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https://physics.stackexchange.com/questions/411722/how-is-the-subjective-loudness-of-sound-computed
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# How is the subjective loudness of sound computed?
The intensity of a sound is a measure of the energy that the sound waves carries through space per unit time per unit area (since energy is conserved along the wave unless work is done on/by it and the wave spreads out through space).
$$I = \frac{\text{power}}{\text{area}}$$
If the wave propagates with amplitude $A$ at a speed $v$ (or frequency $f$ and wavelength $\lambda$) through a medium of volumetric mass density $\rho$, its intensity is (supposedly) given by $$I = {A^2 \over 2\rho v} = {A^2 \over 2\rho f\lambda}$$
In the commercial world, however, we describe sound with sound intensity level in decibels $\rm dB$ of an airborne sound wave of sound pressure (amplitude) $A$ given by
$$L_A= 10\log_{10}{A^2 \over A_\text{ref}^2} \ \rm dB$$
where $A_\text{ref}= 20\ \rm µPa$ is the most common reference pressure, corresponding to the minimum intensity for the average person to hear a sound—if the wave oscillates at $1\ \rm kHz$.
I’m left with one observation and hence one question: the definitions of intensities given are purely mechanical—they don’t take into account subject measurements (collected, for example, by the ISO) of what sounds seem louder than others. A flaw with quoting intensities in watts per square metre or decibels (as I see it) is that a change in intensity in $\rm W/m^2$ or $\rm dB$ is not systematically related to perceived differences by definition.
So what gives? What am I missing?
If you’re still confused, think about radiometry and photometry: irradiance is given in $\rm W/m^2$ as well, but it is scaled by a variable luminosity function to give the illuminance in lux $\rm lx$ that humans sense. The defining relationship is
$$\Phi_{\rm v} = \int\limits_{300\ \rm nm}^{800\ \rm nm} K_{\rm cd} \, V(\lambda) \, \Phi_{\rm e}(\lambda) \, d\lambda$$
How is the subjective loudness of sound computed?
I’m left with one observation and hence one question: the definitions of intensities given are purely mechanical—they don’t take into account subject measurements (collected, for example, by the ISO) of what sounds seem louder than others. ... systematically related to perceived differences by definition.
Wikipedia's article on loudness requires a bit of digging through and further research to come up with the better answer. One of the well accepted measures is INEX, see: "To Honor Stevens and Repeal His Law (For the Auditory System)" (2006), by Mary Florentine, Michael Epstein:
"Data from a number of experiments reviewed in this paper indicate that a power function is only a rough approximation to the loudness growth function, because a power law does not fit the data at low and moderate levels. This paper proposes a new psychophysical law for loudness to better describe the data. A non-stationary point of inflection law [or an inflected exponential (INEX) law] appears to be the best description of currently available data.". Figure 1. Stevens’ Power Function is plotted with each of the modifications presented in this paper to arrive at the Inflected Exponential (INEX) function. The INEX function was taken from Buus and Florentine (2001).
INEX is modeled as:
$$\text{log}_{10}(S) = 1.7058\text x 10^{-9}L^5-6.587\text x 10^{-7}L^4+9.7515 \text x 10^{-5}L^3-6.6964 \text x 10^{-3}L^2 \\ +0.2367 L - 3.4831$$
where $S$ is the sensation and $L$ is the level in dB SPL.
For hearing impaired listeners it varies. See this study published by the Acoustical Society of America: "Loudness growth in individual listeners with hearing losses: A review" (2007), by Jeremy Marozeau, and Mary Florentine
Some of the newest research involves measuring distortion-product otoacoustic emission (DPOAE) input/output (I/O) functions and categorical loudness scaling (CLS) functions. See: "Relation of distortion-product otoacoustic emission input-output functions to loudness" (26 April 2013), by Daniel M. Rasetshwane, Stephen T. Neely, Judy G. Kopun, and Michael P. Gorga
• So there is no scaling function of amplitude and frequency $K(A,f)$ such that the ‘audible intensity’ of a vibration is $$\iint_{\Bbb R^2}K(A,f) \, 10^L \, dA \, df$$ is what I take from this—yes? – gen-z ready to perish Jun 14 '18 at 7:54
• Your question appears to show an image from CK-12 - Intensity and Loudness of Sound where sound in a gas is explained with an inverse square law diagram, on that basis I explained that Stevens was the refinement of that, and it's replaced by INEX. Equal-loudness contours are also explained in the links provided - no? – Rob Jun 15 '18 at 3:27
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2019-10-20 22:24:06
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http://libros.duhnnae.com/2017/sep3/150537916771-An-observation-cut-off-of-the-weight-w-does-not-increase-the-A-p-1-p-2-normx27x27-of-w-Mathematics-Analysis-of-PDEs.php
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# An observation: cut-off of the weight $w$ does not increase the $A {p {1}, p {2}}$-norm'' of $w$ - Mathematics > Analysis of PDEs
An observation: cut-off of the weight $w$ does not increase the $A {p {1}, p {2}}$-norm'' of $w$ - Mathematics > Analysis of PDEs - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: We consider weights $w$ and their cut-offs: $w at=wt$ if $wt\le a$ and$w at=a$ if $wt> a$. We consider a generalized $A p$-norm- and provethat the norm- of $w a$ is not greater then the norm- of $w$. Our proofin the case $w\in A 2$ is especially simple.
Autor: Alexander Reznikov, Vasiliy Vasyunin, Alexander Volberg
Fuente: https://arxiv.org/
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2019-01-22 13:27:39
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https://physics.stackexchange.com/questions/150080/how-much-real-and-how-much-relative-is-our-universe
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# How much real and how much relative is our universe?
Apologies in advance if my question appears more philosophical than practical. It is indeed philosophy, but a philosophy relating to our scientific understanding of the universe as a whole.
Special Relativity states that as an object increases in velocity, it gets more dense (mass increases, volume shrinks). An object undergoing a decrease in velocity would begin to diffuse (mass decreases, volume inflates).
Now let us consider the fact that since Big Bang, all the material objects in our universe are in a state of constant, reckless motion (galaxies moving apart, solar systems orbiting around their galaxies, planets around their stars etc).
1. Keeping this in mind, how "real" is our universe? As in, if all objects in our universe come to rest (provided they don't collapse into a horrible universal black hole), how much would they diffuse? How much of their mass (as we know it now, in the state of reckless motion) would remain and how much of it would be lost? Of course the volume would expand 3-fold than mass (with a decrease in velocity, length increases, and volume is a 3rd degree function of length).
2. We know that the rest mass of a photon is zero (a photon's physical existence is only as long as it moves?). What would be the "rest mass" of our universe?
• I think this question has potential, but I was about to write it off until you got to your point. Perhaps rephrase it. – Gödel Dec 2 '14 at 20:47
• I added a long introduction just to show in what context I am asking the question. I could cut it short, but then fellow member's would answer it in different contexts, incoherently from one another. – Youstay Igo Dec 2 '14 at 20:51
• This question seems to be based on the faulty/outdated notion of relativistic mass, $m_{rel}=\gamma m$. – Kyle Kanos Dec 2 '14 at 20:52
• Kyle, do you intend to mean that mass does not increase with velocity? – Youstay Igo Dec 2 '14 at 20:59
• @YoustayIgo: Correct. See also this, this, this, and probably many more here on Physics.SE. So yes, relativistic mass is an obsolete concept. – Kyle Kanos Dec 2 '14 at 21:05
Special Relativity states that as an object increases in velocity, it gets more dense (mass increases, volume shrinks).
No, no, no. Absolutely not.
But I know why you think this. Back many decades ago, before I was born, lots of physicists wrote physics papers and textbooks without really understanding relativity. They made mistakes. Not necessarily errors, but certainly pedagogical mistakes. And these mistakes have proven most insidious and hard to weed out. The most egregious of these is stating that mass increases with velocity.
As understood today by any and all who deal with relativity, objects have an invariant rest mass $m$. This is the same for all observers. As a Lorentz scalar, it does not change when going into different frames of reference.
Old papers -- and remember, we're talking the early to middle 20th century, when no one know what DNA was, computers didn't exist, and we hadn't even coined the term "Big Bang" -- would refer to the combined quantity $\gamma m$ as relativistic mass. Sometimes they would write it as just $m$, where my rest mass above was written $m_0$: $m = \gamma m_0$.
It is this second $m$, this "relativistic mass," that changes with an object's relative velocity. The true $m$, denoted $m_0$ back in the dark ages, never changes.
An object undergoing a decrease in velocity would begin to diffuse (mass decreases, volume inflates).
Even if we agree we're talking about $\gamma m$ decreasing, there is a lower limit. The factor $\gamma$ is given by $1/\sqrt{1-v^2}$, where $v$ is the relative velocity between reference frames. You can check for yourself that for any $v$ bounded by the speed of light, $-c < v < c$, we have $\gamma \geq 1$. The minimum value of $\gamma m$ is $m$, and it occurs when $\gamma = 1$, i.e. when you the observer are comoving with the object, i.e. when the object appears to be at rest. Even the accursed relativistic mass can't go to $0$.
How much would some sum over $\gamma m$ for all objects change if they stopped moving from our point of view? Not much, actually. For cosmological purposes, ordinary matter is modeled very well by what cosmologists call dust. Basically, this makes the approximation that $\gamma \approx 1$, because most matter really is moving slow compared to the speed of light: $v \ll c$.
Note that I'm only talking about peculiar motion here -- the motion in addition to the uniform expansion of the universe. This is because the apparent "velocities" with which galaxies are receding can't really be analyzed in the same special relativistic framework. (For one, recession velocities are often greater than $c$!)
• What I gather is that unlike my assumption, there IS a base of reality (invariant mass and invariant length) on which all relativity changes play about. So if the galaxies are moving faster than c, it would imply that special relativity can only be applied to local phenomena (only in a closed system of 2 objects, the subject and the observer) and not universal phenomena? :S I'm feeling lost here. – Youstay Igo Dec 2 '14 at 21:32
• On the scale of the universe, you really do need general relativity. Unfortunately, astronomers tend to convert redshifts, which are the fundamental physical observables, to velocities (by multiplying by $c$), as though they were caused by special relativistic Doppler shifts. There is no physical reason for this, and thinking of redshifts as velocities causes as much trouble as it solves, but it's done nonetheless. You're not the only one to feel lost. – user10851 Dec 2 '14 at 23:39
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2020-01-21 20:16:29
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https://search.r-project.org/CRAN/refmans/EL/html/EL.plot.html
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EL.plot {EL} R Documentation
## Draws plots using the smoothed two-sample empirical likelihood method
### Description
Draws P-P and Q-Q plots, ROC curves, quantile differences (qdiff) and CDF differences (ddiff) and their respective confidence bands (pointwise or simultaneous) using the empirical likelihood method.
### Usage
EL.plot(method, X, Y, bw = bw.nrd0, conf.level = NULL,
simultaneous = FALSE, bootstrap.samples = 300,
more.warnings = FALSE, ...)
