darklight03/StackMIAsub huggingface dataset:
In the most basic sense, what is abstract algebra about? Wolfram Mathworld has the following definition: "Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields." I find this, however, to say the least, not very informative. What do they mean by abstract algebraic structures? Along these lines, what are groups, rings, and fields then? I've been told by a friend that groups, essentially, are sets of objects, although, this still leaves me wondering what he means by objects (explicitly). I don't need anything rigorous. Just some intuitive definitions to give me some direction. Thanks!
I'm a programmer and like to name my variables as accurately as possible (who knows who will be reading my code in a few years' time?) I've been thinking about sports video games recently, and have thought about the idea of a generic sports game engine. Most sports games have an arena, crowds, a playing surface and players. They also have a puck, ball, discus, javelin, etc. and this has me wondering: What is a generic term for this object? Something that could transcend all sports. Edit: Since it seems there may be no exact term for this type of object, I'd gladly settle for some sort of analog.
I think to answer this question we would have to fully understand the nature of black holes. It seems to me that the smaller black hole could have a lower density than the larger one. In this case the smaller black hole might be effected by the tidal forces of the larger black hole. But if the densities of the two black holes were the same, wouldn't the smaller black hole be immune to spaghettification?
Is it somehow possible to extend TexStudio to use dictionary words in autocompletion? For example, when I type "som", I want the autocompletion list to show me all words from the dictionary starting with "som". I know TexStudio uses autocompletion for words that already appear in the same document. I've tried to create a .CWL file, but apparently it is only for commands and plain words are not supported.
I'm trying to create my own ultrasonic humidifier. I ordered the misting part which works great but it only functions correctly in shallow water. So I'd like to feed from a large water reservoir to a smaller one. My question is how can I fill the smaller reservoir to a desired water level? Will I have to use a closing/opening valve or is there a simpler way? (I was thinking a small balloon hooked up to a pulley that opens and closes a latch much like a toilet but I am trying to avoid complexity.)
My assignment asks us to prove or provide a counter example for If R is symmetric, then Rc is symmetric. I know that if R is symmetric, then (x,y) and (y,x) are both in R, but what I do not understand is what is R^c, what does R^c do to the relation? I believe that complement basically means "not", so does that mean the complement of R is NOT symmetric? I can't seem to wrap my head around this concept, any help would be appreciated. Thanks
The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as has been pointed out here and elsewhere, this explanation seems (to a layman like me, at least), to be "hopelessly circular", and in the end contributes little to an understanding of how modern theories of gravitation work. Are there other (or additional) metaphors that might be helpful in illustrating to lay readers (a) what motivates modern gravitational theory and (b) why it has greater explanatory power than Newtonian gravitation?
A field F is algebraically closed if every non constant polynomial in F[x] has a root in F. Is this the right definition? I am wondering if only one root in F and the rest of the roots not in F can also be considered 'algebraically closed'? I remember reading somewhere that if a root is in F then all roots are in F. Is this a special case of something? If so, could someone enlighten me on what it is? Thank you
Assuming an object is moving in a straight line propelled by a force. How much energy would that force have to exert so that there are no known forces or objects that could stop it from moving in that straight line? I'd guess limits like the speed of light might come into play here, but it would be interesting to know what the values would be if those limits weren't there.
I am in sales and when I make a cold call I typically begin the conversation with, "I just wanted to..." Some common phrases are, "I just wanted to see if you might be interested..." or "I just wanted to follow up with you..." I hate this phrase as it shows a lack of confidence and it's not truthful. I want more than JUST to do something, I want to engage in a conversation so I feel disingenuous starting the conversation with this statement. Does anyone have any alternative ways of beginning these statements? Thanks!
I am a newbie to Mac OS X. I installed TeXmaker and found that the Chinese characters in the interface are garbled completely (see figure below). I tried a lot to fix this but nothing worked. Finally I realized that this is related to the "Interface fonts". However, on my mac there's no such setting option!!! (Previously I used ArchLinux and there was indeed such a button) Does someone happen to know how to modify "interface fonts" for mac TeXmaker? Many thanks in advance!
Sorry for the elementary question, but I am confused. Suppose I am telling someone about a conversation I had with a friend the previous day. Which would be correct? "I asked him if he were well" "I asked him if he is well" "I asked him if he was well" Am I right in saying that the third sentence would be "double past tense", as in referring to a previous conversation where I asked my friend if he was well at an even earlier point in time?
