Bill's views are more popular than you may think.
5. But, a point still is that unless the opposition (if any) expresses their views in meta we will not know about the existence of those views. So, we should welcome opposing views, and make good faith attempts to see their points. If only to keep the thesis, antithesis, synthesis triad rolling.

The usual caveat is that I don't necessarily know the difference between a moderator being transparent about their views and actions and a moderator indulging in public introspection.

• I disagree with comparing limiting voting to people who follow meta to racist laws limiting voting to people with power and race. Anyone can put in the hour every two weeks to peruse meta and just see what are the hot topic and who are the active users and their ideas. Nobody is required to be grandfathered in on this or own slaves. – Asaf Karagila Oct 19 '17 at 14:34
• May be I phrased that too dramatically. But on Politics.SE I'm also on record as being against the US way of requiring voters to register themselves as opposed to (the Finnish way of) having a central population registry do it automatically for them. No obstacles to voting IMHO. – Jyrki Lahtonen Oct 19 '17 at 18:32
• Yeah, well, nevertheless, if you need 1000 points to vote, might as well add a meta participation tag(s) to the mix. I don't see much difference at that. – Asaf Karagila Oct 19 '17 at 19:02
• Ah! I may be seeing the light! We are (re)defining the local equivalent of an adult here rather than trying to limit the right to vote only to certain groups of individuals. – Jyrki Lahtonen Oct 19 '17 at 19:42
• @JyrkiLahtonen The states monopoly on violence makes governmental elections an entirely different animal. We are more like a book club. – Michael Greinecker Oct 19 '17 at 20:18
• @AsafKaragila Isn't it 150 points. They should require that your account is at least a month old or something similar. – user222031 Oct 19 '17 at 21:40
• Jyrki: Yes. Exactly right. Being a responsible adult on this site means also following meta. – Asaf Karagila Oct 20 '17 at 6:10
• @user222031: Yes, you're right. I was thinking of candidates. (Which I think should be far less controversial to require them to be active on meta...) – Asaf Karagila Oct 20 '17 at 6:15
• I think that requiring meta-participation is a win-win. People who don't care, won't care. People who care, will come to complain... on meta. – Asaf Karagila Oct 21 '17 at 8:47
• Jyrki, is it possible to ask from the StackOverlords the following statistics, to complement all that was given so far, how many eligible voters visited meta during the election week? – Asaf Karagila Oct 25 '17 at 12:12
• I almost did not vote because I didn't feel sufficiently informed. I browse meta semi-frequently, but only lurk, occasionally vote, rarely comment, and never post. However, it is very hard, IMO, to passively memorize everyone's position on a palate of issues. From my activity here, I recognize many names; I interact with many people and have a decent feel for how "active"/passionate many of the top people are on here. But I simply can't remember, for instance, @JyrkiLahtonen's position on dealing with low-effort questions without actively seeking this information and committing it to memory. – Kaj Hansen Oct 27 '17 at 1:24
• As a result of this, I felt obligated to read through all the provided information about each candidate on both the voting page itself as well as the candidate interview questions thread. Wanting to keep track all the relevant information on each candidate, this proved very time consuming and very boring. I almost quit a little after I started, realizing what I was getting myself into. I wouldn't be surprised if others like me didn't vote from simply not having as much free time or as much motivation to sit down and commit to doing that. – Kaj Hansen Oct 27 '17 at 1:27

I voted for 3 candidates. I am not a very active member, but here is my perspective.

9,261 visited the site during the election.
4,655 visited the election page.
2,161 voted.

I think this makes sense to me. I did not even know there was a meta site for a very long time. I am sure that would be the case for a lot of users. Of the 9261 users who visited the site during election, many would be new/recent members, whose main interest in this site is the answers to their questions. Even if all of them saw the notification, it is not surprising to me that 50% of those didn't want to go to the election page. Having gone to the election page, there are detailed Q&A for each contender. To meaningfully vote, one needs to read through those, which needs time. Plus it is very likely that a recent members do not know the contestants well enough. That was the case for me at least. I knew 2 of the candidates because they have answered my questions in the past and I have general seen their activity on the main site. I voted for the 3rd candidate purely based on the what the candidate had written. So 45% actual votes makes sense again.

• Note that the 9261 users were all eligible to vote in the election. – Wildcard Oct 20 '17 at 15:53

I saw that an election was happening and that candidates had been nominated, and read some of the Q&A, but I didn't realize it was time to vote. My assumption (from not reading the sprawling election-related pages too closely) was that the discussions would go on for at least another week or two before it was time to cast votes.

• Why the assumption? Had you read the election related pages: question suggestions, questionnaire, nomination statements (shorter than reading a comic book). If not, you're the only one you can blame for assuming what was clearly wrong, and stated on the sidebar on the main page, etc. You must have only glanced, because one almost has to try to not engage with the information, to not know the election start and end. – Namaste Oct 19 '17 at 22:53
• @amWhy I'm not blaming anybody (and incidentally, am perfectly fine with the community's choice of new moderators)---simply explaining, in response to Asaf's questioning of the statistics, why I visited the elections page but did not vote. – user7530 Oct 19 '17 at 23:37
• Do you know that you get a notification in your inbox once it's time to cast your vote? – Glorfindel Oct 21 '17 at 11:40
• Once upon a time there was a (I would hope intentionally) disruptive dropdown banner that showed when an election has started. Maybe SE could stand to be less subtle about such announcements. – J. M. is a poor mathematician Oct 22 '17 at 6:09

Voting in an SE election is not a trivial task, especially if one takes it seriously. I'm not really sure if I'm eligible to vote here because I'm eligible on so many SE sites that I tend to get a deluge of inbox messages about upcoming elections.

For all but one site that I'm eligible to vote on, I just don't spend the time on the main site or meta to have any experience with any of the candidates. So I don't even try to vote. I have limited time to spend on SE in general and I assume there are many more engaged community members who will make far more informed moderator decisions.

