darklight03/StackMIAsub huggingface dataset:
Let us assume that the standard model is correct up to Planck mass. (Yes, I know, this is a big assumption.) If we continue the running of quark masses with energy (due to renormalization), what are the mass values we get for the six quarks at Planck energy? Is the sequence of mass values the same at Planck energy or do some quarks "catch" up with others? Is there some literature on this issue?
I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary derivatives with covariant derivatives. But I have read somewhere that this generalization is not unique and it is just the simplest one. Can anyone introduce some resources about this subject and how electromagnetism and Maxwell's equations are generalized to curved spacetime?
Possible Duplicate: How does gravity escape a black hole? If nothing in the universe can travel faster than light, how come light can't escape a black hole? I mean, Einstein's relativity says nothing can travel faster than light, but yet, light can't escape a black hole. Does this mean that light really isn't the fastest thing? That the pull of the black hole is really faster than light? That Einstein was wrong, even though it's been backed up by scientific evidence? I'm very confused. If anyone would be able to answer my question, I would appreciate it: Why can't light escape a black hole if nothing can travel faster than light?
I am having trouble understanding this concept, and have not found any good resources on google that explain it in a straightforward manner: An adjacency matching in an undirected graph G is a collection of disjoint edge pairs in G such that if two edges e and e' are paired, then e and e' share a common endpoint. I am asking clarification of this as it is concept presented in homework, to which I will have to develop an algorithm to solve for - in other words, I am asking about the question itself and not the answer.
I would like to know if there is a technical term to cover both interpolation and extrapolation. The reason why I am asking is that I am writing a computer program to do interpolation and extrapolation using a functional-object language called Scala. In there, I would like to define a class/template that abstracts the notion of interpolation and extrapolation. At the moment it is called interpolation but that's not really reflecting all of what it really does since the same methods can be used to do extrapolation. Is there a general term that mathematicians use that cover both these areas?
Recently I wrote the following words. Age gives you the wisdom of experience while youth gives you the intelligence of mental flexibility. There is a horizon time when you have both of these things to a significant extent. Afterwards I looked up "horizon" in online dictionaries and I couldn't find a definition that matched this usage. I see it as similar to calling the point after which light cannot escape a black hole the "event horizon." Is this usage correct?
I was wondering if we could find a set of basis vectors that span the cone of positive semidefinite matrices? I know this question is hard, but I would really appreciate if even someone can share a related paper about this topic in the literature of Linear Algebra. I could not find any paper about this issue. I should mention that any answer to this question should be highly related to the topic of semidefinite programming in the area of mathematical optimization. Thanks
Parallelogram ABCD is bisected by diagonal AD, and produces two triangles ABD and ACD. Prove that triangles ABD and ACD are congruent. My proof (or at least attempt): note I am not a high school student and have yet to learn geometry, I'm attempting to familiar myself with proofs beforehand though. And yes, I know my spelling is atrocious and I should use LaTeX. Thank you!
When calculating the amount of time elapsed for an inertial reference frame over the course of its travel at constant velocity between two points, are the effects of both length contraction and time dilation taken into account (i.e. the distance seems shorter to the traveler and the time for the traveler seems to pass more slowly to a stationary observer), or is only one or the other effect used to calculate the amount of time elapsed in the inertial reference frame in motion? I believe the answer is only one or the other, since the effects are really two sides of the same coin, one applying to an observer within the frame and the other applying to an observer outside the frame.
Ferromagnetism depends on the arrangement of orbitals and spin in the valence electrons of an atom (below its Curie point). But what is so special about the orbitals of iron, nickel and cobalt, to make them the main ferromagnetic materials, and everything else more or less pale in comparison? Please note that I am not asking "how do magnets work?". I know about domains, EM and the like, but on a strictly atomic/QM level, I would like to understand what sets these materials so greatly apart from dozens of others with seemingly similar orbital arrangements.
What's the right word to indicate a type of education based on memorizing facts or a superficial understanding of things, without real insight or critical mind development? In my native language (Italian) we have expressions like "nozionismo" or "educazione nozionistica" or "didattica nozionistica". But, after I looked in the dictionary, it seems to me that the word "notion" in this case is a "false friend". In fact, "nozione" seems different from "notion", which is rather like an opinion.