Apart from Cantor's diagonalization argument, there are a number of ways to show that cardinality of R is greater than that of N (eg: Baire Category theorem, path connectedness of R and so on). Are there any arguments outside Set Theory which naturally lead us to sets of higher cardinality than R ? In other words, if Set Theory never existed, would we be happy to conclude that there are only three types of cardinality - finite, countably infinite and uncountably infinite - or would we have gone beyond ?
In prime numbers, one has the sieve of Eratosthenes, which is a method of computing the next prime, once you have all previous primes: You just cross out the multiples of the previous primes on the number line, and the first remaining number is the next prime. I wonder whether there is such a method for prime gaps. Of course, one could add up the prime gaps and then apply the sieve of Eratosthenes, get the next prime, and then compute the next prime gap from it, but I wonder whether there is a more "direct" way.
I have a problem in Texmaker. I have divided a document into a number of subfiles. I would like to compile the whole document from the current subfile without running the master file. I tried to define the current file as a master file by changing the status of the current subfile to a master file in Options menu. However, I receive errors after running the subfile. Can you please give me some pieces of advice in this respect?
Let's look at an internal combustion engine (more precisely a standard gasoline car engine) as a black box (so without going too much into details about internal processes). The inputs of this system are throttle (gas pedal position), moment of inertia it sees and possibly external torque? And the outputs are torque and angular velocity. Can you provide me with a simple model of these relations? Or in other words, how do I know how throttle affects the movement of the car?
Could anyone briefly explain, or point me towards a resource explaining, the main differences between the main integration theories, namely: Riemann Integration Riemann-Stieltjes Integration Lebesgue Integration Lebesgue-Stieltjes Integration I understand that this a question with a potentially very long answer, since integration is no small theory. I can find information on these integrals separately, but I would really be interested in a comparison of these integrals with one another.
Recently, I have lost a great amount of work on a project in LaTeX because of unwittingly saving changes when cutting out a large chunk of text and copying the remaining part. I was wondering if there was any way to bring back a version of a LaTeX document from a previous time to this incident. I know such a function is available on Google Docs, but is it available here? If so, how? Thanks!
I'd like to ask how verbs 'to be riddled with something' (idiom) and 'to teem with something' (phrasal verb) overlap each other and can we replace with one another in the same sentence? For example: ...the judiciary are riddled with prejudices and the judicial system is filled with flaws, and innocent people will be executed. His body was riddled with cancer. Her typing was slow and riddled with mistakes. The woods are riddled with rabbit holes. The streets were teeming with tourists. A river teeming with fish ( The sentences were excerpted from Oxford Dictionary Online)
I am writing a large Sweave document that will be broken up into many chapters with the final output being a large pdf of everything and an individual pdf for each chapter (with the same page and caption numbering as in the large pdf). I found some great answers about working with multiple files but haven't seen how to also create the individual chapter pdfs with proper pagination. Is there a way to do that?
I am not a native English Speaker, but I work with English speakers on a daily basis and they have always troubles pronouncing my surname, so they will often ask me to tell them how they can pronounce it. My surname is Sulce. I also tried a pronouncing service and they said "Sorry, we can't pronounce that." So, I would like to ask native speakers to help on defining the most correct way to pronounce it. What's the first pronunciation that comes to your mind for the word Sulce?
I've read in books that one can't put one's hand through a table because the table offers a "Normal Reaction" to the hand. And it is also stated that this force is electromagnetic in nature. But what is this force? Can it be explained using classical electromagnetism "in terms of something I'm more familiar with"? Moreover, if it is this force that stops my hand from going through the table, why is it that certain other solid substances, like sand, don't produce the same result? Also, is there any limit to this Normal reaction? I mean on pushing too hard my hand might go through the table. Is there any upper limit to this force?
A location, A, is said to be equidistant from two other locations, B and C, if the distance from A to B is the same as the distance from A to C. What is the equivalent word to use in the context of time? That is, suppose that the distance from A to B is different from the distance from A to C, but it takes the same amount of time to get from A to B as it does from A to C.
i'm having a problem with the definition of open, closed and clopen sets. I have understood the basic definitions, but then the teacher today in class said that the normed space is limitless. A colleague of mine said then that the normed space is clopen, but i can't really see why. To me, a normed space, since it has no limits, it is impossible to find a ball that has points not belonging to the normed space, so it can't be a closed set, right? Then, it must be an open set. Or am I mixing everything up? Thanks in advance!