I wonder how these election statistics compare to other SE sites. It seems that there's a concern here that a small portion of eligible users voted, but having more than two thousand voting members sounds like a lot compared to many other stacks. Maybe it's better that the casual users like me are not voting.

Maybe it would be good to have an obviously accessible page where the bios of existing moderators are given, and each gives a short account of what being a moderator involves "We are the people who ... " and what is actually done behind the scenes to help users and manage the site. That would humanise the task somewhat, and help people to understand what good moderator behaviour might involve.

Another idea would be to have a prompt for each user once when nominations are open and once during the voting period so that when people take an action like posting a question, answer or comment they are prompted "nominations for new moderators are open" or "you are now able to vote in the moderator election for this site" with an option to dismiss or to go to the election page.

Another prompt in the election section could be "how to explore the candidates profiles on the site" - the tools are there, but not everyone knows how to use them.

I voted for three, though I had two very clear preferences and the third was a close call between two. I considered only two votes, but I always try to use all my options.

This isn't a response directly to the question but to a comment by OP: however, I think it's worth pulling out as a separate discussion point.

People who don't want to participate, don't have to participate. But as Jonas Meyer pointed in the comments, the questionnaire thread on meta has much less views than the number of voters. Even if each person only viewed it once (which is grossly not true), this is still a problematic situation. ...

My experience over many elections on various StackExchange sites is that the questionnaire threads are always long and almost completely uninformative. I'm sure that some people find value in them, but I started ignoring them long ago. I prefer to read the candidates' nomination statements, which are both more succinct and IMO more informative, because a candidate's explanation of why they think they're the person for the job tells me what they think moderation is, which is one of the attributes I weight heavily in deciding whom to vote for.

One thing which might persuade me to revisit this opinion would be to transpose the questionnaires. (I suddenly have a sense of déjà vu: I may have made this same comment on another meta site in the past year). Having one Q&A per question rather than one ten-part question with corresponding 10-part answers would make it easier to ignore the anodyne questions and just look at the ones which seem useful for discrimination, and easier to scan the answers to a given question to see whether all of them are near enough identical. Given the importance of elections within the meta-side of a stack, I don't think it would be disproportionate to have 10 active questions in the meta site, with the question solicitation thread edited to serve as an index.

• You've been here a few years ago, when a clearly unsuitable candidate won the election after joining in the last minute, and for the untrained eye, the things written in both the statement and the questionnaire were probably appealing. However, people with more meta experience knew better who is this candidate. And this is all I'm asking for, that people who vote, are people who are vaguely familiar with the candidates, with their interactions and with their general stance on meta issues. Of course, this implies that candidates themselves have some stance on meta issues... :) – Asaf Karagila Oct 30 '17 at 17:58
• I've reduced that quote to the part which I'm actually discussing, because general interaction with the meta site is orthogonal to it. – Peter Taylor Oct 31 '17 at 10:22

Regarding Point 1

We do not elect moderators for the meta and meta alone. We elect them overwhelmingly based on their capability to manage the regular use purpose, which is the main site.

Excluding otherwise-eligible users from voting because they are only interested in asking and answering mathematics questions while being held to high standards, and not the politics or deep management, is nonsensical. They have every right to be represented in their choice of who arbitrates issues during their time here.

