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what we're seeing in the top two pictures. as the scale moves farther out, these particular spirals become more tightly wound and harder to see ( go from the 1st picture to the 5th, then the 3rd, then the 4th ), and the next convergent takes over. in this case, the convergent $ \ frac { 710 } { 113 } $ is an extremely ... | https://api.stackexchange.com |
i think the key will be whether or not libraries start being developed for julia. it's all well and good to see toy examples ( even if they are complicated toys ) showing that julia blows r out of the water at tasks r is bad at. but poorly done loops and hand coded algorithms are not why many of the people i know who u... | https://api.stackexchange.com |
good question. if you look at the spectral energy distribution in the accepted answer here, we see that photons with wavelengths less than ~ 300 nm are absorbed by species such as ozone. much beyond 750 infrared radiation is largely absorbed by species such as water and carbon dioxide. therefore the vast majority of so... | https://api.stackexchange.com |
no, it is not meaningful. 25 % is correct iff 50 % is correct, and 50 % is correct iff 25 % is correct, so it can be neither of those two ( because if both are correct, the only correct answer could be 75 % which is not even an option ). but it cannot be 0 % either, because then the correct answer would be 25 %. so non... | https://api.stackexchange.com |
, it is difficult to argue that there is no possible principle that will cordon off the great pumpkin example as meaningless while still allowing the 60 % variant to be meaningful. in the end, though, these things are more matters of taste and philosophy than they are mathematics. in mathematics we generally prefer to ... | https://api.stackexchange.com |
i've written my own integrator, quadcc, which copes substantially better than the matlab integrators with singularities, and provides a more reliable error estimate. to use it for your problem, i did the following : > > lambda = 0. 00313 ; kappa = 0. 00825 ; nu = 0. 33 ; > > x = 10 ; > > e = @ ( r ) r. ^ 4. * ( lambda ... | https://api.stackexchange.com |
definitely the right method for this type of problem. | https://api.stackexchange.com |
2017 - 10 - 27 update [ note : my earlier notation - focused answer, unchanged, is below this update. ] yes. while having an octet of valence electrons creates an exceptionally deep energy minimum for most atoms, it is only a minimum, not a fundamental requirement. if there are sufficiently strong compensating energy f... | https://api.stackexchange.com |
true bending of the rules for an atom that in nearly all other circumstances prefers to have an octet of valence electrons. that is why my overall answer to this question is simply " yes ". question : why are octets special? the flip side of whether stable non - octet valence shells exist is this : why do octet shells ... | https://api.stackexchange.com |
##s. ) original 2014 - ish answer ( unchanged ) this answer is intended to supplement manishearth's earlier answer, rather than compete with it. my objective is to show how octet rules can be helpful even for molecules that contain more than the usual complement of eight electrons in their valence shell. i call it dona... | https://api.stackexchange.com |
than one anion for elements such as sulfur ( sulfates and sulfites ) and nitrogen ( nitrates and nitrites ). since the oxygen atoms are not needed for the central atom to establish a full octet, some of the pairs in the central octet can remain unattached. this results in less oxidized anions such as sulfites and nitri... | https://api.stackexchange.com |
a whole, the atom at the bottom of a u - bond is saying " i don't like it, but if you are that desperate for a pair of electrons, and if you promise to stay very close by, i'll let you latch onto a pair of electrons from my already - completed octet. " carbon monoxide with its baffling " why does carbon suddenly have a... | https://api.stackexchange.com |
both thawing and evaporation involve heat exchange between the stone tile, the water sitting atop the stone tile, any water that's been absorbed by the stone tile, and the air around. the basic reason that the center and the edges of the tile evaporate differently is that the gaps between the tiles change the way that ... | https://api.stackexchange.com |
paper, especially when freshly cut, might appear to have smooth edges, but in reality, its edges are serrated ( i. e. having a jagged edge ), making it more like a saw than a smooth blade. this enables the paper to tear through the skin fairly easily. the jagged edges greatly reduce contact area, and causes the pressur... | https://api.stackexchange.com |
