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this answer may have a slightly more mathematical bent than you were looking for. the important thing to recognize is that all of these means are simply the arithmetic mean in disguise. the important characteristic in identifying which ( if any! ) of the three common means ( arithmetic, geometric or harmonic ) is the "... | https://api.stackexchange.com |
– time example appears to be popular, so let's use it. constant distance, varying times consider a fixed distance traveled $ d $. now suppose we travel this distance $ n $ different times at speeds $ v _ 1, \ ldots, v _ n $, taking times $ t _ 1, \ ldots, t _ n $. we now play our game. suppose we wanted to replace our ... | https://api.stackexchange.com |
bar v _ { \ mathrm { am } } \ >. $ $ here the additive structure we are trying to maintain is proportional to the measurements we have, so the arithmetic mean applies. equal volume cube suppose we have constructed an $ n $ - dimensional box with a given volume $ v $ and our measurements are the side - lengths of the bo... | https://api.stackexchange.com |
to my knowledge, yes. a partial list of recently emerged / emerging viral diseases ( i certainly could have missed some ), with probable reservoir hosts : chikungunya * ( birds, rodents ) coronaviruses / sarbecoviruses ( sars [ bats ], mers [ camels ], covid - 19 [?? bats?? pangolins?? ] ) ebola and other filoviruses (... | https://api.stackexchange.com |
solder fumes aren't very good for you. some people can become sensitized to flux fumes, especially from the older rosin flux used in cored solder, and get breathing problems : controlling health risks from rosin ( colophony ) based solder fluxes the no - clean flux isn't as bad. i once felt quite ill after assembling a... | https://api.stackexchange.com |
yes. if the datasheet says " fully static operation ", then you can clock it at any speed, even 0 hz. a " dynamic " chip needs to have a clock at a specific rate or it loses its state. | https://api.stackexchange.com |
a short summary of the paper mentioned in another answer and another good site. basically planes fly because they push enough air downwards and receive an upwards lift thanks to newton's third law. they do so in a variety of manners, but the most significant contributions are : the angle of attack of the wings, which u... | https://api.stackexchange.com |
researchers from the national physical laboratory ( npl ), in london, in cooperation with partners in2teck ltd and gwent electronic materials ltd, have developed a 3d printable circuit board that separates into individual components when immersed in hot water. the goal of the reuse project was to increase the recyclabi... | https://api.stackexchange.com |
there's not particularly any " physical " meaning to the convolution operation. the main use of convolution in engineering is in describing the output of a linear, time - invariant ( lti ) system. the input - output behavior of an lti system can be characterized via its impulse response, and the output of an lti system... | https://api.stackexchange.com |
keep in mind that ridge regression can't zero out coefficients ; thus, you either end up including all the coefficients in the model, or none of them. in contrast, the lasso does both parameter shrinkage and variable selection automatically. if some of your covariates are highly correlated, you may want to look at the ... | https://api.stackexchange.com |
here is a partial and positive result, valid around the " triple point " $ a = b = c = \ frac13 \ mathbb 1 $. let $ a, b, c \ in m _ n ( \ mathbb c ) $ be hermitian satisfying $ a + b + c = \ mathbb 1 $, and additionally assume that $ $ \ | a - \ tfrac13 \ mathbb 1 \ | \,, \, \ | b - \ tfrac13 \ mathbb 1 \ | \,, \, \ |... | https://api.stackexchange.com |
2 } + \ tfrac1 { 3 ^ 3 } \ mathbb 1 \ big ) \ \ \ ; = \ : \ sum _ \ text { cyc } a _ 0 ^ 3 \ : + \ : \ sum _ \ text { cyc } a _ 0 ^ 2 \ : + \ : \ tfrac19 \ mathbb 1 $ $ to obtain $ $ 6 \ sum _ \ text { cyc } \ big ( a _ 0 + \ tfrac13 \ mathbb 1 \ big ) ^ 3 + \ mathbb 1 \ ; - \ ; 5 \ sum _ \ text { cyc } \ big ( a _ 0 +... | https://api.stackexchange.com |