• Moderating, by definition, is a meta issue. You don't choose a moderator for their reputation, mathematical or otherwise pedagogical abilities. We had a disastrous experience with that sort of approach before. When I say that voting rights should be earned by meta participation, I don't mean that we vote on moderators for the meta site, but that moderation is a meta activity. – Asaf Karagila Oct 19 '17 at 7:07
• It still doesn't require involvement in the meta area, beyond looking at who a voter wants to have handling the issues they face on main. – Nij Oct 19 '17 at 7:28
• I completely disagree with your last comment, Nij. There's hardly any moderation issues that you see on main. Sure, there's reviewing, and there's comment discussions from time to time, but those are sparse, scarce, and far from representative of a moderator's work. Most of meta is issues related to moderation, to policy, to normative behavior, meta includes heated arguments by well-established users, and meta includes much more. – Asaf Karagila Oct 19 '17 at 8:56
• And yet, you made no objection whatsoever to all of these non-meta moderator actions being named: "... to deal with infrequent exceptions that normal users cannot deal with, e.g. users trying to game the voting system, dealing with problematic users that create toxic environment for others, users persistently and consciously violating agreed upon policies, quickly deleting occasional spam posts, calming down and resolving heated discussions that lead to "requires moderator attention" flags, and a bit more authority in explaining what the policies and norms of the site are to new users. ". – Nij Oct 19 '17 at 9:26
• All of those things are issues that are discussed on meta, and meta is the place one really learns the norms that are relevant in dealing with them. – Tobias Kildetoft Oct 19 '17 at 10:12
• Nij, people who don't want to participate, don't have to participate. But as Jonas Meyer pointed in the comments, the questionnaire thread on meta has much less views than the number of voters. Even if each person only viewed it once (which is grossly not true), this is still a problematic situation. I don't want people who have little interest in how this site is run to have a say in how the site is run. And as far as I am concerned, people who don't at least passively follow meta at least on occasion have absolutely no interest in how the site is run. – Asaf Karagila Oct 19 '17 at 10:15
• Nij, I totally agree with you in that you should have a say in who is arbitrating the decisions affecting your use of the site (this is why I won't downvote your post). I just admire your ability to determine how a person arbitrates based on how they answer/explain math in the main site. Can you share the secret :-) It is IMHO better if the voters would know about the candidates views on how they want to arbitrate before making voting decisions. – Jyrki Lahtonen Oct 19 '17 at 12:26
• I disagree with deleting this answer. Deleting meta content should be reserved to extreme cases. – Asaf Karagila Oct 19 '17 at 13:58
• @Asaf, I think there are trade off. Say we only allow people who are active on meta to vote, what are the cons and pros? One major con is that normal users will feel less invested in the site. Say we have users who are very active in answering questions on the main site, they are the people who actually make the site a valuable place, does it make sense to not allow them to have a say on how the site is run? imho that would do more harm than good. So before taking strong positions on the issue I think we should step back and reflect holistically at what would the consequences be of that. – Kaveh Oct 19 '17 at 21:04
• Also I think if user who is actively participating on the main site and spending say half an hour reading and answering questions and answers would have over time see the interactions of other users and can be informed enough to vote. I think active participation on meta is needed for moderator candidates but not for those who are voting to elect them. Finally, I think rather than discussing the issue abstractly it might be more useful to think about how can we improve the election process (and come to terms with the fact that it will never be perfect :). – Kaveh Oct 19 '17 at 21:08
• @Kaveh: I think that the key issue here is "active on meta". What does it mean? Does it mean posting or commenting on every other question? Does it mean having a bronze badge in one of the core tags? Does it mean that you just know what are the issues that are currently "trending on meta"? When you write "active on meta", someone who is against this position would likely interpret this as "actively posting a lot"; whereas my intended use is "at least voted on some recent issues". And I disagree with you completely about the main site activity. – Asaf Karagila Oct 20 '17 at 9:57
• @Kaveh: I think that the fact people think that main participation is enough is one of the reasons we had candidates this, and in previous elections, who thought that being a moderator with zero meta participation is a good idea, or that moderators are in charge of correcting answers; and worse, it was one of the reasons that in the first few elections the users with the most reputation always won, which then led to some problems when some of these users were... hrm... not very well fitting with the rest of the moderators. No. Main participation is not enough. – Asaf Karagila Oct 20 '17 at 10:00
• @Nij, I do apologize. I conflated your post with an another critical post. Sorry about that. – Jyrki Lahtonen Oct 20 '17 at 17:12
• I undeleted this post as I cannot understand why it would be justified to delete it, and judging from @Asaf's comment this seems not an isolated opinion. If somebody really wants it deleted, could you please, explain it to me. – quid Oct 21 '17 at 21:26
• People are almost deliberately missing the point, disagree with their misunderstanding, then overreact and cast delete votes. Whether it is liked or , this is a valid position to hold, should not and cannot be stifled merely for not agreeing with the original post. Especially when it is not the only answer doing so. – Nij Oct 21 '17 at 22:20


text:
Errata in "Partial Differential Equations, an Introduction", SECOND Edition, by Walter A. Strauss
(John Wiley and Sons, New York, ISBN-13 978-0470-05456-7)

Page
21, line -8: no vertical component of the tension.

28, Ex. 6: with u(x,0)=\phi(x).

34, line -13: The second + should be -.

44, lines -2 and -3: u and v should be u_1 and u_2.

53, Ex. 11, line 4: Assume uniqueness.

55, line -11: initial data exp(-x^2/4k).

89, Ex. 5: This exercise is difficult.

102, Ex. 14: Permit m to be a complex number.

111, Ex. 1, line 1: sin n\pi should be sin nx.

128, line 5: The numerator should be N.

135, Ex. 11(b): Assume a_0=0. Write the series for F(x), not f(x).

141, eq. (15): for n nonzero.

143, line 2: sin n\pi should be sin nx.

180, line 4: D should be a bounded region.

219, midpage: u_{jgk} should be u_{j,k}.

237, eq. (10): The subscript should be t, not r.

243: Lines -8 to -6 are confusing and should be omitted.

278, Ex. 8(b): Find a simple equation satisfied by the eigenvalues, not a simple formula for them.

280, (iii): Should be cones, not horizontal planes.

286, line -6: The second integral should go from 0 to \pi.

287, line 9: The exponent should be -in\theta.

313, Ex. 2: ...among all C^2 functions such that the integral over D of f plus the integral over bdy(D) of g vanishes.

407, line -6: Assume that \rho=1.

409, line 8: change two-dimensional to uni-directional.

441, line -1: The + should be -. In the exponent the a should be a^2.

I thank David H. Wagner and Douglas Baldwin for pointing out some of these errors in the Second Edition.

End of Errata for the Second Edition.

Errata in "Partial Differential Equations"
Errata in "Partial Differential Equations, an Introduction", FIRST Edition, by Walter A. Strauss
(John Wiley and Sons, New York, ISBN 0-471-54868-5)

The following errata are for the 6th (or later) printing of the First Edition.
(To identify which printing your copy is, look at the last number on the page before the preface.) If you have an earlier printing and you wish a list of errata for it, please send me an e-mail message to that effect.

Page
13, last line: ds should be dxdy.

17-18: The second, third and fourth triple integrals should be over all of R^3.

19, Ex. 8: Assume u and grad(u) tend to zero as |x| tends to infinity. (This exercise is difficult.)

42: The bottom line of the page got dropped in the 6th printing! It should be:
u(x,0)=phi(x), u(0,t)=g(t), u(ell,t)=h(t).

42: In some printings, near the bottom of the page, change L to ell.

42: Four lines got dropped in the 9th printing!
Below equation (2) it should say:
.....which is the "diffusion inequality". Now suppose that v(x,t) attains its maximum at an interior point (x_0,t_0). By ordinary calculus, we know that v_t=0 and v_{xx} <=0 at (x_0,t_0). This contradicts the diffusion inequality (2). So there can't be an interior maximum. Suppose now.....

44, line 7: Change min to max.

49, line 2: Omit the phrase "letting..."

57, eqn. (8): Change the second >= to <= .

58, Ex. 4: Let f(x)=x+1-exp(2x) for x<0 [instead of x+1].

60, below eqn.(3): Change ct to c|t|.