course depends on its stiffness. this is why office paper is much more likely to cut you than toilet paper. the paper's density ( mass per unit area ), also known as grammage, has a direct influence on its stiffness. | https://api.stackexchange.com |
there are two points relevant for the discussion : air itself carries a very small amount of thermal energy and it is a very poor thermal conductor. for the first point, i think it is interesting to consider the product $ \ text { density } \ times \ text { specific heat } $, that is the amount of energy per unit volum... | https://api.stackexchange.com |
ok, here's my favorite. i thought of this after reading a proof from the book " proofs from the book " by aigner & ziegler, but later i found more or less the same proof as mine in a paper published a few years earlier by josef hofbauer. on robin's list, the proof most similar to this is number 9 ( edit :... which is a... | https://api.stackexchange.com |
2 ( \ frac { \ pi } { 2 } - x ) } = \ frac { \ cos ^ 2 x + \ sin ^ 2 x } { \ cos ^ 2 x \ cdot \ sin ^ 2 x } = \ frac { 4 } { \ sin ^ 2 2x }. $ $ therefore, if we pair up the terms in the sum $ s _ n $ except the midpoint $ \ pi / 4 $ ( take the point $ x _ k $ in the left half of the interval $ ( 0, \ pi / 2 ) $ togeth... | https://api.stackexchange.com |
sequences both tending to $ \ pi ^ 2 / 6 $. voila! | https://api.stackexchange.com |
i reproduce a blog post i wrote some time ago : we tend to not use higher derivative theories. it turns out that there is a very good reason for this, but that reason is rarely discussed in textbooks. we will take, for concreteness, $ l ( q, \ dot q, \ ddot q ) $, a lagrangian which depends on the 2nd derivative in an ... | https://api.stackexchange.com |
= \ frac { \ partial l } { \ partial \ ddot q }. \ end { align } note that the non - degeneracy allows $ \ ddot q $ to be expressed in terms of $ q _ 1 $, $ q _ 2 $ and $ p _ 2 $ through the second equation, and the first one is only necessary to define $ q ^ { ( 3 ) } $. we can then proceed in the usual fashion, and f... | https://api.stackexchange.com |
this is easy to check, you can download both specs in. tex format and do diff. changes to the v4. 2 compared to v4. 1 : information field format : adding source and version as recommended fields. info field can have one value for each possible allele ( code r ). for all of the # # info, # # format, # # filter, and # # ... | https://api.stackexchange.com |
i don't know which algorithm google uses. but, since you wanted a best guess, let me give some ideas on how a similar system could be constructed. the whole field dealing with search - image - base - by - image is called content based image retrieval ( cbir ). the idea is somehow to construct an image representation ( ... | https://api.stackexchange.com |
, but still, here they are : binary partition trees and mention of min / max trees : p. salembier, m. h. f wilkinson : connected operators binary partition trees : v. vilaplana, f. marques, p. selembier : binary partition trees for object detection tree of shapes ( component tree ) : p. monasse, f. guichard : fast comp... | https://api.stackexchange.com |
no, d - is not ground. data is sent over a differential line, which means that d - is a mirror image of d +, so both data lines carry the signal. the receiver subtracts d - from d +. if some noise signal would be picked up by both wires, the subtraction will cancel it. so differential signalling helps suppressing noise... | https://api.stackexchange.com |
if you ran an electrical current through a material today, it would travel at the same speed as if you did it with the same material 50 years ago. with that in mind, how is it computers have become faster? what main area of processor design is it that has given these incredible speed increases? you get erroneous conclu... | https://api.stackexchange.com |
here's what's really going on with the dual problem. ( this is my attempt to answer my own question, over a year after originally asking it. ) ( a very nice presentation of this material is given in ekeland and temam. these ideas are also in rockafellar. ) let $ v $ be a finite dimensional normed vector space over $ \ ... | https://api.stackexchange.com |
^ *, x \ rangle - f ( x ). \ end { equation } if this supremum is finite, then $ \ langle m ^ *, x \ rangle - f ^ * ( m ^ * ) $ is the best affine minorant of $ f $ with slope $ m ^ * $. if $ f ^ * ( m ^ * ) = \ infty $, then there is no affine minorant of $ f $ with slope $ m ^ * $. the function $ f ^ * $ is called th... | https://api.stackexchange.com |
problem is simply to evaluate $ h ( 0 ) $. from our knowledge of conjugate functions, we know that \ begin { equation * } h ( 0 ) \ geq h ^ { * * } ( 0 ) \ end { equation * } and that typically we have equality. for example, if $ h $ is subdifferentiable at $ 0 $ ( which is typical for a convex function ) then $ h ( 0 ... | https://api.stackexchange.com |