i don't believe you have enough information in the source image to produce the mask image. you might start by segmenting on color, i. e. green is not trail, gray / brown is. however, there are gray / brown regions on the " trail borders " that are not represented in your mask. ( see the lower left quadrant of your sour... | https://api.stackexchange.com |
there are only two possibilities to consider. for every positive integer $ n $, the string $ 0 ^ n $ appears in the decimal representation of $ \ pi $. in this case, the algorithm that always returns 1 is always correct. there is a largest integer $ n $ such that $ 0 ^ n $ appears in the decimal representation of $ \ p... | https://api.stackexchange.com |
short answer shedding or reabsorbing the endometrial lining is energetically advantageous to the female. the advantage of shedding over re - absorption may be that sperm - born pathogens are removed from the uterus. a more parsimonious explanation, however, is that the endometrium in primates has developed into too lar... | https://api.stackexchange.com |
be an effective way to get rid of sperm - based pathogens. the accompanying bleeding, profet hypothesizes, delivers immune cells into the uterine cavity that can combat pathogens. hypothesis 2 : strassmann ( 1996 ) surmises that the endometrial microvasculature is designed to provide the blood supply to the endometrium... | https://api.stackexchange.com |
i've only done a little bit of functional programming, so take this answer with a grain of salt. pros : functional programming looks very mathematical ; it's a nice paradigm for expressing some mathematical concepts there are good libraries available for things like formal verification of programs and theorem proving, ... | https://api.stackexchange.com |
for productivity, and even then, python and matlab both have facilities for implementing interfaces to compiled code in c or c + + so that performance - critical code can be implemented to execute quickly. most languages have a foreign function interface to c, which would be enough to interface with most libraries of i... | https://api.stackexchange.com |
when is a mosfet more appropriate as a switch than a bjt? answer : 1 ) a mosfet is better than a bjt when : when you need really low power. mosfets are voltage - controlled. so, you can just charge their gate once and now you have no more current draw, and they stay on. bjt transistors, on the other hand, are current -... | https://api.stackexchange.com |
faster your switching frequency, the more mosfet transistors lose their efficiency gains they otherwise naturally have over bjt transistors, and the more bjt transistors begin to be appealing from a " low power " stand - point. also ( see the book reference, quotes, and example problem below! ) bjt transistors can swit... | https://api.stackexchange.com |
to miniaturise and etch into ics ( chips ), so most computer chips are mosfet - based. [ i need to find a source for this - - please post a comment if you have one ] when voltage spike robustness is not your primary concern. if i recall correctly, bjt transistors are more resistant to having their voltage ratings momen... | https://api.stackexchange.com |
##os transistor ( n - channel mosfet ) which only reached a transition frequency of 9. 7 ghz at a drain current, i _ d, of 1 ma. you need to make an op - amp. the textbook i cite farther below says bjts are good for this ( being used to make op - amps ) here ( emphasis added ) : it can thus be seen that each of the two... | https://api.stackexchange.com |
, charge pumps, expensive gate driver ics, etc., just to turn on the stinking thing. contrast this to a bjt where all you need is one resistor and your 3. 3v microcontroller can turn it on just fine, especially if it's a darlington bjt transistor so it has a huge hfe gain ( of around 500 ~ 1000 or more ) and can be tur... | https://api.stackexchange.com |
bias current. also, as mentioned earlier, the mosfet provides an excellent implementation of a switch, a fact that has made cmos technology capable of realizing a host of analog circuit functions that are not possible with bipolar transistors. it can thus be seen that each of the two transistor types has its own distin... | https://api.stackexchange.com |
##jt ) mean for tri - state gpio pins in microcontrollers : search this page for " open drain " : | https://api.stackexchange.com |