Noncommutative algebraic geometry is a developing field. Things have not yet got the final form as in commutative geometry. But one might wonder whether things are any better in the case of skew-fields, ie division rings, ie possibly noncommutative rings in which each nonzero element has a multiplicative inverse. Algebraic geometry is much simpler in the case of fields. So are things better in the case of skew fields? For instance, is there any particularly nice geometry over the quaternions, like there is one over the complex numbers?
The definition of an inner product in Linear Algebra Done Right by Sheldon Axler assumes that the vector space is over either the real or complex field. PlanetMath makes the same assumption. Is there a definition of an inner product over, for example, finite fields? I sometimes find finite fields easier to reason about, so it would be nice to have a definition of an inner product for vector spaces over them.
I am a sophomore in high school. When I approach a math problem or concept, I normally try to determine a formula or systematic method of solving all similar problems. However, since I entered precalculus, I have found that this approach does not work. I really love math and find it interesting and exciting, but I find that I am unable to solve the kinds of conceptual problems that I have been doing more recently. For example, when I try to do a counting problem, it is often unclear how to approach it. How can I improve my problem-solving and critical thinking skills? Also, how can I approach problems logically to solve ones that are not clear at first?
Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had to reverse direction, thus undergoes acceleration, and therefore cannot claim to be a stationary observer. However, what if the traveling twin simply Skypes the twin that is on Earth. The twin on earth will still appear older, which would make no sense since in that case the rocket can be seen as the stationary frame of reference while the Earth "travels" at a speed close to the speed of light. No acceleration is undergone, yet the paradox remains. Is Griffiths just completely glossing over important nuance again?
Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system of two point particles in equilibrium with each other upon which a constraint acts so that the reaction forces are directed in a direction that is not collinear. Is such a situation possible?
My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measuring instruments? If we can somehow know our initial conditions exactly, wouldn't we still be able to calculate what the system will be like at some time t in the future?
Is there a word (other than asshole) to describe someone who always says things in a way that makes other people look incompetent in order to make themselves look better? A different word to describe their language would also suffice. Edit: for clarification, here are a few sentences they might use: "I wouldn't have done it that way" "Do you even know what you're talking about?" (Implying that they do and you don't.) "Well, it wouldn't have happened if you knew about such and such." Basically a kind of blame-passing system to cover up the fact that they are the actual problem.
I'm having a bit of trouble understanding the semiconductor band gap diagram on Wikipedia: (from Band gap article). Why is the size of the band gap increasing with the Density of States (DOS) in the semiconductor material? I would expect the opposite given the intuiton that more occupiable energy states would mean a higher probability of an electron moving from a valence band to a conduction band? Should the x-axis here maybe be something like "# electrons in the conducting band" to show the increasing amount of energy needed to promote electrons to the conduction band as a function of the electrons already promoted to the conduction band? And why the ovoid geometry, which I've seen elsewhere?
I am interested in finding out about the current status of the planned book: The Triangle Book by John H. Conway and Steve Sigur. I understand that Steve Sigur died some time back. I got no reply from Prof. Conway; is there someone who knows the fate of this project. Is it abandoned or is it still under preparation? Here is some information about the planned book.
It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero. What exactly is the reason behind this? Except for, of course, the mathematics behind it. Is there any logic why the field intensity should be zero within a sphere? For example, it is logical to say that the field intensity would be zero at the center, as all the intensities cancel out. However, this cannot be the case for any point within the sphere.
Let's say we have a multi-slit experiment with N slits.Since the central fringe has the most intensity, is there an equation to calculate the intensity of central fringe in terms of the intensity of the original light wave? I searched Fraunhofer Diffraction and Fraunhofer Diffraction Equation but neither of them helped me since they calculate the intensity of a fringe in terms of the intensity of the central fringe.Thanks.
I understand that one of the great things about LaTeX is that, as long as you're using the same source file, the output is guaranteed to be identical regardless of the platform that you're generating it on. I'm assuming this is the case because LaTeX is controlling everything from the typesetting to the fonts themselves. If I use XeTeX, do I get the same guarantee, even assuming the I use the same TrueType fonts on two different platforms?
Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an averaged electronic cloud. My question is: As the word 'adiabatic' suggests no heat/energy transfer, does this mean that the energies associated with nuclear and electronic motions are non-transferable? If my understanding is right, the limiting criterion of the approximation is when transfer can no longer be neglected. My other question is how to judge when the transfer is significant?