} & \ quad g ( x ) \ leq 0, \ end { align * } can be perturbed as follows : \ begin { align * } \ operatorname * { minimize } _ x & \ quad f ( x ) \ \ \ text { subject to } & \ quad g ( x ) + y \ leq 0. \ end { align * } this perturbed problem has the form given above with \ begin { equation * } \ phi ( x, y ) = \ begi... | https://api.stackexchange.com |
end { cases } \ end { equation * } this is the expected result. | https://api.stackexchange.com |
summary : yes " polarised " aluminum " wet electrolytic " capacitors can legitimately be connected " back - to - back " ( ie in series with opposing polarities ) to form a non - polar capacitor. c1 + c2 are always equal in capacitance and voltage rating ceffective = = c1 / 2 = c2 / 2 veffective = vrating of c1 & c2. se... | https://api.stackexchange.com |
works ok if ratings are not exceeded.'kind of like " you can't make a bjt from two diodes "'reason for comparison is noted but is not a valid one. each half capacitor is still subject to same rules and demands as when standing alone. " it is a process that a tinkerer cannot do " tinkerer can - entirely legitimate. so i... | https://api.stackexchange.com |
while it may appear that the capacitance is between the two foils, actually the capacitance is between the anode foil and the electrolyte. the positive plate is the anode foil ; the dielectric is the insulating aluminum oxide on the anode foil ; the true negative plate is the conductive, liquid electrolyte, and the cat... | https://api.stackexchange.com |
most of the other answers focus on the example of unbalanced classes. yes, this is important. however, i argue that accuracy is problematic even with balanced classes. frank harrell has written about this on his blog : classification vs. prediction and damage caused by classification accuracy and other discontinuous im... | https://api.stackexchange.com |
use proper scoring - rules. these are loss functions that map predicted probabilities and corresponding observed outcomes to loss values, which are minimized in expectation by the true probabilities $ ( p, 1 - p ) $. the idea is that we take the average over the scoring rule evaluated on multiple ( best : many ) observ... | https://api.stackexchange.com |
these are not very strict terms and they are highly related. however : loss function is usually a function defined on a data point, prediction and label, and measures the penalty. for example : square loss : $ l ( f ( x _ i | \ theta ), y _ i ) = \ left ( f ( x _ i | \ theta ) - y _ i \ right ) ^ 2 $, used in linear re... | https://api.stackexchange.com |
" and " cost " functions being something that want wants to minimise, and objective function being something one wants to optimise ( which can be both maximisation or minimisation ). | https://api.stackexchange.com |
the fact that the result is complex is to be expected. i want to point out a couple things : you are applying a brick - wall frequency - domain filter to the data, attempting to zero out all fft outputs that correspond to a frequency greater than 0. 005 hz, then inverse - transforming to get a time - domain signal agai... | https://api.stackexchange.com |
in the time domain ( below image shamelessly borrowed from wikipedia ) : the $ sinc $ function has very broad support in the time domain ; it decays very slowly as you move in time away from its main lobe. for many applications, this is not a desirable property ; when you convolve a signal with a $ sinc $, the effects ... | https://api.stackexchange.com |
when the plug starts to slip out of the jack, very often it's the ground contact ( sleeve ) that breaks its connection first, leaving the two " hot " leads ( left and right, tip and ring ) still connected. with the ground open like this, both earpieces still get a signal, but now it's the " difference " signal between ... | https://api.stackexchange.com |
your wire is not quite round ( almost no wire is ), and consequently it has a different vibration frequency along its principal axes1. you are exciting a mixture of the two modes of oscillation by displacing the wire along an axis that is not aligned with either of the principal axes. the subsequent motion, when analyz... | https://api.stackexchange.com |
) * np. exp ( - k * t ) a2 = a2 * np. cos ( 2 * pi * f2 * t ) * np. exp ( - k * t ) # rotate the axes of detection y1 = cos ( theta ) * a1 - sin ( theta ) * a2 y2 = sin ( theta ) * a1 + cos ( theta ) * a2 plt. figure ( ) plt. subplot ( 2, 1, 1 ) plt. plot ( t, - 20 * y2 ) # needed additional scale factor plt. xlabel ('... | https://api.stackexchange.com |
added mid 2022 : a lightly edited version of a comment by @ littlewhole in 2022 the world is moving towards the far more robust and convenient usb - c connector. while there are still issues with usb - c ( including even mechanical incompatibilities ), things are slowly being addressed ( i. e. usb4 standard on the prot... | https://api.stackexchange.com |