genomes are commonly stored as either fasta files (. fa ) or twobit (. 2bit ) files. fasta files store the entire sequence as text and are thus not particularly compressed. twobit files store each nucleotide in two bits and contain additional metadata that indicates where there's regions containing n ( unknown ) bases.... | https://api.stackexchange.com |
white gaussian noise in the continuous - time case is not what is called a second - order process ( meaning $ e [ x ^ 2 ( t ) ] $ is finite ) and so, yes, the variance is infinite. fortunately, we can never observe a white noise process ( whether gaussian or not ) in nature ; it is only observable through some kind of ... | https://api.stackexchange.com |
power supplies are slow... they take roughly 10 us to respond ( i. e. bandwidth up to 100 khz ). so when your big, bad, multi - mhz microcontroller switches a bunch of outputs from high to low, it will draw from the power supply, causing the voltage to start drooping until it realizes ( 10 us later! ) that it needs to ... | https://api.stackexchange.com |
notice : i have altered my answer slightly from the original as i have turned the original script into a pip installable program ( with tests ) and have updated the links and code snippets accordingly. the essence of the answer is still exactly the same. this is something i have been meaning to get around to for a whil... | https://api.stackexchange.com |
the answer is complex due to the way the gps system operates, so i'm going to simplify a number of things so you understand the principle, but if you are interested in how it's really implemented you'll need to go find a good gps reference. in other words, what's written below is meant to give you an idea of how it wor... | https://api.stackexchange.com |
satellites ) of 32 seconds, assuming we don't make any assumptions, or perform any clever tricks, the received signal is good, etc. however, if you have two correlators, you've just halved that time because you can search for two satellites at once. get 12 correlators on the job and it takes less than a few seconds. ge... | https://api.stackexchange.com |
it's a 100mw power drain all the time. if, however, you only need to turn it on once per second for only 10ms each time, then you just cut your power consumption down to 1mw. this means your cell phone, location beacon, etc can operate for two orders of magnitude longer time on the same set of batteries while still mai... | https://api.stackexchange.com |
a flip flop is built from two back to back latches with opposite polarity clocks, which form a master slave topology. the type of latch is irrelevant ( jk, sr, d, t ) to this constraint, but it is important that the transparency is controlled by some pin ( call it clock or enable or whatever you like ). sr latches thro... | https://api.stackexchange.com |
in my opinion, the catalytic, solar - driven conversion of carbon dioxide to methanol, formic acid, etc. is much more interesting and promising, but since enrico asked for the conversion of carbon dioxide to carbon itself : the group around yutaka tamaura was / is active in this field. in one of their earlier publicati... | https://api.stackexchange.com |
you can best look at it in the frequency domain. if $ x [ n ] $ is the input sequence and $ h [ n ] $ is the filter's impulse response, then the result of the first filter pass is $ $ x ( e ^ { j \ omega } ) h ( e ^ { j \ omega } ) $ $ with $ x ( e ^ { j \ omega } ) $ and $ h ( e ^ { j \ omega } ) $ the fourier transfo... | https://api.stackexchange.com |
n ] * h [ - n ] $ and get the same result with ordinary filtering. it is more interesting to use this method with iir filters, because they cannot have zero - phase ( or linear phase, i. e. a pure delay ). in sum : if you have or need an iir filter and you want zero phase distortion, and processing delay is no problem ... | https://api.stackexchange.com |
short answer eigenvectors make understanding linear transformations easy. they are the " axes " ( directions ) along which a linear transformation acts simply by " stretching / compressing " and / or " flipping " ; eigenvalues give you the factors by which this compression occurs. the more directions you have along whi... | https://api.stackexchange.com |