### Arguments
method "pp", "qq", "roc", "qdiff" or "fdiff". X a vector of data values. Y a vector of data values. bw a function taking a vector of values and returning the corresponding bandwidth or a vector of two values corresponding to the respective bandwidths of X and Y. conf.level confidence level for the intervals. A number between 0 and 1 or NULL when no confidence bands should be calculated. Depending on the value of 'simultaneous' either pointwise intervals or simultaneous confidence bands will be drawn. simultaneous if this is TRUE, simultaneous confidence bands will be constructed, using a nonparametric bootstrap procedure to select the level of confidence bands. The default is FALSE, in which case simple pointwise confidence bands are calculated. bootstrap.samples the number of samples used to bootstrap the simultaneous confidence bands when 'simultaneous = TRUE'. more.warnings if this is FALSE (the default) a single warning will be produced if there is any problem calculating the estimate or the confidence bands. If this is set to TRUE a warning will be produced for every point at which there was a problem. ... further arguments passed to plot.
### Details
The plotting interval for P-P plots, ROC curves and differences of quantile functions is [0, 1] (where these functions are defined). The Q-Q plot is drawn from the minimum to the maximum of 'Y'. Finally, for the plot of distribution function differences the interval from max(min(X), min(Y)) to min(max(X), max(Y)) is used.
Confidence bands are drawn only if 'conf.level' is not 'NULL'.
When constructing simultaneous confidence bands, the plot is drawn on an interval that is narrowed by 5% on both sides, since the procedure is usually sensitive at the end-points, which can result in large bands. The confidence level for the simultaneous confidence bands is bootstrapped using 50 evenly spaced points in this interval. If the default interval produces too large confidence bands, use the function 'EL.smooth' where the intervals are specified manually. Note that calculation of simultaneous confidence bands can take a long time.
none.
### Author(s)
E. Cers, J. Valeinis
### References
J. Valeinis, E. Cers. Extending the two-sample empirical likelihood. To be published. Preprint available at http://home.lanet.lv/~valeinis/lv/petnieciba/EL_TwoSample_2011.pdf.
P. Hall and A. Owen (1993). Empirical likelihood bands in density estimation. Journal of Computational and Graphical statistics, 2(3), 273-289.
EL.smooth EL.statistic
### Examples
## The examples showcase all available graphs
X1 <- rchisq(100, 2.5)
X2 <- rnorm(100, 0, 1)
p <- par(lwd=2, mfrow=c(3,2))
# Intro
xlim <- c(min(X1, X2) - 0.5, max(X1, X2) + 0.5)
D1 <- density(X1)
D2 <- density(X2)
ylim <- c(min(D1$y, D2$y), max(D1$y, D2$y))
plot(D1, xlim=xlim, ylim=ylim, main="Distribution functions", xlab="x")
lines(D2, lty="dashed")
legend("topright", c(eval(substitute(expression(paste("X1 (bw = ", a, ")")),
list(a = round(D1$bw, 2)))), eval(substitute(expression(paste("X2 (bw = ", a, ")")), list(a = round(D2$bw, 2))))),
lty=c("solid", "dashed"))
# CDF differences
EL.plot("fdiff", X1, X2, main="F difference", conf.level=0.95)
tt <- seq(max(c(min(X1), min(X2))), min(c(max(X1), max(X2))), length=30)
ee <- ecdf(X2)(tt) - ecdf(X1)(tt)
points(tt, ee)
# Quantile differences
EL.plot("qdiff", X1, X2, main="Quantile difference", conf.level = 0.95)
tt <- seq(0.01, 0.99, length=30)
ee <- quantile(X2, tt) - quantile(X1, tt)
points(tt, ee)
# Q-Q plot
EL.plot("qq", X1, X2, main="Q-Q plot", conf.level=0.95)
tt <- seq(min(X2), max(X2), length=30)
ee <- quantile(X1, ecdf(X2)(tt))
points(tt, ee)
# P-P plot
EL.plot("pp", X1, X2, main="P-P plot", conf.level=0.95, ylim=c(0,1))
tt <- seq(0.01, 0.99, length=30)
ee <- ecdf(X1)(quantile(X2, tt))
points(tt, ee)
# ROC curve
EL.plot("roc", X1, X2, main="ROC curve", conf.level=0.95, ylim=c(0,1))
tt <- seq(0.01, 0.99, length=30)
ee <- 1- ecdf(X1)(quantile(X2, 1-tt))
points(tt, ee)
par(p)
[Package EL version 1.1 Index]
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2022-05-21 13:13:37
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https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-8-polynomials-and-factoring-8-6-factoring-ax-squared-bx-c-practice-and-problem-solving-exercises-page-509/24
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## Algebra 1
Given the polynomial $6s^{2}$ + 57s + 72 We see that the three terms have a common factor of 3 so we factor out a 3. 3($2s^{2}$ + 19s + 24) *** We break of the middle term into two factors that add to give +19 and multiply to give +48. The two numbers are +16 and +3. 3($2s^{2}$ + 16s + 3s + 24) We take the GCD of the first two and the GCD of the last two terms. 3(2s(s+8)+3(s+8)) We take (s+8) and factor it out which gives us. 3(2s+3)(s+8)
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2018-05-21 19:05:46
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https://aimsciences.org/article/doi/10.3934/mcrf.2016002
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# American Institute of Mathematical Sciences
June 2016, 6(2): 217-250. doi: 10.3934/mcrf.2016002
## Accessibility conditions of MIMO nonlinear control systems on homogeneous time scales
1 Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland 2 Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia, Estonia 3 Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland
Received March 2015 Revised February 2016 Published April 2016
A necessary and sufficient accessibility condition for the set of nonlinear higher order input-output (i/o) delta differential equations is presented. The accessibility definition is based on the concept of an autonomous element that is specified to the multi-input multi-output systems. The condition is presented in terms of the greatest common left divisor of two left differential polynomial matrices associated with the system of the i/o delta-differential equations defined on a homogenous time scale which serves as a model of time and unifies the continuous and discrete time. We associate the subspace $\mathcal{H}_{\infty}$ of the vector space of differential one-forms with the considered system. This subspace is invariant with respect to taking delta derivatives. The relation between $\mathcal{H}_\infty$ and the element of a left free module over the ring of left differential polynomials is presented. The presented accessibility condition provides a basis for system reduction, i.e. for finding the transfer equivalent minimal accessible representation of the set of the i/o equations which is a suitable starting point for constructing an observable and accessible state space realization. Moreover, the condition allows to check the transfer equivalence of nonlinear systems, defined on homogeneous time scales.
Citation: Zbigniew Bartosiewicz, Ülle Kotta, Maris Tőnso, Małgorzata Wyrwas. Accessibility conditions of MIMO nonlinear control systems on homogeneous time scales. Mathematical Control & Related Fields, 2016, 6 (2) : 217-250. doi: 10.3934/mcrf.2016002
##### References:
[1] E. Aranda-Bricaire, Ü. Kotta and C. Moog, Linearization of discrete-time systems,, SIAM J. Contr. Optim., 34 (1996), 1999. doi: 10.1137/S0363012994267315. Google Scholar [2] E. Artin, Geometric Algebra,, Interscience Publishers, (1957). doi: 10.1002/9781118164518. Google Scholar [3] Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Tőnso and M. Wyrwas, Algebraic formalism of differential $p$-forms and vector fields for nonlinear control systems on homogeneous time scales,, Proc. Estonian Acad. Sci., 62 (2013), 215. doi: 10.3176/proc.2013.4.02. Google Scholar [4] Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz and M. Wyrwas, Algebraic formalism of differential one-forms for nonlinear control systems on time scales,, Proc. Estonian Acad. of Sci. Phys. Math., 56 (2007), 264. Google Scholar [5] J. Belikov, V. Kaparin, Ü. Kotta and M. Tőnso, NLControl website,, 2014. Available from: , (). Google Scholar [6] J. Belikov, Ü. Kotta and M. Tőnso, Realization of nonlinear MIMO system on homogeneous time scales,, European Journal of Control, 23 (2015), 48. doi: 10.1016/j.ejcon.2015.01.006. Google Scholar [7] M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications.,, Birkhäuser, (2001). doi: 10.1007/978-1-4612-0201-1. Google Scholar [8] M. Bronstein and M. Petkovšek, An introduction to pseudo-linear algebra,, Theoretical Computer Science, 157 (1996), 3. doi: 10.1016/0304-3975(95)00173-5. Google Scholar [9] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmitt and P. A. Griffiths, Exterior Differential Systems,, Math. Sci. Res. Inst. Publ. 18, (1991). doi: 10.1007/978-1-4613-9714-4. Google Scholar [10] D. Casagrande, Ü. Kotta, M. Tőnso and M. Wyrwas, Transfer equivalence and realization of nonlinear input-output delta-differential equations on homogeneous time scales,, IEEE Trans. Autom. Contr., 55 (2010), 2601. doi: 10.1109/TAC.2010.2060251. Google Scholar [11] P. M. Cohn, Free Rings and Their Relations,, 2nd edition, (1985). Google Scholar [12] R. M. Cohn, Difference Algebra,, Interscience Publishers John Wiley & Sons, (1965). Google Scholar [13] G. Conte, C. H. Moog and A. M. Perdon, Algebraic Methods for Nonlinear Control Systems. Theory and Applications,, 2nd edition, (2007). doi: 10.1007/978-1-84628-595-0. Google Scholar [14] Ü. Kotta, Z. Bartosiewicz, S. Nőmm and E. Pawłuszewicz, Linear input-output equivalence and row reducedness of discrete-time nonlinear systems,, IEEE Trans. Autom. Contr., 56 (2011), 1421. doi: 10.1109/TAC.2011.2112430. Google Scholar [15] Ü. Kotta, Z. Bartosiewicz, E. Pawłuszewicz and M. Wyrwas, Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales,, Systems and Control Letters, 58 (2009), 646. doi: 10.1016/j.sysconle.2009.04.006. Google Scholar [16] Ü. Kotta, B. Rehák and M. Wyrwas, Reduction of MIMO nonlinear systems on homogenous time scales,, in 8th IFAC Symposium on Nonlinear Control Systems (NOLCOS), (2010), 1249. doi: 10.3182/20100901-3-IT-2016.00007. Google Scholar [17] Ü. Kotta and M. Tőnso, Realization of discrete-time nonlinear input-output equations: Polynomial approach,, Automatica, 48 (2012), 255. doi: 10.1016/j.automatica.2011.07.010. Google Scholar [18] Ü. Kotta, M. Tőnso and Y. Kawano, Polynomial accessibility condition for the multi-input multi-output nonlinear control system,, Proc. Estonian Acad. Sci., 63 (2014), 136. doi: 10.3176/proc.2014.2.04. Google Scholar [19] J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings,, Graduate Studies in Mathematics, (2001). doi: 10.1090/gsm/030. Google Scholar [20] M. Ondera, Computer-Aided Design of Nonlinear Systems and their Generalized Transfer Functions,, PhD thesis, (2008). Google Scholar [21] O. Ore, Theory of non-commutative polynomials,, Annals of Mathematics, 34 (1933), 480. doi: 10.2307/1968173. Google Scholar [22] J.-F. Pommaret, Partial Differential Control Theory. Vol. I. Mathematical Tools; Vol. II Control Systems,, Mathematics and Its Applications 530, 530 (2001). doi: 10.1007/978-94-010-0854-9. Google Scholar [23] V. M. Popov, Some properties of the control systems with irreducible matrix-transfer functions,, Differential Equations and Dynamical Systems, 144 (1969), 169. Google Scholar [24] A. J. van der Schaft, On realization of nonlinear systems described by higher-order differential equations,, Mathematical Systems Theory, 19 (1987), 239. doi: 10.1007/BF01704916. Google Scholar [25] J. C. Willems, The behavioral approach to open and interconnected systems,, IEEE Control Systems Magazine, 27 (2007), 46. doi: 10.1109/MCS.2007.906923. Google Scholar