64, Ex. 10: Change ell to pi/2.

66, midpage: "integral in (5)" should be "integral in (6)". Also, "to formula (3)" should be "to formula (5)".

70, line -4,-3: 1+T+T^2 should be replaced by (1+T+T^2){-1} 77, Ex. 7: Change n to m in the exponent in the sum. The series converges uniformly for bounded t.
Also S"(t)+ A2S(t) = 0.

79, line 13: The integrand should be |p| exp(-p^2/4) instead of p exp(-p^2/4).

94, sentence below eqn. (15): Change "only if a_0 and a_ell have opposite signs" to "only if a_0 or a_ell is negative or else both vanish".

98, Ex. 4, line 5: Reverse the sign of the curve.

98, Ex. 7, line 3: replace \lambda by \beta and delete the square, where \beta^2=\lambda.

100, line 7: Should be x>a.

119, line 8: The sum should start at n=0.

123, Example 2: Change ell to 1.

126, eqn.(11): 4/pi, not pi/4.

127, lines -7,-6: The integrals go from a to b.

127-8: Change E_n to E_N.

129, lines 3,5: Replace \ell by \pi. 133: In the proof of (5), change the sign of the second-to-last line.

136, line -13: Place a factor 2 inside the second square root.

140, Ex. 12: Assume it satisfies the periodic BC.

141, end of second paragraph: See Example 3 in Section 5.4 for the dangers of differentiation.

143, line -3: Switch omega and c.

149, line 15: Replace "less than" by "less than or equal to".

153, line 3: (r, theta, phi)

153, eqn.(7): Delete u.

158, Ex. 5: Take b=1 for simplicity.

162, line -1: The last u(x) should be x.

164, Ex. 3: sin3 theta and sin(3 theta) should be switched.

165, two lines above (5): Replace n by n pi.

168, Ex. 12: The domain should be assumed to be connected.

176, below eqn.(G2): Change (G2) to (G1).

178, eqn. (5): The left side should be u(x_0).

180, line -9: (7.2.1)

187, Ex. 7(d): Change h(y) to h(x).

188, Ex. 18: octant

188, Ex. 19: Change r-3/2 to r-2.

188, Ex. 25: Delete this exercise.

190, line -5: change the third + to -.

194, line below (3): A factor of 4 is missing.

199, Ex. 3: Change 0<x<1 to 0<x<5.

207, Ex. 2(a): Replace 2 by 0.5.

207, Ex. 8: Do it for the equation u_{tt} = u_{xx} - u^3.

207, line -1: The - should be +.

222, Ex. 6: Take the boundary conditions to be homogeneous.

240, Ex. 1, Hint: Exercise 2.4.10 is an alternative hint.

240, Ex. 5: up to a constant factor.

248, line -5: In the last term move the bar to the other v.

251, Ex. 4: Change Robin BC to dv/dy=-v. In (b) change - to +.

251, Ex. 5(b): Put a minus in front of the operator.

254, (18): The coefficients are not correct: see the second edition.

251, Ex. 5(d): Change Dirichlet to Neumann.

252, line below (9): Change n to lambda.

258, line below (4): Change (1) to (2).

262, table: In the third line, the last -1 should be -r2.
In the fifth line, cos(2 theta) should be cos (2 phi).

267, Ex. 2, Hint: The last two factors should be replaced by 3-2sin2x-2sin2y.

270, eqn. (10): Change the second + to -.

271, eqn. (12): Take the square root of 2/pi.

272, eqn. (18): Change 1/pi to 2/pi.

280, two lines above (11): Cahnge 1/r to -1/r.

290, line 14: Change 27.3 to 30.5.

290, formulas for A and B: factors of 2 pi are missing.

290, above eqn. (6): Assume the trial functions are linearly independent.

292, Ex. 4: a=1.

295, eqn. (4): Change j to n.

295, eqn. (6) and above: The subscripts should be N+1.

297, Ex. 3: Delete the boundary integral. Replace the constraint /int w2 dx=1 by w=g on bdy(D).

308, Theorem 4: each Dirichlet eigenvalue.

309: Delete the second paragraph.

312, Ex. 2 and 3: These exercises are difficult.

312, Ex. 5: ellipse

312, Ex. 9(b): On the third line replace D by D+ in two places.

322, line -10: Change (1/2)c to 1/(2c).

322-3, eqns. (9),(10): We have permitted any t, positive or negative, in these formulas.

327, table: In the last entry, a is positive.

342, line 1: Change the signs in the equation. ...the inhomogeneous Maxwell equations.

348, line below (11): The function R is related to Bessel's equation by R(kr) = H-(kr)/sqrt(kr).

348-350: Replace H+ by H- throughout.

348-9, eqn. (12) and eqn. below (17): Divide H-(kr) by sqrt(kR).

350: Replace the first R by r.

353, Ex. 2: The second term is q psi, not psi. Assume Q>0.

364, eqn. (12) and line -1: Several terms are missing their integral signs {line integrals over the curve x=xi(t))}.

372, line -1: Change 3 to 1.

373, Ex. 2: Change + to -.

374, Ex. 12: There is a missing factor of kt^{-1/3}.

378, Ex. 10: Change - to +.

391, line -1: Change the last cos\phi to cos\theta.

394, lines 7 and 19: Change (1) to (2).

In the following pages, there are a few additional errors in the answers and hints. See the second edition for all the corrections.

401, Ex. 1.4.4: Reverse the sign.

401, Ex. 1.6.5: beta = -4 and gamma = 1/sqrt{3}.

402, Ex. 2.2.5: Put rho in the integrand.

403, Ex. 3.2.9(a): Change 11/81 to 4/27.

404, Ex. 4.3.12, line 3: Delete the 2 in the argument of the cosine.

404, Ex. 4.3.18(e): Delete the last sentence.