= \ lambda w \ end { align * } that is, you can " decouple " the system, so that now you are dealing with two independent functions. then solving this problem becomes rather easy : $ z = ae ^ { \ kappa t } $, and $ w = be ^ { \ lambda t } $. then you can use the formulas for $ z $ and $ w $ to find expressions for $ x ... | https://api.stackexchange.com |
let's go through some questions in order and see where it takes us. [ or skip to the bit about complex numbers below if you can't be bothered. ] what are natural numbers? it took quite some evolution, but humans are blessed by their ability to notice that there is a similarity between the situations of having three app... | https://api.stackexchange.com |
are real numbers? i find some more apples and put them in a pie, which i cook in a circular dish. one of my friends decides to get smart, and asks for a slice of the pie whose curved edge has the same length as its straight edges ( i. e. arc length of the circular segment is equal to its radius ). i decide to honour hi... | https://api.stackexchange.com |
the same effect as rotating it by the second angle and then the first $ - $ the order in which i carry out the rotations has no effect on what i end up with, just like with scaling. does this mean we can model rotation with some kind of multiplication, where multiplication of these new numbers corresponds to addition o... | https://api.stackexchange.com |
$ 90 ^ { \ circ } $ in either direction. they are the rotations / scalings which, when performed twice, leave the pie facing backwards ; that is, they are the numbers which square to give negative real numbers. ] what next? i've been asked in the comments to mention quaternions and octonions. these go ( even further ) ... | https://api.stackexchange.com |
very insightful ways of getting $ \ mathbb { c } $ from $ \ mathbb { r } $ in different ways, and discussing how and why complex numbers are useful $ - $ there's only so much use to spinning pies around. a visual, intuitive guide to imaginary numbers $ - $ thanks go to joe, in the comments, for pointing this out to me.... | https://api.stackexchange.com |
it is american woodcock, scolopax minor. superbly camouflaged against the leaf litter, the brown - mottled american woodcock walks slowly along the forest floor, probing the soil with its long bill in search of earthworms. unlike its coastal relatives, this plump little shorebird lives in young forests and shrubby old ... | https://api.stackexchange.com |
several papers have made this distinction, and a few indeed use different terms to distinguish between them. for example, kazaux et al. ( 2016 ) acknowledge that : these constraints favour the use of a version of the de bruijn graph ( dbg ) dedicated to genome assembly – a version which differs from the combinatorial s... | https://api.stackexchange.com |
the normalized counts themselves can be accessed with counts ( dds, normalized = t ). now as to what the basemean actually means, that will depend upon whether an " expanded model matrix " is in use or not. given your previous question, we can see that geno _ treat has a bunch of levels, which means that expanded model... | https://api.stackexchange.com |
to expand on @ believeinvis's answer - - in the early 19th century, when the royal society was really in the swing of things, the dominant language of scholarship was still latin. since latin didn't have words for the new metallic elements, new words were coined from the existing terms for the substances and given lati... | https://api.stackexchange.com |
if you want something quick and dirty you could rapidly index the fasta with samtools faidx and then put the lengths column through r ( other languages are available ) on the command line. samtools faidx $ fasta cut - f2 $ fasta. fai | rscript - e'data < - as. numeric ( readlines ( " stdin " ) ) ; summary ( data ) ; hi... | https://api.stackexchange.com |
one simple way to derive this is to come up with a parabola approximation. just getting the roots correct we have $ $ f ( x ) = x ( \ pi - x ) $ $ then, we need to scale it ( to get the heights correct ). and we are gonna do that by dividing by another parabola $ p ( x ) $ $ $ f ( x ) = \ frac { x ( \ pi - x ) } { p ( ... | https://api.stackexchange.com |