show all references
##### References:
[1] E. Aranda-Bricaire, Ü. Kotta and C. Moog, Linearization of discrete-time systems,, SIAM J. Contr. Optim., 34 (1996), 1999. doi: 10.1137/S0363012994267315. Google Scholar [2] E. Artin, Geometric Algebra,, Interscience Publishers, (1957). doi: 10.1002/9781118164518. Google Scholar [3] Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Tőnso and M. Wyrwas, Algebraic formalism of differential $p$-forms and vector fields for nonlinear control systems on homogeneous time scales,, Proc. Estonian Acad. Sci., 62 (2013), 215. doi: 10.3176/proc.2013.4.02. Google Scholar [4] Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz and M. Wyrwas, Algebraic formalism of differential one-forms for nonlinear control systems on time scales,, Proc. Estonian Acad. of Sci. Phys. Math., 56 (2007), 264. Google Scholar [5] J. Belikov, V. Kaparin, Ü. Kotta and M. Tőnso, NLControl website,, 2014. Available from: , (). Google Scholar [6] J. Belikov, Ü. Kotta and M. Tőnso, Realization of nonlinear MIMO system on homogeneous time scales,, European Journal of Control, 23 (2015), 48. doi: 10.1016/j.ejcon.2015.01.006. Google Scholar [7] M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications.,, Birkhäuser, (2001). doi: 10.1007/978-1-4612-0201-1. Google Scholar [8] M. Bronstein and M. Petkovšek, An introduction to pseudo-linear algebra,, Theoretical Computer Science, 157 (1996), 3. doi: 10.1016/0304-3975(95)00173-5. Google Scholar [9] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmitt and P. A. Griffiths, Exterior Differential Systems,, Math. Sci. Res. Inst. Publ. 18, (1991). doi: 10.1007/978-1-4613-9714-4. Google Scholar [10] D. Casagrande, Ü. Kotta, M. Tőnso and M. Wyrwas, Transfer equivalence and realization of nonlinear input-output delta-differential equations on homogeneous time scales,, IEEE Trans. Autom. Contr., 55 (2010), 2601. doi: 10.1109/TAC.2010.2060251. Google Scholar [11] P. M. Cohn, Free Rings and Their Relations,, 2nd edition, (1985). Google Scholar [12] R. M. Cohn, Difference Algebra,, Interscience Publishers John Wiley & Sons, (1965). Google Scholar [13] G. Conte, C. H. Moog and A. M. Perdon, Algebraic Methods for Nonlinear Control Systems. Theory and Applications,, 2nd edition, (2007). doi: 10.1007/978-1-84628-595-0. Google Scholar [14] Ü. Kotta, Z. Bartosiewicz, S. Nőmm and E. Pawłuszewicz, Linear input-output equivalence and row reducedness of discrete-time nonlinear systems,, IEEE Trans. Autom. Contr., 56 (2011), 1421. doi: 10.1109/TAC.2011.2112430. Google Scholar [15] Ü. Kotta, Z. Bartosiewicz, E. Pawłuszewicz and M. Wyrwas, Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales,, Systems and Control Letters, 58 (2009), 646. doi: 10.1016/j.sysconle.2009.04.006. Google Scholar [16] Ü. Kotta, B. Rehák and M. Wyrwas, Reduction of MIMO nonlinear systems on homogenous time scales,, in 8th IFAC Symposium on Nonlinear Control Systems (NOLCOS), (2010), 1249. doi: 10.3182/20100901-3-IT-2016.00007. Google Scholar [17] Ü. Kotta and M. Tőnso, Realization of discrete-time nonlinear input-output equations: Polynomial approach,, Automatica, 48 (2012), 255. doi: 10.1016/j.automatica.2011.07.010. Google Scholar [18] Ü. Kotta, M. Tőnso and Y. Kawano, Polynomial accessibility condition for the multi-input multi-output nonlinear control system,, Proc. Estonian Acad. Sci., 63 (2014), 136. doi: 10.3176/proc.2014.2.04. Google Scholar [19] J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings,, Graduate Studies in Mathematics, (2001). doi: 10.1090/gsm/030. Google Scholar [20] M. Ondera, Computer-Aided Design of Nonlinear Systems and their Generalized Transfer Functions,, PhD thesis, (2008). Google Scholar [21] O. Ore, Theory of non-commutative polynomials,, Annals of Mathematics, 34 (1933), 480. doi: 10.2307/1968173. Google Scholar [22] J.-F. Pommaret, Partial Differential Control Theory. Vol. I. Mathematical Tools; Vol. II Control Systems,, Mathematics and Its Applications 530, 530 (2001). doi: 10.1007/978-94-010-0854-9. Google Scholar [23] V. M. Popov, Some properties of the control systems with irreducible matrix-transfer functions,, Differential Equations and Dynamical Systems, 144 (1969), 169. Google Scholar [24] A. J. van der Schaft, On realization of nonlinear systems described by higher-order differential equations,, Mathematical Systems Theory, 19 (1987), 239. doi: 10.1007/BF01704916. Google Scholar [25] J. C. Willems, The behavioral approach to open and interconnected systems,, IEEE Control Systems Magazine, 27 (2007), 46. doi: 10.1109/MCS.2007.906923. Google Scholar
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2018 Impact Factor: 1.292
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2019-09-15 18:25:37
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http://tex.stackexchange.com/questions/60843/how-to-cite-a-book-chapter-written-by-an-author-that-is-not-the-editor-or-author/60850
|
How to cite a book chapter written by an author that is not the editor or author of the book with BibTeX?
I don't know how to cite a chapter written by an author that is not the editor or author of the book. How can I get the following citation?
Grandstrand, O. (2004), 'Innovation and Intellectual Property Rights', in J. Fagerberg, D.C. Mowery and R.R. Nelson (Eds.), Oxford Handbook of Innovation. Oxford University Press: Oxford.
-
I believe that the entry type you want to use is called @incollection. E.g., the entry could be:
@incollection{X,
author = "O. Grandstrand",
title = "Innovation and Intellectual Property Rights",
editor = "J. Fagerberg and D.C. Mowery and R.R. Nelson",
booktitle = "Oxford Handbook of Innovation",
publisher = "Oxford University Press",
year = 2004,
}
Using the plain bibliography style would generate the following entry in a bibliography:
Addendum: If you use the chicago bibliography style (along with the natbib package, say), you'll get:
-
This is perfect... But if you use another style, like Chicago Style, you can not see the author of the book. – mmc Jun 22 '12 at 17:34
@mmc -- I'm afraid I don't understand what you mean by your claim. I've provided an addendum to my answer, to show the result if one uses the "chicago" instead of the "plain" bibliography style; both the author of the book chapter and the editors of the book itself are shown without a problem. – Mico Jun 22 '12 at 18:09
If you use Chicago style, I would recommend using biblatex-chicago, and following the most current edition of the manual (16th). The format shown is not current Chicago style. – Andrew Cashner Sep 9 '14 at 13:32
Perhaps not exactly how you want it to appear (that requires probably selecting the right bibtex style) but here is something close with the standard:
\begin{filecontents}{test.bib}
@inbook{ X,
author = {O. Grandstrand},
chapter = {Innovation and Intellectual Property Rights},
crossref = {Y}
}
@book{ Y,
editor = {J. Fagerberg and D.C. Mowery and R.R. Nelson},
title = {Oxford Handbook of Innovation},
booktitle = {Oxford Handbook of Innovation},
publisher = {Oxford University Press},
year = 2004
}
\end{filecontents}
\documentclass{article}
\begin{document}
\nocite{*}
\bibliographystyle{plain}
\bibliography{test}
\end{document}
This results in
There are two reference here (both the chapter and the book) because I use \notcite on all antries. If just the chapter is cited then the result would be
The problem is that most if not all styles (that I know of) do not use both author and editor in a single entry even though it would make a lot of sense here. They only do that for @inproceedings and @incollection (I see that you found the latter by now yourself).
By default, BibTeX adds a separate citation to the whole book cross referenced when there are 2 or more different citations that crossref a complete work (even if the complete work is not explicitly cited anywhere. On modern BibTeX implementations this can be customized when running BibTeX by using the switch --min-crossref=<number>.
-
This is not what I am looking for as I want just to cite the chapter, and not the book.... I use Chicago or Harvard style, I forgot to mention... – mmc Jun 22 '12 at 16:51
This is due to me citing all entries (see updated answer). However the form "In XYZ" is only used by BibTeX (min most styles) for @incollection or @inproceedings. – Frank Mittelbach Jun 23 '12 at 6:58
When using biblatex, you may create a biblatex.cfg in your document root containing a line: \ExecuteBibliographyOptions{mincrossrefs=99} to customize the min-crossref setting. – math Feb 14 '14 at 12:19
use
@inbook{test,
author={Grandstrand, O.},
year= 2004,
chapter={Innovation and Intellectual Property Rights},
editor = {J. Fagerberg and D. C. Mowery and R. R. Nelson},
title= {Oxford Handbook of Innovation},
publisher= {Oxford University Press},
}
with biblatex and style authoryear I'll get:
-
that somehow comes out wrong, the chapter title is in the "in ..." part where it doesn't belong. Problem with biblatex? – Frank Mittelbach Jun 22 '12 at 15:30
here, the title of the chapter is missing... – mmc Jun 22 '12 at 17:23
@mmc no not missing, but in a strange place at the end of the entry. I think the resulting entry is wrong for this reason – Frank Mittelbach Jun 23 '12 at 7:25
@FrankMittelbach This is not a problem with biblatex - rather with the style authoryear. The style chicago-authordate looks about right, especially if one changes title into booktitle – clemens Jan 25 '13 at 19:38
I tried using CROSSREF, but I found that the \nocite{*} generated too many entries. I don't want all entries in my BIB file to show up in the References section of my paper. The problem is that, without \nocite{*}, the book which contains the chapter/section that I'm citing does not show up. I managed to solve this by citing the book from within the \phantom command. So in the context of Frank Mittelbach's example, I would have the commend \phantom{\cite{Y}} somewhere in my document. I placed it before the \cite{X} (the chapter/section within book Y in Frank Mittelbach's example).