I'm confused about the how the notion of distance is used in Conformal Field Theory. Let's take for example the Operator Product Expansion (OPE). In a conformal field theory, due to the scale invariance only angles - and not distances - matter. But in the very definition of the OPEs one speaks about two operators evaluated at nearby points. How can one make sense of this apparent contradiction?
I am developing a database application where a user should be able to store multiple ways of contacting someone in a database table. This database table can for e.g. contain: phone numbers mobile numbers email addresses twitter IDs facebook IDs whatsapp numbers Now I am looking for a table name. The obvious choice would be contacts. However, the term 'contacts' is used when referring to people and not ways of contacting this person. I am looking for a single word to describe all ways of contacting a person.
Im wrong about something here, but Im not sure what. As far as I know the product of two normal distributed variables is not normal distributed. However, if the joint distribution of Y and X is bivariate normal then Y given X is normal distributed as well as the marginal distribution of X. Furthermore, the joint distribution of Y and X is the product of the condtional distribution of Y given X and the marginal distribution of X which are both normal. If we define a new variable Z to be distributed as the condional distribution of Y given X, then the product of Z and X (which are both normal distributed) is bivariate normal. Am I on the right track or did I miss understand something somewhere?
Suppose you have a tetrahedron. It doesn't have to be regular. Now suppose you have another tetrahedron contained inside the first tetrahedron. Again do not assume it is regular and do not assume that both tetrahedrons are similar. Could it happen that the perimeter of the tetrahedron in the inside is larger then the tetrahedron on the outside? Whether it is or not prove it. Do a proof by contradiction. This one is tricky. I have been thinking about this problem for a long time now and do not see any way to come up with a reasonable solution. The help would be greatly appreciated!
Recently some of my colleagues has started using the phrase "touch space" a lot, for example in sentences like "I just called you to touch space", or "I will touch space with him tomorrow". I can deduce that it means something like "talk to" or "meet with", but what is the original meaning, what is the advantage of using "touch space", and where does it originate from ?
I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was Galois theory. I am interested in doing 'my own' research, if you catch my drift. That is, I would like to apply the Galois theory I will be studying to something, and do some research. My professor mentioned some possible applications within coding-theory and cryptography. Do you have any specifics in mind? I would be happy to hear your insights.
I want to tell someone the following: "I bring an e-reader with me on the bus every day so that I have something to do during my commute to work." Does the phrase "commute to work" clearly refer to the trip there and the trip back from work? Or is it more proper to say "commute to and from work" in order to ensure that it is clear that I mean both directions?
I want to get the density of a fluid going through a pipe. I can measure the flow and pressure with a flowmeter and the temperature using a thermometer. With this information, I want to calculate (or approximate) the instantaneous density of the fluid passing through my instruments. How would I go about doing this? I'm looking at a liquid (not a gas), mostly incompressible. Think water with varying amounts of solute (salt, sugar) in it.
Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit towards a detector. While in transit to the detector, what if the other entangled particle, lets call it "Particle B" was observed / had it's wave function collapsed? Would "Particle A" still generate a wave-like interference pattern or would the wave function for both be collapsed? In theory you cannot send classical data by entanglement, so this experiment must somehow fail, but I can't quite figure out why. If this experiment were to succeed, then you could read and send data about wave function states over entangled particles.
I am trying to remember the phrase that describes a particular kind of folly - trying to "beat the house", or willingness to play a rigged game. As I recall it has the form of "a fool's errand" - that is, the game is referred to as belonging to the person who is silly enough to play it. I'd appreciate knowing the origin of the phrase, too.
I believe that pigs can fly I think here "that" is being used as a conjunction to combine the independent clause (pigs can fly) with the dependent clause (I believe) That the boys painted the pig green annoyed the pig. This one I'm not so sure about. "The boys painted the pig green" is an independent clause, and "annoyed the pig" is a dependent clause; but in this case "that" doesn't join them. Any insight?
The critics against Copernicus and Galileo argued that, if the earth moved, then, a heavy body that was dropped from a very high tower should fall to the west of the foot of the tower. Galileo argued, however, that this body would fall slightly to the east. My first guess is that the body would fall directly under the point in which it was dropped. Who is right?