i think this is a symptom of how students are taught basic algebra. rather than being told explicit axioms like $ a ( x + y ) = ax + ay $ and theorems like $ ( x + y ) / a = x / a + y / a, $ students are bombarded with examples of how these axioms / theorems are used, without ever being explicitly told : hey, here's a ... | https://api.stackexchange.com |
the third pin is usually for an internal temperature sensor, to ensure safety during charging. cheap knock - off batteries sometimes have a dummy sensor that returns a " temp ok " value regardless of actual temperature. some higher - end batteries have internal intelligence for charge control and status monitoring, in ... | https://api.stackexchange.com |
training set a set of examples used for learning : to fit the parameters of the classifier in the multilayer perceptron ( mlp ) case, we would use the training set to find the “ optimal ” weights with the back - prop rule validation set a set of examples used to tune the hyper - parameters of a classifier in the mlp ca... | https://api.stackexchange.com |
for one - offs or prototypes i use : press - n - peel transfer film with a laser printer ( the blue one ) steel wool and detergent to clean the pcb blank, then a short etch in ammonium persulphate : that gives a very clean surface, important for a good transfer from the film a laminator to transfer the pattern to the p... | https://api.stackexchange.com |
2 mm or 8 mil diameter. this takes some time! and to solder i place solder paste with a fine - tipped syringe, place parts with fine tweezers then reflow in an electric frying pan. a few more pictures : syringing solder paste onto smd pads. placing component with tweezers a finshed board - the pcb was professionally ma... | https://api.stackexchange.com |
i think it would help to understand how a capacitor blocks dc ( direct current ) while allowing ac ( alternating current ). let's start with the simplest source of dc, a battery : when this battery is being used to power something, electrons are drawn into the + side of the battery, and pushed out the - side. let's att... | https://api.stackexchange.com |
" side can have a lot more electrons sucked out of it, and the " negative " side can have a lot more electrons pushed into it : so if you apply an alternating current source to a capacitor, some of that current will be allowed to flow, but after a while it will run out of electrons to push around, and the flow will sto... | https://api.stackexchange.com |
in most countries, cosmetic product labels use the international nomenclature of cosmetic ingredients ( inci ) for listing ingredients. the inci name “ aqua ” indeed just describes water ( which is used as a solvent ). | https://api.stackexchange.com |
the best book to answer your question would probably be : cooper and torczon, " engineering a compiler, " 2003. if you have access to a university library you should be able to borrow a copy. in a production compiler like llvm or gcc the designers make every effort to keep all the algorithms below $ o ( n ^ 2 ) $ where... | https://api.stackexchange.com |
and a pass over the flow graph takes time $ o ( n ) $ where $ n $ is the number of 3 - address instructions. for more sophisticated optimizations you might want to do more sophisticated analyses. at this point you start running into tradeoffs. you want your analysis algorithms to take much less than $ o ( n ^ 2 ) $ tim... | https://api.stackexchange.com |
the earliest mention of the 30x paradigm i could find is in the original illumina whole - genome sequencing paper : bentley, 2008. specifically, in figure 5, they show that most snps have been found, and that there are few uncovered / uncalled bases by the time you reach 30x : these days, 30x is still a common standard... | https://api.stackexchange.com |
dfam has recently launched a sister resource, dfam _ consensus, whose stated aim is to replace repbase. from the annoucement : dfam _ consensus provides an open framework for the community to store both seed alignments ( multiple alignments of instances for a given family ) and the corresponding consensus sequence mode... | https://api.stackexchange.com |
one example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two - body problem. the two - body problem here means the task of calculating the dynamics of two interacting particles which, for example, interact by gravitational or coulomb forces. the solution to th... | https://api.stackexchange.com |