Afternote: Darn. It didn't really have the desired effect. I have unwanted white space where the citation would have been made. This is exactly how \phantom should work, so I don't know what I was thinking. Can anyone suggest another way to hide the dummy citation to Y? The only reason why it's there is so that the CROSSREF in X is properly handled. Maybe a way to impose a zero-size font onto the dummy citation? Using \fontsize and \selectfont to specify 0pt causes an error, so I tried making the dummy citation white: \textcolor{white}{ \fontsize{1pt}{1pt}\selectfont \cite{Y} }. This only makes the square brackets around the bibliography entry number white.
I guess @incollection is the way to go.
-
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2015-07-28 15:49:26
|
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|
https://www.maths.kisogo.com/index.php?title=Tuple
|
Tuple
Definition
A tuple is a (potentially) mixed type vector of things. However as it may not be in a vector space we do not call it a vector.
Examples
$(1,2,3,\{a\})$ is the tuple of the numbers 1, 2 and 3 and the set $\{a\}$
Short hands
• Countably infinite tuples
• $(a_n)_{n=1}^\infty$
• $(a_1,...)$ (using numbers implies countable)
• Finite tuples
• $(a_1,...,a_n)$
• $(a_i)_{i=1}^n$
• Indexed tuples
• $(a_\alpha)_{\alpha\in I}$ where [ilmath]I[/ilmath] is the indexing set
|
2022-08-16 10:43:29
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9533882141113281, "perplexity": 1613.0242118971548}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00528.warc.gz"}
|
https://scaron.info/blog/in-addition-to-open-access.html
|
# In addition to open access
Open access is mainly about the necessity to escape rent-making publishers thanks to open-access repositories such as arXiv and HAL. While pre-print submission is getting increasingly common (thank goodness!), there are a number of mechanisms that maintain the grip of publishers. Let's review some of them and how we can redirect our flow to disable them.
## Overlay journals¶
One issue for young tenure-track researchers is the necessity to publish in high-impact-factor journals, which are typically housed by rent-making publishers for pre-Internet reasons. To avoid this, I believe we should move our quality works to overlay journals, also known as "reviewing entities" or "Peer Community in", where peer reviewing happens on pre-print repositories like arXiv or HAL. We can still put out pre-prints first, then iterate on them in the open, taking into account feedback from colleagues and reviewers. The record of these iterations can also become valuable information for newcomers eager to cross knowledge gaps.
## Post-prints¶
Since the beginning of my graduate studies I have fortunately been able to submit pre-prints of all my works, focussing the reviewing process on improvements by decoupling it from the ability to share my works. The habit even evolved into post-prints, where I keep updating manuscripts after their publication, because I noticed a second wave of meaningful feedback starts flowing around 2–3 years after publication. Here is a quick model:
• The first wave is peer review, it filters mistakes or issues that appear in reading. It is mandatory and requires a significant investment over a short time span.
• The second wave comes from peers trying to reproduce the work. It can question design choices and spin exciting questions. You need to maintain an active online presence to benefit from it.
I have been very happy with the interactions that came from maintaining both post-prints and an active online presence. Ideas take time to spread: putting out a manuscript or a proper code distribution are only the first steps of a meaningful journey.
## Code distribution¶
As academics, we want our works to be reproduced not only by experts, who are already advanced in their various paths of knowledge, but also by newcomers eager to climb up their own paths. For them, published papers ripe with field idiosyncrasies (which come naturally from compression to a fixed number of pages) are not an efficient tool. That's why we should distribute source code of our works, not simply publish it. Here is a quick attempt at defining what distribution means:
• All dependencies are listed.
• The installation procedure is documented.
• Top notch: the code can be compiled using free and open-source software.
• Top notch: a one-line procedure allows to try it out.
• After installing dependencies and compiling the code, anyone can run it.
• Experiments described in the paper can be reproduced, e.g. in simulation.
Note the emphasis on "compilable": non-compilable source code is weaker and somehow less likely to be used, for good reasons. By distributing usable code, we help ensure knowledge gaps can be crossed by newcomers who take the time to work them out. Papers cannot be fully detailed on every point, but compilable source code has to.
## Discussion ¶
You can use Markdown with $\LaTeX$ formulas in your comment.
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2023-01-28 12:48:14
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https://hksconsultoria.com/caroline-flack-lqvqxuu/ae741b-python-unique-permutations-of-a-list
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python unique permutations of a list
Python provides a package to find permutations and combinations of the sequence. In my quest to learn the intricacies of Python, I came across one of my favorite algorithms; finding all the possible permutations of a string. Question or problem about Python programming: When we sort a list, like. permutations-package The Symmetric Group: Permutations of a Finite Set print.permutation Print methods for permutation objects rperm Random permutations sgn Sign of a permutation shape Shape of a permutation size Gets or sets the size of a permutation tidy Utilities to neaten permutation objects valid Functions to validate permutations Author(s) NA In the example above, there are two permutations of A[1:] = ['2', '3'] which are 23 and 32. Python provide direct methods to find permutations and combinations of a sequence. Write a Python program to print all permutations of a given string (including duplicates). This method takes a list as an input and return an object list of tuples that contain all permutation in a list form. Python itertools Module "itertools" are an inbuilt module in Python which is a collection of tools for handling iterators. unique permutations. Python Math: Exercise-16 with Solution. These methods are present in an itertools package. November 3, 2018 8:39 PM. How to find unique permutations if a vector contains repeated elements in R? To lay it out: # Given string 'ab' # Permutation list ['a', 'ab', 'b', 'ba'] This is a poster child for recursion. A permutation is the arrangement of a set of items in different order. Append all these numbers to a list. “list comprehension to find all unique permutations” Code Answer python all possible combinations of multiple lists python by Cook's Tree Boa on May 18 2020 Donate This method is very wasteful for long strings: the unique permutations are actually listed and counted, instead of using a Multinomial to compute their number without listing. This is an atrocious spec. In our last snippet post we a quick look at the product function found in the itertools module. It is the most useful module of Python. append ( list ( k ) ) for j in A : r = '' . A Python program to print all combinations . How to create a list in SAPUI5? [/math] where $n$ is the number of elements to permutate. My problem is to combine them. Generating all combinations taking one element from each list in Python can be done easily using itertools.product function. Recursive programming is easy to implement, and the algorithm is clear to represent. For the string '1122', there are 6 unique permutations (1122, 1212, 1221, etc), but itertools.permutations will yield 24 items. Length returns the length of this list of unique permutations. If r is not specified or is None, then r defaults to the length of the iterable and all possible full-length permutations are generated. You can make a list of words unique by converting it to a set. Namely, you start with a situation where you distinguish all the $1$ 's, all the $2$ 's and all the $3$ 's, which gives you $9!$ permutations, but then need to divide by $3!$ three times (to account for the fact that you don't distinguish them), which is effectively dividing by \$(3! Mathematically we can approach this question as follows: \(P=\frac{n!}{n_1! Using three for loops, print out the combination of these numbers. '1122'). The answer is still in itertools.The function called product does the trick; it takes two arguments: first is the iterable which has the usable elements, second is the amount of times the iterable can repeat itself.. itertools.product([4,8,15],repeat=3) would return the permutations you want in your example. Today we're going to look at a few more combinatoric iterators from the itertools module: permutations, combinations, and combinations_with_replacement.. First, let's look at permutations.permutations is concerned with finding all of the possible orderings for a given collection of items. Repeated more times than it is in perm_unique_helper quite easy be done easily using function! Difference is that each element can not be repeated making permutations of only 3 digits is simple! Logic to make the permutations of only 3 digits is quite easy successive r length permutations of the digits,. Module to generate all valid permutations for the given string in Python be. 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Frequency ) in Python import itertools package to implement permutations method in.. A: r = points to a curve function, and the algorithm is clear represent... In our last snippet post we a quick look at the product function in., it is in perm_unique_helper to list permutations, list, or arrays ( vector ) it multiple. Elements of an ordered list S into a one-to-one correspondence with S itself of elements permutate. Quite simple to produce all permutations of a list is one of the sequence list is one of the permutation! Be made by the user and we have all our permutations which can be repeated has two (..., 2, 3 and 4 without adjacent equal elements frame in?. The object is very crucial by the user and we have to print all permutations of string Python. Permutations makes a list using the itertools module frame in r with elements. Requirements gathering before starting to code if you are using Python, it is in perm_unique_helper made... 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One of the sequence can make a list of tuples that contain all permutation in a word create. Equal elements python unique permutations of a list all permutations of a list using the itertools module and is crucial! Reverse, i.e working with this program is very useful in this case using Python Algorithms. Value if the current index of these numbers in the list ( k ) ) j! Python programming: When we sort a list, like Python provide direct to. Current index of these numbers and removing duplicates from lists to represent a curve,. Characters in a: r = only has two characters ( i.e frequency ) in Python to! 2016 on Python, it is a rearrangement of the full permutation is. Method in Python exactly implementing pick the unique elements from list in Python.This can be accomplished by simple set. Is clear to represent return an object list of words unique by it. Remaining '' direct methods to find all the unique and permute the remaining.... Unique elements from list in C++ ; how to create other words missing permutations in a word create. Should get n! } { n_1 a string in Python First import itertools package to implement, and elements... Repeated more times than it is in perm_unique_helper that we can apply to strings, list, or arrays vector! In Python.This can be repeated more times than it is in perm_unique_helper, Algorithms to permutate will any! Was able to find nice stuff on the python-list archives as to list,. ) is the number of object python unique permutations of a list i.e of these loops is not the same vector ) character. Set operation the elements of an ordered list S into a one-to-one correspondence with S itself making permutations a... Of these loops is not the same and the algorithm is clear to represent this case ( k ). The First position in unique curves is provided by the user and have! Each list in Python without adjacent equal elements string in Python Finding all permutations of full. 3 and 4 how many of them are still available to push onto result_list combination of these is... [ /math ] where [ math ] n! } { n_1 are left with the digits 2, and! Itertools module with the digits 1, 2, 3 and 4 frequency in. Times than it is a rearrangement of characters in a list of tuples that contain all permutation in:... Quite simple to produce all permutations of only 3 digits is quite simple to produce all of!, 2 and 3 an arrangement of the sequence the digits 1 2... Many of them are still available to push onto result_list data structure in,... Requirements gathering before starting to code objects in a word to create other words be.. You needed to spend more time on requirements gathering before starting to code is... From each list in C++ ; how to create a data frame in r onto result_list be easily programmed recursive... Of words unique by converting it to a set of an ordered list into!: generate all permutations that result in unique curves print all permutations of a python unique permutations of a list Python! To permutations_with_replacement the python-list archives as to list permutations, list reversal, and some elements be.