406, Ex. 5.6.9: Change the last + to -.

406, Ex. 7.1.10: Change 2 to 1/2.

407, Ex. 7.4.1: Divide the given answer by ell.

410, Ex. 10.1.2: Change 16 to 64.

410, Ex. 10.2.5: In the exponent, betan should be squared.

410, Ex. 10.3.6: 193.9 seconds

410, Ex. 10.3.7: 3a2/10 instead of 3/10.

410, Ex. 10.5.15: superscripts + on H.

411, Ex. 10.6.7: Replace A-B by (A-B)/2. Also replace !! by (ell-2)!! in the numerator.

412, Ex. 11.4.4: Replace -sech by 2 sech .

412, Ex. 12.4.1: Replace k by kappa.

(Errata updated as of January 2008)

I take this opportunity to thank all the people who have notified me of errors in the text since its publication. See the Second Edition for specific acknowledgements. (Hopefully I have not forgotten to mention anyone.)

format: plain


text:
An ampere is the unit for the electric current; the flow of electrons. One amp is 1 coulomb passing in one second. One amp is produced by an electric force of 1 volt acting across a resistance of 1 ohm. Sometimes this is abbreviated as I for intensity.

The ampere is equivalent to one coulomb (roughly 6.241×1018 times the elementary charge) per second.[6] Amperes are used to express flow rate of electric charge. For any point experiencing a current, if the number of charged particles passing through it — or the charge on the particles passing through it — is increased, the amperes of current at that point will proportionately increase.

The ampere should not be confused with the coulomb (also called “ampere-second”) or the ampere-hour (A⋅h). The ampere is a unit of current, the amount of charge transiting per unit time, and the coulomb is a unit ofcharge. When SI units are used, constant, instantaneous and average current are expressed in amperes (as in “the charging current is 1.2 A”) and the charge accumulated, or passed through a circuit over a period of time is expressed in coulombs (as in “the battery charge is 30000 C“). The relation of the ampere (C/s) to the coulomb is the same as that of the watt (J/s) to the joule

## Definition

ampere

Illustration of the definition of the ampere unit

Ampère’s force law[7][8] states that there is an attractive or repulsive force between two parallel wires carrying an electric current. This force is used in the formal definition of the ampere, which states that the ampere is the constant current that will produce an attractive force of 2 × 10−7newtons per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in avacuum.[2][9]

The SI unit of charge, the coulomb, “is the quantity of electricity carried in 1 second by a


text:
Journal article Open Access

# Embedding Power Line Communication in Photovoltaic Optimizer by Modulating Data in Power Control Loop

Zhu, Yue; Wu, Jiande; Wang, Ruichi; Lin, Zhengyu; He, Xiangning

### Citation Style Language JSON Export

{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.1287279",
"container_title": "IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS",
"title": "Embedding Power Line Communication in Photovoltaic Optimizer by Modulating Data in Power Control Loop",
"issued": {
"date-parts": [
[
2018,
5,
24
]
]
},
"abstract": "
In Photovoltaic (PV) system, dc-dc power op-timizer (DCPO) is an option to maximize output power. At the same time, data links among DCPOs are often required for system monitoring and controlling. This paper pro-poses a novel power line communication (PLC) method for the DCPOs, in which the data of a DCPO is modulated into the control loop of power converter, and then transmitted through the series-connected dc power line to other DCPOs. In the process of communication, differential phase shift keying (DPSK) modulation and discrete Fourier transformation (DFT) demodulation are employed. To ana-lyze the quality of communication, the communication model of the system is built, based on small-signal model. Furthermore, the noises of the system, including switch-ing, maximum power point tracking (MPPT) and additive white Gaussian noise (AWGN), are discussed and meas-ured to evaluate the signal-to-noise ratio (SNR). At last, an experimental system including 6 DCPOs is established and tested, which verifies the feasibility and effectiveness of the proposed method.
",
"author": [
{
"family": "Zhu, Yue"
},
{
"family": "Wu, Jiande"
},
{
"family": "Wang, Ruichi"
},
{
"family": "Lin, Zhengyu"
},
{
"family": "He, Xiangning"
}
],
"type": "article-journal",
"id": "1287279"
}
99
80
views


text:
# How can I shape my time channel response, in order to have Gaussian shaped Doppler Spread?

I know how to generate a Rayleigh fading channel but I have no clue how I can shape the Doppler spectrum to be Gaussian.

Any help will be really appreciated.

ps: I am coding on matlab

See section 2.4.3 of this reference https://web.stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf

If the doppler spectrum has to be gaussian, the auto-correlation of tap gains should be gaussian (which is correctly mentioned in other answer but I somehow felt more details were not captured). For a coherence time $$T_c$$, proportional to doppler spread $$1/D_s$$, will be expressed as smallest amount of $$n$$ for which your tap at $$l$$ will be significantly different from tap at $$l+n$$. So for example, if $$n=5$$, gain of taps from $$0$$ till $$4$$ will be having a guassian distribution, while the gain at tap $$0$$ will be uncorrelated with tap at $$5$$.

If you model your taps as Rayleigh fading channel, your PSD will not be Gaussian as given in eq 2.60 of the reference. You may need to generate your tap gains such that their auto-correlation function follows gaussian distribution.

Since you are using MATLAB

raychan = comm.RayleighChannel('DopplerSpectrum',{doppler('Gaussian')});

This makes sure that each of the channel taps gain auto-correlation (and PSD) follows Gaussian distribution.

To spread in frequency with a Gaussian shape is to convolve the frequency domain on the waveform with the Gaussian shape. To convolve in frequency is to multiply in time the respective Fourier Transforms. The Fourier Transform of a Gaussian is a Gaussian; so therefore you would multiply in time by a Gaussian window.