I'm looking for a word that describes the act of doing something without a real logical reason but just because they can. A example of what I'm talking about would be like this: The boy hacked the Pentagon just because he could. He didn't steal anything and he didn't want the attention; he just wanted to proclaim his own self-dignity. What would you call someone like that or the act of doing something like that?
I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern treatments? I can't see why a simple parameter change t->it, would be or not be an outdated concept. It doesn't make things significantly prettier, but it doesn't hurt anything either. With that said I've never before heard the specific phrase imaginary time so maybe it is outdated.
I am looking for a word or phrase regarding something that is "impossible". I can't seem to put my finger on it, but I am trying to think of the word to describe something that is the top of the top, and thus impossible to achieve? The only two words I have come up with are elusive and formidable, neither of which really mean what I want them to mean. I want something more clever to put it plainly.
According to Biber's Longman Student Grammar of Spoken and Written English, insterts are one of the three families of words (apart from lexical and functional words). At some point, the author explains that inserts generally carry emotional and discoursal meanings, such as oh, ah, wow, used to express a speaker's emotional response to a situation, or yeah, no, okay used to signal a response to what has just been said. Could someone,please, explain in simple words, what does the 'discoursal meaning' mean?
I believe the answer to this question is yes. I was hoping someone would critique my logic. Let X be a separable and metrizable space. Then it has a countable dense subset A. Let B be a basis for X. For every a in A, choose a basis element U in B such that a is in U (if such exists). This forms a countable collection V. Suppose, for a contradiction, there is an element x that is in no element of V. Then x is in a basis element U. U must contain an element of A since A is dense. But this U is not in our collection V, a contradiction.
I'm running into an issue with my dissertation. I'm using a template created to format my dissertation according to the University's guidelines. When I format it using the twoside argument for the class, I get my list of figures and List of Tables pages each with an extra page afterward saying List of Figures - Continued, but there is nothing else on the page. This only happens with the twoside argument.
For example, if I take a slap shot on a hockey puck, from what I understand, the forces acting on the puck are friction, the normal force, and the puck's weight. And, since I'm not constantly either pushing the puck, or pulling the puck there are no other forces acting on the puck, because me shooting the puck was just a one time force. Am I thinking about this correctly?
Which is the appropriate word to be used in the sentence: The system we were testing was determined to be insecure/unsecure. The usage is in the context of security, specifically a lack thereof. I've always said insecure, because I didn't believe unsecure was a word (although unsecured is). Even as I type this, I'm getting a spell check complaint about it. However, I was laughed at once when I called a particular device "insecure."
With reference to Black holes in particular, how can you approximate the luminosity of an accretion disk? It is possible to quantify the temperature at a given point, but as the disk is not a black body, and this temperature is at a specific point, I am unsure how to equate this to luminosity - surely you could not do so using the Stefan-Boltzmann constant?
I happened upon the following sentence in a textbook: 'An increase in the number and size of islets is characteristic of infants born to diabetic mothers. I get that, as the sentence is presented, the singular noun 'increase' is governing the singular verb 'is', but aren't two different 'increases' being described, one in size and one in number? On another note, I would probably see nothing wrong with 'The love of money and power was his undoing'. I'd imagine a single 'love' that embraces both 'money' and 'power'. So, what's the rule in matters like this?
The person at the desk next to me is writing his Ph.D. thesis, and is trying to decide how to lay out some tables. He has too much data for one table, but is not a fan of rotated tables. So we were talking and had the idea that he could make two tables, and place them on adjacent pages so you could see them at once. However, you'd have to make sure they didn't wind up on the front/back of a single page. Is there a way to do that, or is this sheer madness?
The sentence, "he took my toy away" can be rewritten as, "he took away my toy." However, "he took me away" cannot be rewitten as "he took away me." The second sentence sounds awkward at the very least, and I do not think it is grammatically correct, but I do not know any exact rule stating so. Is the last sentence valid, and if not, why?
I recently found myself in a situation where I wanted to use a line that went something like this: "...we must examine the effects these ideas had on their respective creators..." and I just couldn't find the right word in place of "creators". Something feels off about "creators". We don't create thoughts we have thoughts or we think thoughts. "Owners" doesn't really work as no one can "own" a thought, and "thinkers" sounds too childish. What other words are there that describe "the person who came up with an idea"?