try kicad. now it even does spice simulations, ngspice specifically, and it handles pretty much everything else. other than that, if you wish, kicad has also the tools to design printed circuit boards, and even has a 3d viewer and exporter for the boards! kicad runs on windows, linux and apple os x. there is also a pro... | https://api.stackexchange.com |
if the values lie along a line the distribution has the same shape ( up to location and scale ) as the theoretical distribution we have supposed. local behaviour : when looking at sorted sample values on the y - axis and ( approximate ) expected quantiles on the x - axis, we can identify from how the values in some sec... | https://api.stackexchange.com |
one can disprove string theory by many observations that will almost certainly not occur, for example : by detecting lorentz violation at high energies : string theory predicts that the lorentz symmetry is exact at any energy scale ; recent experiments by the fermi satellite and others have shown that the lorentz symme... | https://api.stackexchange.com |
general features predicted by all string vacua which are not satisfied by the " swampland " qfts as explained by cumrun vafa ; if we lived in the swampland, our world couldn't be described by anything inside the landscape of string theory ; the generic predictions of string theory probably include the fact that gravity... | https://api.stackexchange.com |
string theory and qft as the frameworks are indistinguishable ; they just have different methods to parameterize the detailed possibilities. in qft, one chooses the particle content and determines the continuous values of the couplings and masses ; in string theory, one only chooses some discrete information about the ... | https://api.stackexchange.com |
full - fledged string / m - theory in one of its diverse descriptions. even in the absence of string theory, it could hypothetically happen that new experiments will discover new phenomena that are impossible - at least unnatural - according to string theory. obviously, people would have to find a proper description of... | https://api.stackexchange.com |
it's not an argument. it is a ( a bit strongly stated ) fact that formal normality tests always reject on the huge sample sizes we work with today. it's even easy to prove that when n gets large, even the smallest deviation from perfect normality will lead to a significant result. and as every dataset has some degree o... | https://api.stackexchange.com |
##7 | https://api.stackexchange.com |
when you look at a surface like sand, bricks, etc, the light you are seeing is reflected by diffuse reflection. with a flat surface like a mirror, light falling on the surface is reflected back at the same angle it hit the surface ( specular reflection ) and you see a mirror image of the light falling on the surface. h... | https://api.stackexchange.com |
nobody really knows. using the naive bohr model of the atom, we run into trouble around $ z = 137 $ as the innermost electrons would have to be moving above the speed of light. this result is because the bohr model doesn't take into account relativity. solving the dirac equation, which comes from relativistic quantum m... | https://api.stackexchange.com |
##s and neutrons in the nucleus ( and the resulting nucleus will have become so large ) that the diametrically opposite parts of the nucleus won't be able to " detect " each other, as they are too far away. each additional proton or neutron produces a weaker stabilization via the strong nuclear force. meanwhile, the el... | https://api.stackexchange.com |
there are about $ 10 ^ { 23 } $ stars in the observable universe. thanks to the expansion of the universe, those stars are currently spread over a sphere that is about $ d = 2. 8 \ times 10 ^ { 10 } $ parsecs across. of course some stars will have died whilst their light has been travelling towards us, but others will ... | https://api.stackexchange.com |
$ l = ( n _ * / n _ * ) ^ { 1 / 3 } $ and of voids with side $ ( n _ * / n ) ^ { 1 / 3 } l = ( n _ g / n ) ^ { 1 / 3 } $. the number density of galaxies is the number of galaxies divided by the volume of the observable universe $ n _ g = ( 10 ^ { 23 } / n _ * ) / ( \ pi d ^ 3 / 6 ) $ the number of galaxies intersected ... | https://api.stackexchange.com |