the micro - usb connector was designed with these past failings in mind and has a rated lifetime of about 10, 000 insertion cycles. this despite its apparent frailty and what may appear to be a less robust design. [ this still seems woefully low to me. time will tell ]. latching unlike mini usb, micro usb has a passive... | https://api.stackexchange.com |
of - use when synchronizing and charging portable devices. all change : once all can change, all tend to. a significant driver to a common usb connector is the new usb charging standard which is being adopted by all cellphone makers. ( or all who wish to survive ). the standard relates primarily to the electrical stand... | https://api.stackexchange.com |
the µusb device. maybe useful : usb connector guide — guide to usb cables usb connections compared what is micro usb vs mini usb | https://api.stackexchange.com |
good observation! gene coding for the lactase gene lct mammals have a gene ( called lct c / t - 13910 ) coding for the lactase enzyme, a protein able to digest lactose. lactose is a disaccharide sugar found in milk. expression of lct in mammals, the gene lct is normally expressed ( see gene expression ) only early in d... | https://api.stackexchange.com |
would think so, yes! drink vs digest thoroughly as @ anongoodnurse rightly said in his / her answer " drink " and " digest thoroughly " are two different things pets according to many dog health websites ( such this one for example ) claim that there is also variance among dogs where some dogs are lactose tolerant and ... | https://api.stackexchange.com |
from the manual of velvet : it must be an odd number, to avoid palindromes. if you put in an even number, velvet will just decrement it and proceed. the palindromes in biology are defined as reverse complementary sequences. the problem of palindromes is explained in this review : palindromes induce paths that fold back... | https://api.stackexchange.com |
an epic question. unfortunately, the short answer is : no, there are no widely used solutions. for several thousand samples, bcf2, the binary representation of vcf, should work well. i don't see the need of new tools at this scale. for a larger sample size, exac people are using spark - based hail. it keeps all per - s... | https://api.stackexchange.com |
crystallin proteins are found in the eye lens ( where their main job is probably to define the refractive index of the medium ) ; they are commonly considered to be non - regenerated. so, your crystallins are as old as you are! because of this absence of regeneration, the accumulate damage over time, including proteoly... | https://api.stackexchange.com |
i understand that covalent bonding is an equilibrium state between attractive and repulsive forces, but which one of the fundamental forces actually causes atoms to attract each other? the role of pauli exclusion in bonding it is an unfortunate accident of history that because chemistry has a very convenient and predic... | https://api.stackexchange.com |
##s and electrons get added in. while feynman does not get into how such atoms would interact, there's a problem there too. because the electron charges would be so diffuse in comparison to the nuclei, the atoms would pose no real barrier to each other until the nuclei themselves begin to repel each other. the result w... | https://api.stackexchange.com |
apart from other particles of the same type. for an electron, this address includes : where the electron is located in space, how fast and in what direction it is moving ( momentum ), and one last item called spin, which can only have on of two values that are usually called " up " or " down. " you can force such mater... | https://api.stackexchange.com |
when all the jockeying around wraps up, the lowest energy situations keep the electrons stationed in various ways around the nucleus, not quite touching each other. we call those special solutions to the crowding problem orbitals, and they are very convenient for understanding and estimating how atoms and molecules wil... | https://api.stackexchange.com |
but there is one exception to that energetic infighting : spin! for spin and spin alone, it becomes possible to get significantly closer to that final point - like collapse that all the charges want to do. spin thus becomes a major " hole " - - the only such major hole - - in the ferocious armor of repulsion produced b... | https://api.stackexchange.com |
intel support for ieee float16 storage format intel supports ieee half as a storage type in processors since ivy bridge ( 2013 ). storage type means you can get a memory / cache capacity / bandwidth advantage but the compute is done with single precision after converting to and from the ieee half precision format. inte... | https://api.stackexchange.com |