In the book The Road to Reality by Roger Penrose, projective geometry as developed during the Renaissance is framed as (eventually) playing a pivotal role in quantum mechanics. (In fact, Penrose seems enamored with the idea that there is some connection between painting and physics, particularly where twistor theory is concerned. The book's epilogue is the most blatant example of this, though other examples abound.) Not having studied quantum mechanics, I can't really imagine how projective spaces would be used to formalize what I know intuitively about the way QM works. Can someone provide a very simple example?
Recently, I have had a debate with a friend that "brings all the boys to the yard" is an idiom and he refuses to accept it. Since this has been used as a part of a rapper's lyrics, he says this is not an idiom. All in all, is it an idiom and how to find out if some phrases are idioms or not? Is there a specific dictionary or a thesaurus? The lyrics go like this: My milkshake brings all the boys to the yard, And they're like It's better than yours, Damn right, It's better than yours, I can teach you, But I have to charge See full lyrics at AZLyrics.com
Recently I wanted to write an essay about the women in Jane Austin's time. I wrote the women at that time were concerned much about how to be engaged to a decent husband. Not like women nowadays, they want to be treated equally as men and realize their value in society. So I want to say the women back in Jane Austin's time, their viewpoint toward life was too vulgar. I am not sure if I use this word correctly or it will convey a totally different meaning. Could you please help me?
So according to my understanding, the free energy of the system should be a continuous function of temperature. This is because if the free energy is not continuous at temperature T, then at this temperature the free energy can have two values (i.e. two states) and the two states will mix to eliminate the difference in their free energies. Is that a reasonable explanation for the continuity of free energy? The free energy is a continuous function of temperature does not mean it is differentiable everywhere, because at the point where the phase coexistence start to occur the free energy is not differentiable. Is that the case?
I've been reading some Feynman's books. There's a point that intrigues me. It's the fact how we understand a physics equation, not only mathematically, but digging deeply into its roots as a physicist. I'm just a first- year- physics student, but I would like to understand the basic equations I'm studying through its physical meaning, but to be honest I don't really know what Feynman meant. I hope you can help me. For example a equation such as: F=ma Thanks!
Dark energy is introduced as a constant inside Einstein's equations. Its primary purpose, from what I understand, is to make Einstein's equations compatible with the accelerating expansion of the universe. As a consequence, of the "predictions" of dark energy is the expansion of the universe according to Hubble's law. I know there are numerous experiments that verify this expansion (and its acceleration), and thus indirectly support the dark energy theory. My question is: Are there other factors that give credit to the existence of dark energy? Are there any experiments that support this theory, but not only through the verification of Hubble expansion?
Consider the category of finite dimensional vector spaces with morphisms being linear transformations. Is it still true that monics and epics are actually injective and surjective linear maps, respectively? The converse is surely true since the category is concrete. I know this monics and epics are precisely the injective and surjective maps in the category of Sets and in the category of groups, but it is not necessarily true in the category of topological spaces, so I'm just curious if it is true or not in the category of f.d. vector spaces, and if so why?
We were learning about Boyle's law (pressure is inversely proportional to volume of a gas) and in the experiment to prove the law, we were told that we cannot change the volume of a gas too rapidly without affecting its temperature. I have two questions about this: Why does temperature of a gas change when its volume changes very rapidly? This process (rapid changes in volume) is used in the liquefaction of gases. How is this done?
In my Astronomy class, I learned that temperature results from the speed of air molecules colliding into your skin. Thus, if the air molecules in the room have a high kinetic energy and thus collide with you at high speeds, your temperature will increase. So how does a breeze of wind, in which I imagine air molecules would be moving very fast (or if they're not moving fast, YOU are moving fast relative to them), result in feeling cooler?
When I say "I cannot attend to it" it sounds like I'm saying "I'm not able to attend to it", while what I want to express is that I'm capable of doing it, but I just don't need to. In Slavic languages it's resolved by changing the negation particle position: [negation] [can] [do something] vs. [can] [negation] [do something]. In the first case I negate "can", while in the second I negate the "do" verb. How to achieve the same in English and not be ambiguous?
I'm studying basic topological, metric and normed spaces and I am curious why one of the axioms of both a metric and a norm is the triangle inequality. It makes some sense to me having the triangle inequality satisfied sometimes, but I don't quite understand why you necessarily need it for a general metric/norm, since there are still topologies arising from it. Could someone maybe elaborate a little bit?
I guess the title says it all. However, I have skimmed through several books, and while they all tell you how to use generating functions to find an expression for the n'th term of a recurrence relation, none of them say why it works. I think I have a somewhat intuitive understanding of what is going on, but I think I need a more definitive explanation.
Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?