I'm attempting to build a regular expression that will accept only strings of the form: Begins with: /# Ends with: #/ Contains the following in between /# and #/: Any combination of {a, b, /, #} but not the combination #/ Bascially, a regular expression that determines whether a string is appropriately comment delimited. I've tried many expressions, but can't find anything that quite works. I'm not sure how to allow all other combinations of a,b,/,# but disallow #/. Any help putting me on the right track would be much appreciated.
I have been trying to approach this by finding the gravitational torque of the person on the merry-go-round, however I can't find a way to relate that to angular velocity in the given circumstances. If this problem requires angular momentum to solve, then I won't need to know the solution because it won't be on my final, however I still want to make sure that I'm not missing something.
I read this article where the title suggests the iPhone was dropped from space, but it looks more like it was dropped from an airplane I would think that if astronauts dropped an iPhone from space that it wouldn't land on Earth, but rather, float on for infinity (our Universe keeps expanding), or would the iPhone be captured in some planet's gravitational force and drop there. Help me understand this physics principle.
Please, take a look at the following: "Friends" and "foes" are, according to Carl Schmitt, defined in function of their capacity to respectively enhance or diminish the power of one's own state. Does "in function of" equal something along the line of "in relation to"? I'm aware that the "in function of" thing was once covered here, but I'm afraid there was no answer there I'm now looking for. EDIT: THANKS EVERYONE FOR THE ANSWERS.
I have been recently reading quite a little about Kaluza Klein theories. I am still far from mastering this but I am curious if any experiment that may disprove or give hints of the existence of extra spatial dimensions is to be expected to be performed relatively soon. This page of CERN, for example, says that the LHC might give some clues, but it doesn't really dive into much detail. So, in some detail, which experiments might say something about this, and when might they be expected?
I just finished reading Richard Feynman's lectures on Quantum Electrodynamics (QED: The Strange Theory of Light and Matter) and it fascinated me. However, there's an unanswered question I have from reading it. If, as Feynman argues, "light doesn't really travel only in a straight line; it 'smells' the neighboring paths around it and uses a small core of nearby space" (though it is overwhelmingly likely to appear to be traveling in a straight line over long distances), how does this not defy the law of conservation of momentum? My understanding is that this law applies to light as well, with a momentum defined by p = E/c. If so, light curving would clearly defy it, would it not?
I was wondering where the term 'button-down' comes from. I tried to do some research but I was not very successful... How was the word button-down formed? Is it a compound ? Does it originate from the noun "button", which then became the verb "to button" meaning to fasten? Then, how did it become an adjective ? If the adjective "button-down" originates from the verb "to button (stg) down", shouldn't the adjective be "buttoned-down"? If so, how did it change to become only "button-down" ? I looked up etymonline and the online merriam-webster but could not find any answer. Can anybody answer this ?
If I grant someone a Boon, I am granting them a temporary positive effect. If I were to grant someone a temporary negative effect, what would an adequate word to describe that be? I was initially drawn to Bane, as it's another four-letter B-word, with a negative connotation, but I'm not sure if the two terms are inherently equitable. Is this an appropriate usage of Bane? Is there a better word entirely?
A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic book that explains basic facts, rules etc., about integrals. I think this means Riemann integral and that it should not be too complicated. I do not know such a book, do you know a book that deal with basic things concerning integrals for a non-mathematician? Thanks for your tips!
What word aptly describes a job or position that requires more than is reasonable from the person occupying it? An example of usage might be: "Today, John finally resigned his ___________ job." To clarify, John is fully qualified to perform his duties and genuinely enjoys his work. Unfortunately, John's job at Evil Corp is unreasonably demanding. John's superiors have been frequently forced to increase his workload while lowering his pay. Long term employees are leaving the company in alarming numbers. John has a very loyal personality that has urged him to stick it through, but alas, John has reached his limit and must resign.
Possible Duplicate: Are collective nouns always plural, or are certain ones singular? Which is correct: The rest of the staff is or are? The rest of my family is or are? I've done a bit of research and I understand that "family" should be preceded by singular or plural verb depending on how you want it to be treated. For example, His family is one of the oldest in the county. and His family are all doctors. These are apparently both correct. But in the following instance, could a grammar expert tell me which should be be? When his family are abducted or When his family is abducted ? Thanks.