logical and : use the linear constraints $ y _ 1 \ ge x _ 1 + x _ 2 - 1 $, $ y _ 1 \ le x _ 1 $, $ y _ 1 \ le x _ 2 $, $ 0 \ le y _ 1 \ le 1 $, where $ y _ 1 $ is constrained to be an integer. this enforces the desired relationship. see also logical or : use the linear constraints $ y _ 2 \ le x _ 1 + x _ 2 $, $ y _ 2 ... | https://api.stackexchange.com |
and, or, and not. and, as a bonus, one more technique that often helps when formulating problems that contain a mixture of zero - one ( boolean ) variables and integer variables : cast to boolean ( version 1 ) : suppose you have an integer variable $ x $, and you want to define $ y $ so that $ y = 1 $ if $ x \ ne 0 $ a... | https://api.stackexchange.com |
works nothing else needs to define an objective function ( if, apart from the casts to boolean, you were planning to just check the feasibility of the resulting ilp, not try to minimize / maximize some function of the variables ). for some excellent practice problems and worked examples, i recommend formulating integer... | https://api.stackexchange.com |
one approach that i have used in the past is to maintain a phase accumulator which is used as an index into a waveform lookup table. a phase delta value is added to the accumulator at each sample interval : phase _ index + = phase _ delta to change frequency you change the phase delta that is added to the phase accumul... | https://api.stackexchange.com |
haha! the student probably has a more reasonable interpretation of the question. of course, cutting one thing into two pieces requires only one cut! cutting something into three pieces requires two cuts! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 cuts / 1 piece / 0 minutes - - - - - - - - - - - - -... | https://api.stackexchange.com |
three sentence version : each layer can apply any function you want to the previous layer ( usually a linear transformation followed by a squashing nonlinearity ). the hidden layers'job is to transform the inputs into something that the output layer can use. the output layer transforms the hidden layer activations into... | https://api.stackexchange.com |
do individually. an example with logical functions : for example, if we only allow $ f $ and $ g $ to be simple logical operators like " and ", " or ", and " nand ", then you can't compute other functions like " xor " with just one of them. on the other hand, we could compute " xor " if we were willing to layer these f... | https://api.stackexchange.com |
and some are not? " the disconnected nodes in the network are called " bias " nodes. there's a really nice explanation here. the short answer is that they're like intercept terms in regression. " where do the " eye detector " pictures in the image example come from? " i haven't double - checked the specific images i li... | https://api.stackexchange.com |
you are correct that the fwt is better thought of as a " cousin " of the stft, rather than the ft. in fact, the fwt is just a discrete sampling of the cwt ( continuous wavelet transform ), as the fft / dft is a discrete sampling of the fourier transform. this may seem like a subtle point, but it is relevant when choosi... | https://api.stackexchange.com |
of a signal ( you can reconstruct it using only the coefficients at this scale ). i'm not so sure about the rationale of sampling the scale. i've seen this suggested as logarithmic, with ( i think ) closer spacing between shorter scales. i think this is because the wavelets at longer scales have a broader fourier trans... | https://api.stackexchange.com |
look at candiedorange's answer this answer was accepted, but candiedorange has the right answer. see this document page 21 : the second way in which reflection can interfer e with controller ’ s vision is light sources within the cab ( or direct sunlight that enters the cab ), which can cause disturbing reflections dur... | https://api.stackexchange.com |
according to the fgsea preprint : we ran reference gsea with default parameters. the permutation number was set to 1000, which means that for each input gene set 1000 independent samples were generated. the run took 100 seconds and resulted in 79 gene sets with gsea - adjusted fdr q - value of less than 10−2. all signi... | https://api.stackexchange.com |
i know that you are referring to the commonly ribosome - translated l - proteins, but i can't help but add that there are some peptides, called nonribosomal peptides, which are not dependent on the mrna and can incorporate d - amino acids. they have very important pharmaceutical properties. i recommend this ( 1 ) revie... | https://api.stackexchange.com |
that's right, the parity of the universe is not conserved in nuclear decay. these chiral electrons once again preferrentially degrade d amino acids vs. l amino acids. thus due to the chirality of sunlight and the chirality of nuclear radiation, l amino acids are the more stable enantiomers and therefore are favored for... | https://api.stackexchange.com |