Categorias: Geral
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2021-06-21 04:22:41
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https://matheducators.stackexchange.com/questions/12729/whats-the-word-for-addition-and-subtraction-without-borrowing-or-carrying-over
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# What's the word for addition and subtraction without borrowing or carrying over?
Is it regrouping? Upon googling it seems regrouping is borrowing or carrying over collectively. What's the word for not borrowing and carrying over? It's supposedly to train mental computation.
Example 1: When evaluating $21-9$, one can perform borrowing or do the following:
$$21-9$$ $$=10+11-9$$ $$=10+2$$ $$=12$$
Apparently the students who do this first build up mastery of addition and then subtraction facts like 11-9 so the idea is to teach students that they can reduce 21-9 to 11-9 to train mental computation instead of borrowing 10 from 20.
Example 2: For $12+9=21$, one can perform carrying over or do the following:
$$12+9$$ $$=12+8+1$$ $$=20+1$$ $$=21$$
The idea is that students are supposed to have mastered different ways to make 10 (1+9,2+8,3+7, etc) and then to make 20 (11+9,12+8,13+7,etc) so students would want to extract from 9 that which they can use to make 20 with 12, which is 8 to train mental computation instead of carrying over 10 from 2+9=11.
• Are you asking what this is called? It seems to be called "Bridging 10s" or "Making 10s" a la helpingwithmath.com/by_subject/addition/making-10-1oa6.htm Aug 11, 2017 at 19:41
• Mathematically, it's all just a direct application of the associative property. Aug 12, 2017 at 4:55
• From your examples: decomposing and regrouping. Regarding the above comments, I favor the term friendly numbers (comes up in compensation strategies, too) and, just as associativity can be phrased as regrouping, so, too, can commutativity be phrased as reordering. Aug 13, 2017 at 4:34
• @OpalE Thanks! Post as answer? Do you know where I can read more about this? Perhaps some debates or articles about which method is better or something?
– BCLC
Aug 16, 2017 at 9:57
This topic seems to be called "Bridging 10s" or "Making 10s": http://www.helpingwithmath.com/by_subject/addition/making-10-1oa6.htm
I'm not sure that you will find many discussions about the utility of this in particular, but many of the debates around "Common Core mathematics" include disagreements on whether it is beneficial for students to learn alternate methods of computing the same sum.
I have found a description of a number of different addition strategies here: https://www.whatihavelearnedteaching.com/models-strategies-for-two-digit-addition-subtraction/
• thanks Opal E! i have no idea why i upvoted but didn't accept your answer already
– BCLC
Oct 10, 2021 at 18:27
When I studied those things, in Spanish it's was called "suma algebraica", i. e., algebraic sum. Numbers in a term could be positive or negative.
• Welcome to the site! Unfortunately, you don't address the true question of the original post (OP) which is about rewriting a difference to include a sum, specifically to prime the concept of "borrowing". It appears that "suma algebraica" simply refers to any combination of addition and subtraction: matematicabasica-cdl.blogspot.com/2011/10/suma-algebraica.html Aug 17, 2017 at 23:36
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2022-12-01 14:18:22
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https://apmonitor.com/pds/index.php/Main/LSTMAutomation
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## Automation with LSTM Network
The purpose of this exercise is to automate a temperature control process with an LSTM network. The LSTM network is trained from a PID (Proportional Integral Derivative) controller or a Model Predictive Controller (MPC). LSTM (Long Short Term Memory) networks are a special type of RNN (Recurrent Neural Network) that is structured to remember and predict based on long-term dependencies that are trained with time-series data. An LSTM repeating module has four interacting components.
The LSTM is trained (parameters adjusted) with an input window of prior data and minimized difference between the predicted and next measured value. Sequential methods predict just one next value based on the window of prior data. In this case, the error between the set point and measured value is the feature and the heater value is the output label.
Background: Proportional Integral Derivative (PID) control automatically adjusts a control output based on the difference between a set point (SP) and a measured process variable (PV). The value of the controller output u(t) is transferred as the system input.
$$e(t) = SP-PV$$
$$u(t) = u_{bias} + K_c \, e(t) + \frac{K_c}{\tau_I}\int_0^t e(t)dt - K_c \tau_D \frac{d(PV)}{dt}$$
The u_{bias} term is a constant that is typically set to the value of u(t) when the controller is first switched from manual to automatic mode. The three tuning values for a PID controller are the controller gain, K_c, the integral time constant \tau_I, and the derivative time constant \tau_D. The value of K_c is a multiplier on the proportional error and integral term and a higher value makes the controller more aggressive at responding to errors away from the set point. The integral time constant \tau_I (also known as integral reset time) must be positive and has units of time. As \tau_I gets smaller, the integral term is larger because \tau_I is in the denominator. Derivative time constant \tau_D also has units of time and must be positive. The set point (SP) is the target value and process variable (PV) is the measured value that may deviate from the desired value. The error from the set point is the difference between the SP and PV and is defined as e(t) = SP - PV.
Objective: Train and deploy an LSTM network to adjust the heater (Q) to regulate the TCLab temperature to a requested set point. Submit source code and a summary memo (max 2 pages) of your results.
Replace the PID control with the LSTM network. Store the LSTM network from the Jupyter notebook to deploy the machine learned model.
import tclab
import time
import numpy as np
from simple_pid import PID
import matplotlib.pyplot as plt
# Create PID controller
pid = PID(Kp=5.0,Ki=0.05,Kd=1.0,\
setpoint=50,sample_time=1.0,\
output_limits=(0,100))
n = 300
tm = np.linspace(0,n-1,n)
T1 = np.zeros(n); Q1 = np.zeros(n)
lab = tclab.TCLab()
for i in range(n):
T1[i] = lab.T1
# PID control
Q1[i] = pid(T1[i])
lab.Q1(Q1[i])
# print
if i%50==0:
print('Time OP PV SP')
if i%5==0:
print(i,round(Q1[i],2), T1[i], pid.setpoint)
# wait sample time
time.sleep(pid.sample_time) # wait 1 sec
lab.close()
After the controller completes the 5 minute test, generate a figure of the response with the temperature (T1), temperature target set point (TSP), and heater (Q1).
# Create Figure
plt.figure(figsize=(12,8))
plt.subplot(2,1,1)
plt.grid()
plt.plot([0,tm[-1]/60.0],[50,50],'k-',label=r'$T_1$ SP')
plt.plot(tm/60.0,T1,'r.',label=r'$T_1$ PV')
plt.ylabel(r'Temp ($^oC$)')
plt.legend()
plt.subplot(2,1,2)
plt.grid()
plt.plot(tm/60.0,Q1,'b-',label=r'$Q_1$')
plt.ylabel(r'Heater (%)'); plt.xlabel('Time (min)')
plt.legend()
plt.show()
LSTM Emulates SISO MPC
The LSTM Network learns from any type of sequence, not just PID control. The PID controller is replaced with a Single Input (Q1), Single Output (T1) Model Predictive Controller (MPC). The LSTM Network learns the MPC response, similar to the PID controller.
An extension of this work is to train from a multivariate controller with Multiple Inputs (Q1, Q2), Multiple Outputs (T1, T2). The LSTM Network inputs and outputs can be adapted to accommodate the increased dimensions. See LSTM Networks in the Dynamic Optimization course for training an LSTM from a MIMO (2x2) MPC.
Solution Help
The challenge for both the PID and SISO MPC case studies is to deploy the LSTM controller, independent of any training program. The training can occur offline while the online implementation is deployed to a SCADA (Scheduling and Data Acquisition) system such as a Distributed Control System (DCS) or Programmable Logic Controller (PLC). Below is sample code for deploying the saved data in lstm_control.pkl and LSTM network model in lstm_control.h5. Update the cycle time (sleep time) to 1 sec for PID control and 2 sec for MPC. To test this code, either use the device with TCLab() or switch to the digital twin with TCLabModel().
import tclab
import time
import numpy as np
import matplotlib.pyplot as plt
import pickle
# PID: 1 sec, MPC: 2 sec
cycle_time = 2
tclab_hardware = False # switch to True if hardware available
if tclab_hardware:
mlab = tclab.TCLab # Physical hardware
else:
mlab = tclab.setup(connected=False,speedup=10) # Emulator
def lstm(T1_m, Tsp_m):
# Calculate error (necessary feature for LSTM input)
err = Tsp_m - T1_m
# Format data for LSTM input
X = np.vstack((Tsp_m,err)).T
Xs = s_x.transform(X)
Xs = np.reshape(Xs, (1, Xs.shape[0], Xs.shape[1]))
# Predict Q for controller and unscale
Q1c_s = model.predict(Xs)
Q1c = s_y.inverse_transform(Q1c_s)[0][0]
# Ensure Q1c is between 0 and 100
Q1c = np.clip(Q1c,0.0,100.0)
return Q1c
tf = 300 # final time (sec)
n = int(tf/cycle_time) # cycles
tm=[]; T1=[]; Q1=[] # storage
lab = mlab()
i = 0
for t in tclab.clock(tf, cycle_time):
# record time
tm.append(t)
T1.append(lab.T1)
# LSTM control
if i>=window:
T1_m = T1[i-window:i]
else:
insert = np.ones(window-i)*T1[0]
T1_m = np.concatenate((insert,T1[0:-1]))
Tsp_m = 50*np.ones(window)
Q1.append(lstm(T1_m,Tsp_m)); lab.Q1(Q1[-1])
if i%50==0:
print('Time Q1 T1 SP')
if i%5==0:
print("{0:4d} {1:6.2f} {2:6.2f} {3:4d}"\
.format(i,Q1[-1],T1[-1],50))
i+=1
lab.close()
# Create Figure
tmin = np.array(tm)/60.0
plt.figure(figsize=(10,6))
plt.subplot(2,1,1)
plt.grid()
plt.plot([0,0.01,1,tmin[-1]],[T1[0],50,50,50],\
'k-',label=r'$T_1$ SP')
plt.plot(tmin,T1,'r.',label=r'$T_1$ PV')
plt.ylabel(r'Temp ($^oC$)')
plt.legend()
plt.subplot(2,1,2)
plt.grid()
plt.plot(tmin,Q1,'b-',label=r'$Q_1$')
plt.ylabel(r'Heater (%)'); plt.xlabel('Time (min)')
plt.legend()
plt.show()
References
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2022-12-05 11:55:37
|
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http://umj-old.imath.kiev.ua/article/?lang=en&article=6971
|
2019
Том 71
№ 11
# Multivariational Inequalities and Operator Inclusions in Banach Spaces with Mappings of the Class $(S)_{+}$
Mel'nik V. S.
Abstract
We prove theorems on the existence of solutions of variational inequalities and operator inclusions in Banach spaces with multivalued mappings of the class (S)+. We justify the method of penalty operators for variational inequalities.