In MATLAB you can use the "gaussian" function to generator a Gaussian window of length $$N$$ with width parameter $$d$$ using the form (gaussian(N, d)) to get the following result:

$$g[n] = e^{-(d n)^2/2}$$

where $$d$$ is the inverse of the standard deviation in samples, and $$n$$ is the sample count over $$N$$ samples.

Using the general form from https://en.wikipedia.org/?title=Fourier_transform#Square-integrable_functions) for the Fourier Transform for the Gaussian function, repeated here:

$$\mathscr{F}\{e^{-\alpha x^2}\} = \frac{1}{\sqrt{2\alpha}}e^{-\omega^2/(4\alpha)}$$

The Fourier transform for $$g[n]$$ is:

$$G(\omega) = \frac{1}{d}e^{-(\omega/d)^2/2}$$

Which is also a Gaussian with the standard deviation in radian frequency given as $$d$$.

Since the Gaussian Doppler Spectrum has a Gaussian shaped power spectral density (for a single tone), to get a Gaussian shaped power spectral density the kernel (Fourier transform of the time domain window) would be the square root of $$G(\omega)$$ given above to be:

$$W(\omega) = \sqrt{G(\omega)} =\sqrt{\frac{1}{d}}e^{-(\omega/d)^2/4}$$

resulting in the time domain window: $$w(t) = \sqrt{2}e^{-(dn)^2}$$

Which is again a Gaussian function. Notice that starting with a desired standard deviation of a power spectral density as $$d$$, the square root of this is a Gaussian function with standard deviation $$\sqrt{2}d$$, and the inverse transform representing the desired time domain window is also a Gaussian function with standard deviation $$1/(\sqrt{2}d)$$.

Thus if we desire through windowing in the time domain a Gaussian spreading in the power spectral density with a standard deviation of $$\sigma$$, in units of normalized radian frequency, this can be generated from the MATLAB "gaussian" function given above using the relationship for the expression "gaussian(N,d)" with N samples:

$$d = \sqrt{2}\sigma$$

This will provide the Gaussian time domain window to multiplying with the time data. This will have the same effect as convolving all the frequency components with the desired Gaussian Doppler spread such that the power spectral density of this spread will have a standard deviation of $$\sigma$$ in normalized radian frequency ($$f_s = 2\pi$$).

Example: $$f_s= 1e6$$, $$N = 1024$$, desired Doppler spread $$= 5e3$$ Hz (standard deviation). In normalized radian frequency this would be $$2\pi (5e3/1e6)$$, and the time domain window would be generated using:

win = gaussian(1024, sqrt(2)*2*pi*5/1e3)

This would provide a simple way to create the effect of a Doppler spread channel through the process of time domain windowing. However, this results in a significant window loss since much of the signal is masked by the window in the time domain. Other statistical based approaches which would be more representative of a Doppler channel model typically used are described in this paper:

• Hi @Dan_Boschen (for some reason I am not able to tag if there is space in the name), if you take the PSD of gaussian-windowed time data, wouldn't the PSD be different from Gaussian? The ACF of time data shows when the correlation goes to zero, thereby giving an idea of coherence time. We want ACF to be gaussian (because we want PSD to be gaussian). But since ACF is itself is $x(t).*w(t)$, the effect of gaussian window is disturbed by actual time data $x(t)$. Hence I doubt if PSD will be Guassian. – jithin Apr 7 '20 at 6:11


text:
# How to expand this generating function

I am new to generating functions / power series and I am struggling with expanding following generating function: $$F(x)=\frac{(x^2-x^{10})(1-x^{10})^3}{(1-x)^4}$$ I tried to pattern my solution on that answer and expand generating function in the same way, so i rewrote $F(x)$ as: $$F(x)=\frac{x^2(1-x^8)(1-x^{10})^3}{(1-x)^4}$$ and in order to obtain coefficient at $x^{20}$ I tried to calculate: $${(20-2)+3 \choose 3}-{(20-2)-8+3 \choose 3}-{(20-2)-10+3 \choose 3} \cdot 3$$ The result of this is $549$ which is smaller by $3$ than proper solution which is $552$. I don't know what I did wrong. In fact, I don't understand this method of expanding coefficients so if you could provide the name of this technique or some resources to read about I would be thankful. I mean, I see the pattern this technique follows, but I don't see why it works.

This generating function gives solution to one problem that I solved first in purely combinatoric way. My calculations were nearly identical to these presented above, but I had to exclude intersection of two sets which was of size $3$. So I understand that there should be $+3$ term in solution above, but I don't know where it would come from in case of expanding generating function.

Using negative binomial series,

\begin{align} F(x) &= x^2(1-x^8)(1-3x^{10}+3x^{20}-x^{30})(1-x)^{-4}\\ &= x^2(1-x^8)(1-3x^{10}+3x^{20}-x^{30})\sum_{k=0}^\infty \binom{4+k-1}{k} x^k\\ &= (x^2-x^{10})(1-3x^{10}+3x^{20}-x^{30})\sum_{k=0}^\infty \binom{3+k}{k} x^k\\ &= (x^2-3x^{12}-x^{10}+\color{blue}{3x^{20}}+p(x))\sum_{k=0}^\infty \binom{3+k}{3} x^k\\ \end{align}

where $p(x)$ are higher order terms that are not interesting for the question.

Hence

$$\binom{18+3}{3}-3\binom{11}{3}-\binom{13}{3}+3\binom{3}{3}$$

I suspect you left out the case where we let $k=0$.