to understand the difference between kinetic and thermodynamic stability, you first have to understand potential energy surfaces, and how they are related to the state of a system. a potential energy surface is a representation of the potential energy of a system as a function of one or more of the other dimensions of ... | https://api.stackexchange.com |
has. it needs at least enough kinetic energy to overcome all of the local maxima along the path between its current local minimum and the global minimum. if it doesn't have enough kinetic energy to move out of its current position, we say that it is kinetically stable or kinetically trapped. if it has reached the globa... | https://api.stackexchange.com |
##ynamically unstable. however, you would have to wait a very long time for methane to react without some outside help. the reason is that the transition states along the lowest - energy reaction path have a much higher thermodynamic potential energy than the average kinetic energy of the reactants. the reactants are k... | https://api.stackexchange.com |
i doubt that we will ever know the exact integral that vexed feynman. here is something similar to what he describes. suppose $ f ( z ) $ is an analytic function on the unit disk. then, by cauchy's integral formula, $ $ \ oint _ \ gamma \ frac { f ( z ) } { z } dz = 2 \ pi i f ( 0 ), $ $ where $ \ gamma $ traces out th... | https://api.stackexchange.com |
) \ cos \ left ( \ frac { \ sin \ phi } { 10 + 6 \ cos \ phi } \ right ) \ right ) \ \ & \ times \ cos \ left ( \ exp \ left ( \ frac { 7 + 5 \ cos \ phi } { 10 + 6 \ cos \ phi } \ right ) \ sin \ left ( \ frac { \ sin \ phi } { 10 + 6 \ cos \ phi } \ right ) \ right ) = 2 \ pi e ^ { e ^ { 2 / 3 } }. \ end { align * } | https://api.stackexchange.com |
cross - correlation and convolution are closely related. in short, to do convolution with ffts, you zero - pad the input signals a and b ( add zeros to the end of each. the zero padding should fill the vectors until they reach a size of at least n = size ( a ) + size ( b ) - 1 ) take the fft of both signals multiply th... | https://api.stackexchange.com |
of the peak is the offset, which could be negative or positive. i've only seen this used to find the offset between two waves. you can get a more precise estimate of the offset ( better than the resolution of your samples ) by using parabolic / quadratic interpolation on the peak. to get a similarity value between - 1 ... | https://api.stackexchange.com |
you are getting reflections from the front ( glass surface ) and back ( mirrored ) surface, including ( multiple ) internal reflections : it should be obvious from this diagram that the spots will be further apart as you move to a more glancing angle of incidence. depending on the polarization of the laser pointer, the... | https://api.stackexchange.com |
the planet neptune's discovery was an example of something similar to this. it was known that newtons's equations gave the wrong description of the motion of uranus and mercury. urbain le verrier sat down and tried to see what would happen if we assumed that the equations were right and the universe was wrong. he set u... | https://api.stackexchange.com |
finite element : volumetric integrals, internal polynomial order classical finite element methods assume continuous or weakly continuous approximation spaces and ask for volumetric integrals of the weak form to be satisfied. the order of accuracy is increased by raising the approximation order within elements. the meth... | https://api.stackexchange.com |
finite volume methods, see this answer for more. reconstruction dg methods ( aka. $ p _ n p _ m $ or " recovery dg " ) use both fv - like conservative reconstruction and internal order enrichment, and are thus a superset of fv and dg methods. | https://api.stackexchange.com |
another example : euler's sum of powers conjecture, a generalization of fermat's last theorem. it states : if the equation $ \ sum _ { i = 1 } ^ kx _ i ^ n = z ^ n $ has a solution in positive integers, then $ n \ leq k $ ( unless $ k = 1 $ ). fermat's last theorem is the $ k = 2 $ case of this conjecture. a counterexa... | https://api.stackexchange.com |
the previous answers all restate the problem as " work is force dot / times distance ". but this is not really satisfying, because you could then ask " why is work force dot distance? " and the mystery is the same. the only way to answer questions like this is to rely on symmetry principles, since these are more fundam... | https://api.stackexchange.com |
moving, double - mass ball, which is also $ 2me ( v ) $. due to conservation of energy, those two terms need to add up to the kinetic energy of the second ball before the collision : $ $ me ( 2v ) = 2me ( v ) + 2me ( v ) $ $ $ $ e ( 2v ) = 4 e ( v ) $ $ which implies that $ e $ is quadratic. non - circular force - time... | https://api.stackexchange.com |