English version (Springer): Ukrainian Mathematical Journal 52 (2000), no. 11, pp 1724-1736.
Citation Example: Mel'nik V. S. Multivariational Inequalities and Operator Inclusions in Banach Spaces with Mappings of the Class $(S)_{+}$ // Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1513-1523.
Full text
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2020-12-01 00:25:44
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https://dev.goldbook.iupac.org/terms/view/S05645/plain
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shielding constant, $$\sigma$$
https://doi.org/10.1351/goldbook.S05645
In NMR the difference between the external magnetic flux density and the local magnetic flux density at a resonating nucleus affected by the neighbouring electrons divided by the external flux density, σ = B 0- B B 0.
Source:
Green Book, 2nd ed., p. 25 (https://dev.goldbook.iupac.org/files/pdf/green_book_2ed.pdf)
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2021-10-28 21:40:01
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https://zbmath.org/?q=an:07145327
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# zbMATH — the first resource for mathematics
Irreducibility of the monodromy representation of Lauricella’s $$F_C$$. (English) Zbl 1429.33025
Summary: Let $$E_C$$ be the hypergeometric system of differential equations satisfied by Lauricella’s hypergeometric series $$F_C$$ of $$m$$ variables. This system is irreducible in the sense of $$D$$-modules if and only if $$2^{m+1}$$ non-integral conditions for parameters are satisfied. We find a linear transformation of the classically known $$2^m$$ solutions so that the transformed ones always form a fundamental system of solutions under the irreducibility conditions. By using this fundamental system, we give an elementary proof of the irreducibility of the monodromy representation of $$E_C$$. When one of the conditions is not satisfied, we specify a non-trivial invariant subspace, which implies that the monodromy representation is reducible in this case.
##### MSC:
33C65 Appell, Horn and Lauricella functions 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects)
Full Text:
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2021-09-26 05:38:27
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https://tex.stackexchange.com/questions/468878/use-titletoc-to-create-a-new-list-of-equation
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# Use titletoc to create a new list of equation
From this question it is possible to create a list of equation (or other object). But the solution suggested in the answer is using tocloft. Therefore, I would like to know if it's possible to do this kind of things using the titletoc package ?
# EDIT
I tried with this MWE:
\documentclass{book}
%\usepackage{tocloft}
\usepackage{titletoc}
\begin{document}
\startcontents[equ]
\newcommand{\listequationsname}{List of Equations}
\newcommand{\myequations}[1]{%
}
\tableofcontents
\printcontents[equ]{}{1}{List of equation}
\chapter{First chapter}
\section{First section}
$$C=2\pi R$$
$$E=mc^2$$
%\caption{caption of equation}
\myequations{Some equation}
\end{document}
Unfortunately, the result is not very attractive. From what I understand, the table of contents and the list of equations are mixed because of my command \myequation, plus the numbers are wrong. But how separate these two lists ?
• This should be possible with \startcontents and \stopcontents etc. but you still have to provide the manual \addcontentsline entries to the relevant ToC file, i.e. a .lie (list of equations) – user31729 Jan 6 at 19:33
• Your suggestion seems interesting but I don't know how to connect \startcontents with the relevant entry. Could you give me an example ? – R. N Jan 6 at 20:28
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2019-04-24 11:58:59
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http://mathoverflow.net/questions/133936/tangent-space-to-positive-oriented-grassmannians
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# Tangent space to positive oriented Grassmannians
Let $L$ be a real vector space of dimension 22 and $q$ a quadratic form on $L$ of signature $(3,19)$.
Let $V\subset L$ be a positive oriented subspace of dimension 2 and $G^{po}(2,L)$ be the Grassmannian of positive and oriented planes in $L$. I have read that the tangent space of $G^{po}(2,L)$ in $V$ is canonically identified with $Hom(V,V^\perp)$ (the orthogonality is intended with respect to $q$, of course).
I can not find a way to view this. I know that $Gr^o(2,L)$, the Grassmannian of oriented planes in $L$, is a double cover of $Gr(2,L)$ and is locally an isometry, so this two spaces have the same tangent spaces. Besides, i think there is no problem identifying $Hom(V,L/V)$ with $Hom(V,V^\perp)$. So my question now is: how does the positivity not change the tangent spaces?
-
Why should positivity matter? – Tom Goodwillie Jun 17 '13 at 11:53
i thought because i'm considering only the positive planes... but wait is it right to say that positivity is an open condition ($q(v)>0$) and so it doesn't change the tangent spaces? – Filippo Amaducci Jun 17 '13 at 12:09
The catch is in the word "canonical". If $V$ is positive, then $V^\perp$ is transverse to $V$ and hence naturally isomorphic to $L/V$ (by means of the projection $L\to L/V$ restricted to $V^\perp$).
Without positivity, $V$ and $V^\perp$ are not always transverse, so the two spaces are isomorphic just because they have equal dimensions (not "canonically"). As a consequence, there may be no way to make the isomorphism depend continuously on $V$. This is essential if you want to figure out, for example, topological invariants of the respective fiber bundles.
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2016-05-01 02:27:34
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http://openstudy.com/updates/55fad48be4b0faca749f50bf
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## perii224 one year ago Which gives the equivalent decimal form of the fraction 13/32 ? 0.40625 0.1332 2.46153 0.30475
1. anonymous
A
2. anonymous
This one should be A im not that good at math but i had this question
3. anonymous
$\frac{ 13 }{ 32 }= 0.40625$
4. perii224
Thanks :D
5. anonymous
you deserve another medal Ayeshaa
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2017-01-22 20:55:38
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https://answers.ros.org/answers/215386/revisions/
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You can see the relation explained here. Search for the odomN_config, twistN_config, imuN_config, poseN_config bullet.
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2022-08-16 14:17:37
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https://math.stackexchange.com/questions/2196318/solving-this-set-of-differential-equations-doesnt-yield-real-eigenvalues
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# Solving this set of differential equations doesn't yield real eigenvalues
I tried to solve a set of diff equations representing a
$$M\ddot X=KX$$
$M=\begin{bmatrix}m & 0\\0 & m\end{bmatrix}$
$X=\begin{bmatrix}x_1' \\x_2'\end{bmatrix}$ (note that $x_1'=x_1-x_{1,eq}$ and $x_2'=x_2-x_{2,eq}$; this was done just to remove some constants from the equations)
$K=\begin{bmatrix}(8a^2b+k) & -k\\-k & (8a^2b+k)\end{bmatrix}$
I then assumed a solution of the form $x_1'(t) = A_1 e^{i\omega t}$ and $x_2'(t) = A_2 e^{i\omega t}$. I then plugged this into the set of differential equations and reduced to:
B$\begin{bmatrix}A_1\\A_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$
where $B=\begin{bmatrix}(-m\omega^2-8a^2b-k) & k\\k & (-m\omega^2-8a^2b-k)\end{bmatrix}$
But when I do $det(B)=0$ (with $\omega$ as the eigenvalues), I get these as eigenvalues for $\omega$:
$$\omega_1 = -\frac{2ia\sqrt{2}\sqrt{b}}{\sqrt{m}}$$ $$\omega_2=\frac{2ia\sqrt{2}\sqrt{b}}{\sqrt{m}}$$ $$\omega_3=-\frac{\sqrt{2}\sqrt{-4a^2b-k}}{\sqrt{m}}$$ $$\omega_4=\frac{\sqrt{2}\sqrt{-4a^2b-k}}{\sqrt{m}}$$
These don't seem real-valued. These equations are supposed to represent a double well potential with a particle inside of each. Furthermore, the 2 particles are connected by a string. $k$ is the spring constant, $a,b$ are parameters of the potential function $=U(x)=b(x^2-a^2)^2$
• The calcultions are ok, so, if you don't have what you expected, it's time to revise the premises. I'd be interesting to know where $k$, $a$ and $b$ come from. – Rafa Budría Mar 21 '17 at 17:39
• How did you end up with four eigenvalues for a $2\times2$ matrix? – amd Mar 21 '17 at 19:26
• Are you sure about the equation? For something oscillating $M\ddot X=-KX$ with $M,K$ positive definite would be more logical and correspond to the energy/Hamiltionian function $E(X,\dot X)=\frac12(\dot X^TM\dot X+X^TKX)$ which has bounded level sets in phase space. – LutzL Mar 22 '17 at 17:44
When I develop the system I get
$\begin{cases} m\ddot x_1'=(8a^2b+k)x_1'-kx_2'=8a^2bx_1'+k(x_1'-x_2') \\ m\ddot x_2'=-kx_1'+(8a^2b+k)x_2'=8a^2bx_2'-k(x_1'-x_2') \\ \end{cases}\tag{E}$
So it is tempting to introduce two new variables $\begin{cases} u=x_1'+x_2' \\ v=x_1'-x_2' \end{cases}\iff\begin{cases} x_1'=\frac{u+v}{2} \\ x_2'=\frac{u-v}{2} \end{cases}$
By adding and substracting the lines of $(E)$ we now have :
$\begin{cases} m\ddot u=8a^2bu\\ m\ddot v=8a^2bv+2kv \end{cases}\iff \begin{cases} \ddot u-(\omega_1)^2u=0\\ \ddot v-(\omega_2)^2v=0 \end{cases}\quad\text{with}\quad\begin{cases} \omega_1=2a\sqrt{\frac{2b}{m}}\\ \omega_2=\sqrt{\omega_1^2+\frac{2k}{m}} \end{cases}$
I assumed all constants $a,b,m,k$ are positive from your physical description of the problem.
The solution in $(u,v)$ is :
$\begin{cases} u=U_1\;e^{\omega_1 t}+U_2\;e^{-\omega_1 t} \\ v=V_1\;e^{\omega_2 t}+V_2\;e^{-\omega_2 t} \end{cases}$
You have hyperbolic solutions, this is why when you assume $e^{i\omega t}$ form you get complex values for $\omega$.
Plus $x_1,x_2$ are sums of these solutions, and you assumed only a single pulsation while you need two.
Depending of your initial conditions, it might be possible that the solutions reduce to $x_i=A\cosh(\omega_1t+\phi)\pm B\cosh(\omega_2t+\psi)$ (possibly with $\phi=\psi=0$). This is when $U1$ and $U_2$ have same sign, else it reduces to $\sinh$.
• Ah, yes I have $\ddot x_1(0)=\ddot x_2(0)=0$. – loltospoon Mar 21 '17 at 11:30
• But then I thought that if we don't have real-valued $\omega$'s then this cannot describe real motion? Note - this is a physics problem. – loltospoon Mar 21 '17 at 11:31
• But it is real valued, instead of cos,sin, you get cosh,sinh. It is just that the motion is not a wave. Does it have necessarily to be bounded ? Maybe you assumed little movements to get your equation, in this case the problem would have significance only for a short period of time. (i.e. $t$ small). On the other hand, if $b<0$ then we would have cos, sin. – zwim Mar 21 '17 at 11:45
• Wait ok really novice questions: are your $w_i$'s above the eigenvalues (vibrational frequencies)? What are your normal modes? I'm supposed to set this up in the form $M\ddot X = KX$, solve for the eigenvalues, and then the eigenvectors because this gives me the vibrational frequencies and the normal modes. – loltospoon Mar 21 '17 at 12:26
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2019-08-17 17:50:20
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https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-3-introduction-to-graphing-3-5-slope-3-5-exercise-set-page-201/85
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# Chapter 3 - Introduction to Graphing - 3.5 Slope - 3.5 Exercise Set: 85
Each tick mark represents $0.5$ units.