• I misunderstood the process of expanding generating function. Looking at the example I linked to, I didn't realize it's author skipped some part of calculations and just gave the final result. This is why I was confused. Thank you for answer. – mrJoe Feb 16 '18 at 18:13

I think that you missed one term. Notice that $$(1-x^8)(1-x^{10})^3=(1-x^8)(1-3x^{10}+O(x^{20}))=1-x^8-3x^{10}+3x^{18}+o(x^{18}).$$ Hence \begin{align} [x^{20}]\frac{x^2(1-x^8)(1-x^{10})^3}{(1-x)^4} &=[x^{18}]\frac{1-x^8-3x^{10}+3x^{18}+o(x^{18})}{(1-x)^4}\\ &=[x^{18}]\frac{1}{(1-x)^4}-[x^{10}]\frac{1}{(1-x)^4}-[x^{8}]\frac{3}{(1-x)^4}+[x^{0}]\frac{3}{(1-x)^4}\\ &=\binom{18+3}{3}-\binom{10+3}{3}-3\binom{8+3}{3}+3=552. \end{align}

• Thank you for explanation. I missed one term because I wrongly deduced the pattern of expanding generating functions. So if there was a term in numerator like (1+x)^123 we would have to calculate it? I thought there is some way to avoid exponentiation. – mrJoe Feb 16 '18 at 18:09
• Could you rephrase your question, please? – Robert Z Feb 16 '18 at 18:24
• I mean, we had to expand numerator and then split function into partial fractions. In my situation there was a value (1+x^10)^3 so it was not hard to expand it. But if the exponent was e.g. 123 we would have a lot of work to do. So I wondered if there is a technique which lets avoid this time-consuming calculation. – mrJoe Feb 16 '18 at 18:54
• No, it suffices to consider $(1-x^{10})^{123}=1-123x^{10}+O(x^{20})$ – Robert Z Feb 16 '18 at 18:59


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# What is the purpose of UV-VIS Spectroscopy?

I understand the purpose behind infrared spectroscopy and mass spectroscopy, but UV-VIS doesn't make much sense to me.

Through research, I see that it has to do with electron orbitals, and it has a relation to Beer's Law.

But what exactly can I learn about a molecule from its absorbance/transmittance of UV/Visible light?

• Emission and absorption in the visible and UV can uniquely identify the material in question. Jun 12 '15 at 22:05
• @JonCuster How so? I mean if I have an unkown compound and run it with a UV VIS spectrophotometer, wouldn't I have to go through thousands of other compounds to see if the spectra match to identify the sample? Jun 12 '15 at 22:08
• And you don't have to do that for IR and mass spec? Jun 12 '15 at 22:09
• It's another way to identify chemicals
– user15489
Jun 12 '15 at 22:11
• Often, IR energies match to vibrational states in a molecule. Vis/UV will probe electronic states. You might very well need both to identify something. Consider how useful color vision is to rapidly distinguishing, say, chlorophyll from xylophyll. All the different phosphor materials have different absorption and emission lines, lifetimes, etc... Often, just as for IR or mass spec, you will need to use some other info to help you out. Jun 12 '15 at 22:18

The broad absorption bands of the electronic transitions observed in UV/Vis spectroscopy/spectrophotometry, as well as the myriad types of electronic transitions that might lead to absorption at a given wavelength, indeed make the technique much less powerful for identification of unknown compounds as compared to, e.g., IR, NMR, microwave, and mass$^*$ spectroscopies.

Jon Custer is correct in his comment to the question that UV/Vis spectra can provide key information in identifying unknown species. However, I know of only two approaches to obtaining predictions of a given UV/Vis spectrum:

• Experimental spectra of compounds suspected to be structurally related to the unknown species
• Quantum chemical computation of the electronic transition spectra of candidate species

The former approach requires the relevant experimental data to exist; the latter is not trivial to perform accurately. Both suffer from significant uncertainties: How similar is a reference experimental spectrum to that of the unknown species? Can I trust that my quantum computation will give realistic band locations and strengths?

In my experience, the strength of UV/Vis lies in its facility for inexpensive, convenient, routine, non-destructive quantitation of known solutes, with known absorption spectra and/or extinction coefficient(s) at given wavelength(s). The following list of strengths is almost certainly incomplete:

• The instrumentation and consumables are relatively inexpensive.

• No auxiliary cooling, gas supply, etc. are required.

• Preparation and analysis of fixed-volume samples is trivial: pour liquid into cuvette; place cuvette into instrument; measure.

• Continuous analysis of dynamic systems (e.g., chromatographic eluates and ongoing reactions) is possible using a flow cell.

• A simple example is described here, unfortunately paywalled.
• A wide variety of configurations is presented at a commercial vendor here.
(No endorsement intended. There are numerous other suppliers out there; I chose this one because it had a good variety shown in schematic.)
• Interference from most solvents is minimal, particularly in the visible range.

• Beer's Law in its linear form has a relatively high dynamic range for most UV/Vis-active solutes$-$that is, the concentration where absorbance deviates from linearity is much greater than the minimum concentration detectable:

$$\frac{C_{\max}}{C_{\min}} \gg 1$$

• Another implication of Beer's Law is that interference(s) from a small number of absorbing co-solutes are relatively straightforward to handle, either by measuring at isobestic points or by measuring multiple wavelengths and solving the linear absorbance equations for the unknown concentrations. For example, if two species $\ce{X}$ and $\ce{Y}$ are present and absorbances are measured at wavelengths $\lambda_1$ and $\lambda_2$, the concentrations can be found by solving the following two expressions:

$$A_{\lambda_1} = \epsilon_{\ce{X},\lambda_1}\cdot C_\ce{X} + \epsilon_{\ce{Y},\lambda_1}\cdot C_\ce{Y}$$ $$A_{\lambda_2} = \epsilon_{\ce{X},\lambda_2}\cdot C_\ce{X} + \epsilon_{\ce{Y},\lambda_2}\cdot C_\ce{Y}$$

• The steady-state nature of the measurements allows for 'deep' examination of a particular sample.