. so the mass - times - height is a measure of the effort required to lift something, and it is a conserved quantity in statics. this quantity should be conserved even if there is dynamics in intermediate stages. by this i mean that if you let two weights drop while suspended on a string, let them do an elastic collisi... | https://api.stackexchange.com |
gpus are bad at doing one thing at a time. a modern high - end gpu may have several thousand cores, but these are organized into simd blocks of 16 or 32. if you want to compute 2 + 2, you might have 32 cores each compute an addition operation, and then discard 31 of the results. gpus are bad at doing individual things ... | https://api.stackexchange.com |
here are a few. the first one is included because it's not very well known and is not general, though the ones that follow are very general and very useful. a great but not very well known way to find the primitive of $ f ^ { - 1 } $ in terms of the primitive of $ f $, $ f $, is ( very easy to prove : just differentiat... | https://api.stackexchange.com |
{ - tx } \ frac { \ sin ( x ) } { x } dx $ instead. let $ $ i ( t ) = \ int _ { 0 } ^ { \ infty } e ^ { - tx } \ frac { \ sin ( x ) } { x } dx, $ $ then $ $ i'( t ) = - \ int _ { 0 } ^ { \ infty } e ^ { - tx } \ sin ( x ) dx = \ frac { e ^ { - t x } ( t \ sin ( x ) + \ cos ( x ) ) } { t ^ 2 + 1 } \ bigg | _ 0 ^ { \ inf... | https://api.stackexchange.com |
want to compute $ \ int _ { - \ infty } ^ { \ infty } \ frac { x ^ 2 } { 1 + x ^ 4 } dx $. the poles of our function $ f ( z ) = \ frac { x ^ 2 } { 1 + x ^ 4 } $ in the upper half plane are $ a _ 1 = e ^ { i \ frac { \ pi } { 4 } } $ and $ a _ 2 = e ^ { i \ frac { 3 \ pi } { 4 } } $. the residues of our function at tho... | https://api.stackexchange.com |
{ it } ) ^ 3 \ over 1 + ( r e ^ { it } ) ^ 4 } dz = { \ pi \ over \ sqrt { 2 } }. $ $ for the integral on the semicircle $ $ \ int _ 0 ^ \ pi { i ( r e ^ { it } ) ^ 3 \ over 1 + ( r e ^ { it } ) ^ 4 } dz, $ $ we have $ $ \ begin { aligned } \ left | \ int _ 0 ^ \ pi { i ( r e ^ { it } ) ^ 3 \ over 1 + ( r e ^ { it } ) ... | https://api.stackexchange.com |
other words : $ $ \ begin { aligned } f ( a ) & = \ frac { 1 } { 2 \ pi i } \ int _ \ gamma \ frac { f ( z ) } { z - a } \, dz \ \ & = \ frac { 1 } { 2 \ pi } \ int _ { 0 } ^ { 2 \ pi } f \ left ( a + e ^ { ix } \ right ) dx. \ end { aligned } $ $ example : we want to compute the very messy looking integral $ \ int _ 0... | https://api.stackexchange.com |
fever is a trait observed in warm and cold - blooded vertebrates that has been conserved for hundreds of millions of years ( evans, 2015 ). elevated body temperature stimulates the body's immune response against infectious viruses and bacteria. it also makes the body less favorable as a host for replicating viruses and... | https://api.stackexchange.com |
* * warning : lithium ion cells * * while this question relates to non - rechargeable aa cells it is possible that someone may seek to extend the advice to testing other small cells. in the case of li - ion rechargeable cells ( aa, 18650, other ) this can be a very bad idea in some cases. shorting lithium ion cells as ... | https://api.stackexchange.com |
sad. try not to do this often or for very long. top aa alkaline cells new will give 5 - 10 a. ( nimh aa will approach 10a for a good cell ). lightly used aa or ones which have had bursts of heavy use and then recovered will typically give a few amps. deader again will be 1 - 3a. anything under 1 a you probably want to ... | https://api.stackexchange.com |
. the more you know, the more you get to know, and this is one more tool along the path towards knowing everything : - ). [ the path is rather longer than any can traverse, but learning how to run along it can be fun ]. | https://api.stackexchange.com |
your question implies that aic and bic try to answer the same question, which is not true. the aic tries to select the model that most adequately describes an unknown, high dimensional reality. this means that reality is never in the set of candidate models that are being considered. on the contrary, bic tries to find ... | https://api.stackexchange.com |
the issue with it is that the choice among the sample - cutting rule ( leave - one - out, k - fold, etc ) is an unprincipled one. | https://api.stackexchange.com |
the simple answer is that no, the big bang did not happen at a point. instead, it happened everywhere in the universe at the same time. consequences of this include : the universe doesn't have a centre : the big bang didn't happen at a point so there is no central point in the universe that it is expanding from. the un... | https://api.stackexchange.com |
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