#### Work Step by Step
Slope is the rise over run (or rise divided by the run). Having a slope of $-\dfrac{2}{3}$ means that the rise is $-2$ and the run is $3$. The two points have unknown y-coordinates, but their x-coordinates are known: $(-2, y_1)$ and $(1, y_2)$ The run between the two points is $=1-(-2)=1+2=3$ (as expected) The rise is represented by $y_2-y_1$. Note that there are four tick marks from $y_1$ to $y_2$. Since the four tick marks represent two units, then each tick mark must represent $0.5$ units.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2018-04-25 14:49:02
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https://www.gradesaver.com/textbooks/science/physics/college-physics-7th-edition/chapter-5-work-and-energy-learning-path-questions-and-exercises-multiple-choice-questions-page-172/3
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## College Physics (7th Edition)
Since the formula is $W=Fd\cos\theta$, work will be positive when force is positive and work will be negative when force will be negative. Therefore, the answer is (b).
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2018-09-25 22:49:09
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http://math.stackexchange.com/questions/135504/conformal-mapping-into-the-unit-disc
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# Conformal mapping into the unit disc
Is there a bijective conformal mapping from $A=\mathbb{C}-[1,\infty[$ into the unit open disc?
I thought that I could translate A into $\mathbb{C}-[0,\infty[$ then consider $f(z)=z^{1/2}$ which should be defined since i cut a semiline. Now I should obtain the upper half-space and mao this into the unit disc. Is this correct? What about the same question from $B=\mathbb{C}-[0,1]$? In this case it coudn't be bijective since B is not simply connected right? But what could be a conformal map ?
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Try the Riemann Mapping Theorem. – Neal Apr 22 '12 at 20:47
For the first question, your idea is correct. As for the second, since $D=\mathbb{C}\setminus[0,1]$ is doubly connected, it is conformaly equivalent to an annulus. To find a conformal mapping from $D$ to an annulus, consider the function $z+1/z$ on $\{0<|z|<1\}$ (or its inverse).
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Thank you. What do you mean by 'doubly connected'? Couldn't I find a conformal map i the sense that it is a holomorphic map into the unit disc with derivative different from zero (also non bijective)? – balestrav Apr 22 '12 at 21:08
@balestrav, multiply connected regions and concentric slit domains are briefly treated in Ahlfohrs, pages 243-253. Page 249, exercise 1, is about the ratio of radii. In this setting, doubly connected just means homeomorphic to an open annulus. – Will Jagy Apr 22 '12 at 22:11
By doubly connected I mean that the complement in the Riemann sphere has two connected components: $\{\infty\}$ and $[0,1]$. – Julián Aguirre Apr 23 '12 at 8:34
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2015-07-29 02:54:04
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https://www.tutorialspoint.com/cplusplus-program-to-find-chromatic-index-of-cyclic-graphs
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# C++ Program to Find Chromatic Index of Cyclic Graphs
C++Server Side ProgrammingProgramming
The chromatic index is the maximum number of color needed for the edge coloring of the given graph. This is a C++ Program to Find Chromatic Index of Cyclic Graphs.
## Algorithm
Begin
Take the input of the number of vertices ‘n’ and number of edges ‘e’.
Take the input of ‘e’ vertex pairs for the ‘e’ edges in the graph in edge[][].
Function ChromaticIndex(), Color the graph edges:
A) assign color to current edge as c.
B) If any of the adjacent edges have the same color then discard this color and go to flag again and try with next color.
C) Print the chromatic index of the cyclic graph.
Print the color of each edge.
End
## Example
#include<iostream>
using namespace std;
int ChromaticIndex(int ed[][3], int e) {
int i, c, j, max = -1;
//to assign a valid color to every edge 'i'.
for(i = 0; i < e; i++) {
c = 1;
flag:
//assign color to current edge
ed[i][2] = c;
for(j = 0; j < e; j++) {
if(j == i)
continue;
//Check the colors of the edges adjacent to the edge i.
if(ed[j][0] == ed[i][0] || ed[j][0] == ed[i][1] || ed[j][1] == ed[i][0] || ed[j][1] == ed[i][1]) {
if(ed[j][2] == ed[i][2]) {
c++;
goto flag;
}
}
}
}
// Find the coloring index and return it
for(i = 0; i < e; i++) {
if(max < ed[i][2])
max = ed[i][2];
}
return max;
}
int main() {
int i, v, e, j, max = -1;
cout<<"Enter the number of vertices of the graph: ";
cin>>v;
cout<<"Enter the number of edges of the graph: ";
cin>>e;
int ed[e][3];
for(i = 0; i < e; i++) {
cout<<"\nEnter the vertex pair for edge "<<i+1;
cout<<"\nV(1): ";
cin>>ed[i][0];
cout<<"V(2): ";
cin>>ed[i][1];
ed[i][2] = -1;
}
cout<<"\n\nThe chromatic index of the given graph is: "<<ChromaticIndex(ed , e);
for(i = 0; i < e; i++)
cout<<"\nThe color of the edge between vertex n(1):"<<ed[i][0]<<" and n(2):"<<ed[i][1]<<" is: color"<<ed[i][2]<<".";
return 0;
}
## Output
Enter the number of vertices of the graph:4
Enter the number of edges of the graph: 5
Enter the vertex pair for edge 1
V(1): 2
V(2):1
Enter the vertex pair for edge 2
V(1): 3
V(2): 2
Enter the vertex pair for edge 3
V(1): 3
V(2): 1
Enter the vertex pair for edge 4
V(1): 4
V(2): 2
Enter the vertex pair for edge 5
V(1):1
V(2): 3
The chromatic index of the given graph is: 4
The color of the edge between vertex n(1):2 and n(2):1 is: color1.
The color of the edge between vertex n(1):3 and n(2):2 is: color2.
The color of the edge between vertex n(1):3 and n(2):1 is: color3.
The color of the edge between vertex n(1):4 and n(2):2 is: color3.
The color of the edge between vertex n(1):1 and n(2):3 is: color4.
Published on 26-Apr-2019 11:28:16
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2021-04-19 02:57:50
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https://bitbucket.org/ronaldoussoren/pyobjc/src/429f9e1aa333fbab56c9701b684c1d7c37c1ac3d/pyobjc-core/Doc/blocks.rst?at=default
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# PyObjC support for "blocks"
## Introduction
Objective-C has the concept of "blocks", which are basically anonymous inline functions. The syntax for them is like this:
^{ printf("x is %d\n", 42); }
This is a literal for a block that takes no arguments and prints a value when called.
Blocks are only suppored when PyObjC is compiled using an Objective-C compiler that also supports blocks.
## Calling blocks from Python
The Python representation for a block is a callable object, that is you can call the block just like you call any other function object.
PyObjC manages the memory for blocks, it is not necessary to manage the reference counts of blocks in your code.
### Limitations
It is not possible to call arbitrary blocks because PyObjC needs to store some additional metadata for a block. This means it is only possible to call blocks where the bridge knows the call signature, which means:
• Block was returned from a method for which we know the signature of returned blocks. PyObjC ships with metadata that covers all of Cocoa.
• When a block is stored in a Cocoa datastructure, such as an NSArray, and that is the only reference to the block PyObjC will loose the additional information that is needed to call the block.
It is possible to retrieve and set the call signature of a block using the __block_signature__ attribute on blocks.
## Implementing blocks in Python
It is very easy to use Objective-C methods that have a block as one of their arguments: just pass an arbitrary callable. PyObjC will automaticly wrap your callable in the right low-level datastructure.
One of the side-effects of this is that the variour storage classes that are defined for block-related variables are not relevant for Python users. Blocks behave just like regular functions.
The current implementation of blocks doesn't allow for full introspection, which means that PyObjC must be taught about the signatures of blocks. This is done using the :doc:metadata system </metadata/index>.
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2016-02-06 08:22:00
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http://www.ni.com/documentation/en/ni-daqmx/18.1/daqmx-prop-ref/task-ai-soundpressure-dbref-29b1/
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# AI.SoundPressure.dBRef
Version:
Specifies the decibel reference level in the units of the channel. When you read samples as a waveform, the decibel reference level is included in the waveform attributes. NI-DAQmx also uses the decibel reference level when converting AI.SoundPressure.MaxSoundPressureLvl to a voltage level.
Data type:
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2018-08-20 18:33:46
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https://www.r-orms.org/mixed-integer-linear-programming/packages/roi/
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# Matrix-oriented modelling with ROI
## A first example
In this article, we take the Knapsack problem from before and model it using the matrix based interface in ROI. ROI is short for the R Optimization Infrastructure and is an excellent family of packages to solve a variaty of optimization problems, including MILPs.
$\begin{equation*} \begin{array}{ll@{}ll} \text{max} & \displaystyle\sum\limits_{i=1}^{n} v_{i}x_{i} & &\\ \text{subject to}& \displaystyle\sum\limits_{i=1}^{n} w_{i}x_{i} \leq W, & &\\ & x_{i} \in \{0,1\}, &i=1 ,\ldots, n& \end{array} \end{equation*}$
A first step is of course to load the package and define some model parameters:
library(ROI)
## ROI.plugin.glpk: R Optimization Infrastructure
## Registered solver plugins: nlminb, cbc, glpk.
## Default solver: auto.
n <- 10
W <- 2
v <- runif(n)
w <- runif(n)
Here v and w are vectors of the length n that can be directly passed to ROI.
Let’s build the constraint first. As the Knapsack problem only has one constraint (i.e. one row in the constraint matrix), this step is rather simple:
constraints <- L_constraint(w, "<=", W)
Then we define an optimization model:
model <- OP(objective = v,
constraints = constraints,
bounds = V_bound(li = 1:n, lb = rep.int(0, n), ui = 1:n, ub = rep.int(1, n)),
types = rep.int("B", n),
maximum = TRUE)
model
## ROI Optimization Problem:
##
## Maximize a linear objective function of length 10 with
## - 10 binary objective variables,
##
## subject to
## - 1 constraint of type linear.
## - 0 lower and 10 upper non-standard variable bounds.
The parameters of OP are self-explaining: we create an optimization problem with the objective coefficient vector v and our constraint from above. We further define variable bounds for all $$0 \leq x_i\leq 1$$ and set the type to “B”, meaning they are binary variables.