• The full UV/Vis spectrum for a given volume of sample can be measured, giving a rich "fingerprint" of the particular solution and the solutes in it
• The absorbance at a particular wavelength can be tracked over time, allowing for detailed kinetic analyses
• At least in the visible range, the quality of the substance being measured is directly perceptible to the human senses. This is actually quite viscerally satisfying, to see that a sample anticipated to contain significantly more of a solute does indeed produce a noticeably stronger coloration of the solution.

While IR and microwave spectroscopies share some of the above advantages, they are far less suited for analysis of solutes, as the solvent absorbance is often much more likely to confound measurements. Further, the instrumentation and sample preparation are generally much more involved.

Mass spec is terrifically expensive and complicated, is an intrinsically destructive method, and is less well suited for direct quantitation since there is no way to know a priori what fraction of the injected sample is actually making it to the detector and thus careful calibration is required.

NMR, though non-destructive, also requires quite expensive equipment that is complicated to operate properly, and interpretation of the spectra requires quite a bit of practice.

I know too little about EPR/ESR, EXAFS, XANES, and others to comment on them here. I believe the above strengths hold in comparison to those methods as well, however.

$^*$ Technically, MS is mass spectrometry, not spectroscopy, since the measurement is of discrete ion impacts on a detector, as opposed to absorbance of portions of the electromagnetic spectrum by a detector.


text:
Translator Disclaimer
2016 Chapter X. Modules over Noncommutative Rings

## Abstract

This chapter contains two sets of tools for working with modules over a ring $R$ with identity. The first set concerns finiteness conditions on modules, and the second set concerns the $\operatorname{Hom}$ and tensor product functors.

Sections 1–3 concern finiteness conditions on modules. Section 1 deals with simple and semisimple modules. A simple module over a ring is a nonzero unital module with no proper nonzero submodules, and a semisimple module is a module generated by simple modules. It is proved that semisimple modules are direct sums of simple modules and that any quotient or submodule of a semisimple module is semisimple. Section 2 establishes an analog for modules of the Jordan–Hölder Theorem for groups that was proved in Chapter IV; the theorem says that any two composition series have matching consecutive quotients, apart from the order in which they appear. Section 3 shows that a module has a composition series if and only if it satisfies both the ascending chain condition and the descending chain condition for its submodules.

Sections 4–6 concern the $\operatorname{Hom}$ and tensor product functors. Section 4 regards $\operatorname{Hom}_R(M,N)$, where $M$ and $N$ are unital left $R$ modules, as a contravariant functor of the $M$ variable and as a covariant functor of the $N$ variable. The section examines the interaction of these functors with the direct sum and direct product functors, the relationship between $\operatorname{Hom}$ and matrices, the role of bimodules, and the use of $\operatorname{Hom}$ to change the underlying ring. Section 5 introduces the tensor product $M\otimes_RN$ of a unital right $R$ module $M$ and a unital left $R$ module $N$, regarding tensor product as a covariant functor of either variable. The section examines the effect of interchanging $M$ and $N$, the interaction of tensor product with direct sum, an associativity formula for triple tensor products, an associativity formula involving a mixture of $\operatorname{Hom}$ and tensor product, and the use of tensor product to change the underlying ring. Section 6 introduces the notions of a complex and an exact sequence in the category of all unital left $R$ modules and in the category of all unital right $R$ modules. It shows the extent to which the $\operatorname{Hom}$ and tensor product functors respect exactness for part of a short exact sequence, and it gives examples of how $\operatorname{Hom}$ and tensor product may fail to respect exactness completely.

## Information

Published: 1 January 2016
First available in Project Euclid: 18 July 2018

Digital Object Identifier: 10.3792/euclid/9781429799980-10

Rights: Copyright © 2016, Anthony W. Knapp

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## Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians. (arXiv:1607.07821v2 [math.AG] UPDATED)

Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we give a classification of such Calabi--Yau 3-folds and determine their topological invariants. We also give alternative descriptions for some of them.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we give a classification of such Calabi--Yau 3-folds and determine their topological invariants. We also give alternative descriptions for some of them.


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# Name

cnvp - calculate the convolution function between two images using padding with zeroes and multiplication in Fourier space.

# Usage

output = cnvp(image, ref, center=True)

## Input

image
input image (real)
ref
second input image (real).
center
if set to True (default), the origin of the result is at the center; if set to False, the origin is at (0,0), the option is much faster, but the result is difficult to use

## Output

output
convolution function between image and ref. Real. The origin of the convolution function (term ccf(0,0,0)) is located at (int[n/2], int[n/2], int[n/2]) in 3D, (int[n/2], int[n/2]) in 2D, and at int[n/2] in 1D.

# Method

• Calculation of the circulant convolution function between image f and reference image g is performed farst by padding with zeroes to twice the size in real space,

next by calculating Fourier transforms of both images, then the product in Fourier space as `hat(f)hat(g)`, then the inverse Fourier transform, and finally the ccf is windowed out using the size of original images.

• In real space, this corresponds to:
• `\cnvp(n)=sum_(k=0)^(nx-1)f(-k+n)g(k)`

• `n = -(nx)/2, ..., (nx)/2`

• with the assumption that `g(k)=0 fo\r k<0 or kgenx`

• Note: cnvp is free from "wrap around" artifacts, although coefficients with large lag n have large error (statistical uncertainty).

# Reference

Pratt, W. K., 1992. Digital image processing. Wiley, New York.

Pawel A. Penczek

category 1
FUNDAMENTALS
category 2
FOURIER

fundamentals.py

# Maturity

stable
works for most people, has been tested; test cases/examples available.

# Bugs

None. It is perfect.

cnvp (last edited 2013-07-01 13:12:44 by localhost)


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# JEE-Mains 2014 (3/30)

Algebra Level 3

If $$a \in \mathbb{R}$$ and the equation $-3(x-\lfloor x \rfloor)^2+2(x-\lfloor x \rfloor)+a^2=0$ has no integral solution, then all possible values of $$a$$ lie in the interval:

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