galaxies ", but if it did there would be about $ 10 ^ 7 $ stellar intersections. | https://api.stackexchange.com |
what is meant by a complete description of a stochastic process? well, mathematically, a stochastic process is a collection $ \ { x ( t ) \ colon t \ in { \ mathbb t } \ } $ of random variables, one for each time instant $ t $ in an index set $ \ mathbb t $, where usually $ \ mathbb t $ is the entire real line or the p... | https://api.stackexchange.com |
= f _ { x ( t _ 2 ), x ( t _ 2 + \ tau ) } ( x, y ) $ any three random variables $ x ( t _ 1 ) $, $ x ( t _ 1 + \ tau _ 1 ) $, $ x ( t _ 1 + \ tau _ 1 + \ tau _ 2 ) $ spaced $ \ tau _ 1 $ and $ \ tau _ 2 $ apart have the same joint cdf as $ x ( t _ 2 ) $, $ x ( t _ 2 + \ tau _ 1 ) $, $ x ( t _ 2 + \ tau _ 1 + \ tau _ 2... | https://api.stackexchange.com |
n ) $ is the same as the $ n ^ { \ text { th } } $ - order joint cdf of $ x ( t _ 1 + \ tau ), x ( t _ 2 + \ tau ), \ ldots, x ( t _ n + \ tau ) $ for all choices of $ t _ 1, t _ 2, \ ldots, t _ n $ and $ \ tau $, then the random process is said to be stationary to order $ n $ and is referred to as a $ n ^ { \ text { t... | https://api.stackexchange.com |
process and avoid this confusion. but note again that a first - order stationary process need not be a finite - power process. consider a random process that is stationary to order $ 2 $. now, since the joint distribution of $ x ( t _ 1 ) $ and $ x ( t _ 1 + \ tau ) $ is the same as the joint distribution function of $... | https://api.stackexchange.com |
the necessary instruments on his workbench ( or programs in matlab / python / octave / c + + in his software library ) are the dc value $ \ frac 1t \ int _ 0 ^ t x ( t ) \, \ mathrm dt $ of $ x ( t ) $ and the autocorrelation function $ r _ x ( \ tau ) = \ frac 1t \ int _ 0 ^ t x ( t ) x ( t + \ tau ) \, \ mathrm dt $ ... | https://api.stackexchange.com |
cos ( t + \ pi / 2 ) = - \ sin ( t ), \ cos ( t + \ pi ) = - \ cos ( t ) $ and $ \ cos ( t + 3 \ pi / 2 ) = \ sin ( t ) $, it is easy to see that in general $ x ( t ) $ and $ x ( s ) $ have different distributions, and so the process is not even first - order stationary. on the other hand, $ $ e [ x ( t ) ] = \ frac 14... | https://api.stackexchange.com |
2 ) & = \ operatorname { cov } ( x ( t _ 1 ), x ( t _ 2 ) ) \ \ & = e [ ( x ( t _ 1 ) - \ mu _ x ( t _ 1 ) ) ( x ( t _ 2 ) - \ mu _ x ( t _ 2 ) ) ] \ \ & = e [ x ( t _ 1 ) x ( t _ 2 ) ] - \ mu _ x ( t _ 1 ) \ mu _ x ( t _ 2 ), \ end { align } is a function only of $ t _ 1 - t _ 2 $ and not of the individual values of $... | https://api.stackexchange.com |
, t _ n $, the $ n $ random variables $ x ( t _ 1 ) $, $ x ( t _ 2 ) $, $ \ ldots, x ( t _ n ) $ are jointly gaussian random variables. now a joint gaussian density function is completely determined by the means $ e [ x ( t _ i ) ] = \ mu _ x ( t _ i ) $, variances \ begin { align } \ operatorname { var } ( x ( t _ i )... | https://api.stackexchange.com |
signal processors, many physical noise processes can be well - modeled as wss gaussian processes ( and therefore strictly stationary processes ), so that experimental observation of the autocorrelation function readily provides all the joint distributions. furthermore since gaussian processes retain their gaussian char... | https://api.stackexchange.com |
the answer to this question is simple and requires only sr, not gr or quantum mechanics. in units with $ c = 1 $, we have $ m ^ 2 = e ^ 2 - p ^ 2 $, where $ m $ is the invariant mass, $ e $ is the mass - energy, and $ p $ is the momentum. in terms of logical foundations, there is a variety of ways to demonstrate this. ... | https://api.stackexchange.com |
to determine what can and cannot be proved by contradiction, we have to formalize a notion of proof. as a piece of notation, we let $ \ bot $ represent an identically false proposition. then $ \ lnot a $, the negation of $ a $, is equivalent to $ a \ to \ bot $, and we take the latter to be the definition of the former... | https://api.stackexchange.com |
##not a $ implies $ a $, which means that in classical logic if we can prove $ \ lnot a $ implies a contradiction then we know that $ a $ holds. in other words : even in intuitionistic logic, if a statement implies a contradiction then the negation of the statement is true, but in classical logic we also have that if t... | https://api.stackexchange.com |
i think if you look at this animation and think about it long enough, you'll understand : why circles and right - angle triangles and angles are all related. why sine is " opposite over hypotenuse " and so on. why cosine is simply sine but offset by $ \ frac { \ pi } { 2 } $ radians. | https://api.stackexchange.com |
there are a couple elements i look for when i consider something " publication - quality " in either my own work, or what i'm considering when looking at others. they are : high resolution, and preferably vector - based. this one should be fairly obvious by now, but you'd be surprised. a lack of clutter. i should be ab... | https://api.stackexchange.com |
there are models that take into account compositional heterogeneity both under the maximum likelihood and bayesian frameworks. although the substitution process is not time - reversible, the computations are simplified by assuming that the instantaneous rate matrix can be decomposed into an " equilibrium frequency vect... | https://api.stackexchange.com |
there are many good reasons not to use the 1968 - vintage lm741 : - minimum recommended power supply rails are + / - 10 volts modern op - amps have power supplies that can be as low as 0. 9 volts. input voltage range is typically from - vs + 2 volt to + vs - 2 volt modern op - amps can be chosen that are rail - to - ra... | https://api.stackexchange.com |
in total. i've been an electronics designer since 1980 and i have never used or specified a 741 in any design i've been associated with. maybe i'm missing out on something? | https://api.stackexchange.com |
first we must assume that eve is only passive. by this, i mean that she truthfully sends the card to bob, and whatever she brings back to alice is indeed bob's response. if eve can alter the data in either or both directions ( and her action remains undetected ) then anything goes. ( to honour long - standing tradition... | https://api.stackexchange.com |
" solutions involving random nonces and symmetric encryption and whatsnot. it is a strong flaw, and its root lies in the huge difference in computing power between eve and bob ( now, if bob also had a computer as big as eve's, then he could use a slow hash function through the use of many iterations ; that's more or le... | https://api.stackexchange.com |
a day ). the result is what bob sends back to alice. alice uses her knowledge of $ p $ and $ q $ to recover $ m $ from the $ m ^ 3 \ mathrm { \ mod \ } n $ sent by bob. the wikipedia page on rsa has some reasonably clear explanations on that process. once alice has $ m $, she can remove the padding ( the'xx'are non - z... | https://api.stackexchange.com |
here's one key difference between the cases. suppose we add to the reals an element $ i $ such that $ i ^ 2 = - 1 $, and then include everything else you can get from $ i $ by applying addition and multiplication, while still preserving the usual rules of addition and multiplication. expanding the reals to the complex ... | https://api.stackexchange.com |
in matlab, the ‘ \ ’ command invokes an algorithm which depends upon the structure of the matrix a and includes checks ( small overhead ) on properties of a. if a is sparse and banded, employ a banded solver. if a is an upper or lower triangular matrix, employ a backward substitution algorithm. if a is symmetric and ha... | https://api.stackexchange.com |
just look up a fractional inch to mm conversion chart. then break out the drill bits. 5 / 64 inch = 1. 9844 mm 3 / 32 inch = 2. 3813 mm 7 / 64 inch = 2. 7781 mm a 5 / 64 bit will fit the 2. 1mm barrel but not a 3 / 32 a 3 / 32 bit will fit the 2. 5mm barrel but not a 7 / 64 | https://api.stackexchange.com |
if you are in the us, there are several thousand institutions of higher learning, and at many of them there is very little " pressure to publish ". at others, the " pressure to publish " can be met by publishing a textbook or some work of scholarship that does not require proofs of interesting ( original ) results. hig... | https://api.stackexchange.com |
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