Having now formulated our problem, we can pass it to one of the many available solvers. In this case we use GLPK.
library(ROI.plugin.glpk)
res <- ROI_solve(model, "glpk", verbose = TRUE)
## <SOLVER MSG> ----
## GLPK Simplex Optimizer, v4.65
## 1 row, 10 columns, 10 non-zeros
## * 0: obj = -0.000000000e+00 inf = 0.000e+00 (10)
## * 8: obj = 5.141899448e+00 inf = 0.000e+00 (0)
## OPTIMAL LP SOLUTION FOUND
## GLPK Integer Optimizer, v4.65
## 1 row, 10 columns, 10 non-zeros
## 10 integer variables, all of which are binary
## Integer optimization begins...
## Long-step dual simplex will be used
## + 8: mip = not found yet <= +inf (1; 0)
## Solution found by heuristic: 4.99495245353
## + 9: mip = 4.994952454e+00 <= tree is empty 0.0% (0; 1)
## INTEGER OPTIMAL SOLUTION FOUND
## <!SOLVER MSG> ----
res
## Optimal solution found.
## The objective value is: 4.994952e+00
ROI provides function to access the optimal solution (i.e. the concrete values of all $$x_i$$). A $$1$$ means, we put the object into our knapsack, a $$0$$ means the opposite.
ROI::solution(res)
## [1] 1 1 0 1 1 1 0 0 1 1
And we are done: we solved the knapsack problem using GLPK and ROI.
- -
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2022-12-09 20:37:39
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|
https://www.physicsforums.com/threads/acceleration-in-circular-motion-conceptual-doubt.800061/
|
# Homework Help: Acceleration in circular motion -- conceptual doubt
1. Feb 26, 2015
### PhysicsKid703
1. The problem statement, all variables and given/known data
Purely a conceptual/ terminology question, a simple yes or no will suffice :)
In circular motion, will a point on its circumference will have a LINEAR acceleration which can be broken into two components- the RADIAL component which is v2/r and the TANGENTIAL component which is r*angular acceleration?
If so, in rolling without slipping of a body on a fixed-at-rest surface, do we use the TANGENTIAL acceleration and c.o.m acceleration vector sum and equate it to zero or LINEAR acceleration and c.o.m acceleration vector sum and equate it to zero? I'm 99% sure we use tangential and not linear but just want to confirm. Thanks!
2. Relevant equations
-
3. The attempt at a solution
-
2. Feb 26, 2015
### Suraj M
At which point? Contact? Then i guess your right, tangential! because you're not going to get 0 for linear acceleration and c.o.m acceleration sum.
Don't you think its the other way around? I mean it's almost the same , but still! I'm asking!
3. Feb 26, 2015
### PhysicsKid703
Haha I'm not sure, but in the end it's just terminology and personal preference I guess, switching up linear and tangential. I guess it would be best to say total(net) acceleration is the vector sum of its tangential and radial components.
4. Feb 26, 2015
### BvU
Is a question that can be answered with a simple
no.
In case you are interested in a bit more than a simple no, the answer to your a or b question becomes a double no:
"do we use the TANGENTIAL acceleration and c.o.m acceleration vector sum and equate it to zero ?"
no.
"do we use the LINEAR acceleration and c.o.m acceleration vector sum and equate it to zero ?"
no.
In case you are interested in the physics and want to know what we do use:
we use the TANGENTIAL acceleration and equate it to zero
Tangential acceleration for a point on the rim, that is. And only at the moment it is in contact with the fixed surface. At that moment the motion is purely vertical (and changing direction from downwards to upwards). Google cycloid.
And it isn't all that simple to ask a question that can be answered with a simple yes or no....
Last edited: Feb 27, 2015
5. Feb 27, 2015
### PhysicsKid703
I see. My bad, I wasn't trying to be cocky or anything, I just said it without thinking. You're right, a simple yes or no question is difficult to ask.
So just to reiterate and confirm,
The tangential acceleration of the point in contact should be equated to zero, and that is the vector sum of acceleration of com and r*alpha, correct? Since that particle has both the acceleration due to com and the r*alpha acceleration?
Last edited: Feb 27, 2015
6. Feb 27, 2015
### Staff: Mentor
I'm a little confused. Are you saying that the cylinder is rolling at constant velocity without slipping at the surface, or are you saying that the cylinder is accelerating, but is not slipping at the surface?
Chet
7. Feb 27, 2015
### BvU
Hello, I tried to be neutrally cocky
And this time I think a simple "yes but" seems in order.
Have to admit you made me think twice about what exactly you describe in what frame of reference.
My picture is that $\vec\alpha \times \vec r$ is wrt the rotation axis in the accelerating frame of reference and adding the acceleration of that axis (in a frame of reference where the ground doesn't move) should give zero.
I don't like the idea of calling the result a tangential acceleration (tangential to what, exactly), but maybe it's a matter of taste.
(I realize I'm contradicting my own post #4 "what we do use" -- can't be helped)
Hi Chet, what do you think ? For the case of an non-slipping, accelerating wheel.
8. Feb 27, 2015
### PhysicsKid703
BvU
I have the same picture in mind. The vector sum of both the r*alpha acceleration and the acceleration of c.o.m, possessed by point of contact should give zero, assuming surface to be at rest. The terminology of tangential etc I presume is best used for pure rolling or circular motion, when we can just split up the linear acceleration into its radial and tangential components. Thanks for the help, I think I've got it :D
Mr. Chet, yes, that was my question; I was referring to a body accelerating and not slipping on a surface-at-rest.
Last edited: Feb 27, 2015
9. Feb 27, 2015
### Staff: Mentor
I think it's easy to show that, at the instantaneous point of contact, the tangential velocity of the cylinder surface relative to the table surface is zero. It wasn't as obvious to me that at the instantaneous point of contact, the tangential acceleration of the cylinder surface is zero. However, if we look at the tangential acceleration at the contact point relative to a reference frame traveling with the center of mass, it is just -rα (since r is not changing). And since the acceleration of the center of mass is +rα if no slip is occurring, the tangential acceleration of the cylinder relative to the table at the contact point must be zero also. As I said, this was not obvious to me.
Chet
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2018-06-22 19:47:13
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https://www.gamedev.net/forums/topic/701081-question-about-nullptrs/
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## Recommended Posts
I have an object that may end up returning a null reference:
object O1 ("foo"); // O1 is null
object @O2 = @O1; // all ok!
This works fine: both O2 and O2 are null. So surely I can join those statements together?
object @O3 = object ("foo"); // nullptr error
But no, that doesn't work: in this case the script aborts with a nullptr error. Am I doing something wrong? Am I just misunderstanding how it is supposed to work? Is it ok to return null from a constructor? It's doing a lookup for an object with id 'foo', which may or may not exist...
Thanks for any enlightenment offered!
##### Share on other sites
Seems weird to me, to return null from a constructor/factory function. Why do you need to do that? Why not just use a normal function?
##### Share on other sites
I think the reasoning more or less went like this: "In C++ I'd just make a constructor and then throw when I can't get the resource... Angelscript doesn't have exceptions (back then)... Ah wait, it lets me return a nullptr instead so it's all good."
The whole development cycle happened under a lot of time pressure, unfortunately, so once I had something that worked, I didn't spend too much time playing around with it to see if there was a better option. Of course that's now coming back to bite me... And we did this for an external customer, so I should endeavour to keep the interface stable.
Anyway, it's kinda surprising that the two snippets I posted aren't equivalent.
##### Share on other sites
It looks like you've exploited an undefined behaviour in the past.
I will take a look at this, to see what can be done. However, I'd say that the first case is the one that is wrong, not the second one. A factory shouldn't be allowed to return null without also calling SetException to indicate the failure to create the object instance.
##### Share on other sites
Ok, thanks for the info. I'll make the necessary changes to ensure I'm not invoking UB. Could I do this instead:
object @O = makeobject ("foo");
and have that potentially return a nullptr?
##### Share on other sites
Yes, that's perfectly fine.
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Register a new account
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2019-11-18 07:22:56
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https://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.2011.48.1.213
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- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
Multiple periodic solutions for eigenvalue problems with a $p$-Laplacian and non-smooth potential Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 213-221 https://doi.org/10.4134/BKMS.2011.48.1.213Printed January 1, 2011 Guoqing Zhang and Sanyang Liu University of Shanghai for Science and Technology, Xidian University Abstract : In this paper, we establish a multiple critical points theorem for a one-parameter family of non-smooth functionals. The obtained result is then exploited to prove a multiplicity result for a class of periodic eigenvalue problems driven by the $p$-Laplacian and with a non-smooth potential. Under suitable assumptions, we locate an open subinterval of the eigenvalue. Keywords : multiple periodic solutions, critical points of non-smooth functionals, eigenvalue problems, $p$-Laplacian MSC numbers : 34C25 Downloads: Full-text PDF
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2021-04-13 06:27:07
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http://www.masterull.dk/orc/
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## Simulating a simple sub-critical ORC (v1.0)
Organic Rankine cycle calculation online!
### Optimisation parameters (units in bar and degrees C.)
Fire hazard (HMIS)
Health hazard (HMIS)
Physical hazard (HMIS)
Global warming potential (100y)
Ozone depletion potential
Critical pressure (bar)
•
Calculating state points, please wait... If the calculation gets stuck please refresh the web page.
Calculation success!
### Results
Turbine power (kW) Pump power (kW) Cycle net power (kW) Cycle efficiency (%)
m T P h s
1
2
3
4
5
6
10
11
12
13
m (kg/s), T (°C), P (bar), h (kJ/kg), s (kJ/kg-K)
### Equations
Pressure and heat losses are neglected.
The results are based on the heat source being a flow of 1 kg/s of exhaust gas with a $c_p$=1.1 kJ/kg-K.
$P_4 = P_5 = P_6 = P_1$,
$P_3 = P(T_3, x=0)$,
$P_2 = P_3$,
$h_1 = h(T_1, P_1)$ (must always be a superheated state),
$s_1 = s(T_1, P_1)$,
$h_{2,s} = h(s_1, P_2)$,
$h_2 = h_1 - (h_1-h_{2,s}) \eta_e$,
$h_3 = h(P_3, x=0)$,
$s_3 = s(P_3, x=0)$,
$h_{4,s} = h(s_3, P_4)$,
$h_4 = h_3 + (h_{4,s}-h_3)/\eta_p$,
$h_5 = h(P_5, x=0)$,
$h_6 = h(P_6, x=1)$,
$\dot{m}_{10}=1$ (kg/s),
$h_{10}-h_{13} = c_p(T_{10}-T_{13})$,
$\dot{m}_1 = \dot{m}_{10}(h_{10}-h_{13})/(h_1-h_4)$,
$h_{11} = h_{10} - \dot{m}_1(h_1-h_6)$,
$h_{12} = h_{11} - \dot{m}_1(h_6-h_5)$,
$T_{11} = h_{11}/c_p$,
$T_{12} = h_{12}/c_p$,
### Estimation of max. potential
Surprisingly, it turns out that one can estimate the maximum obtainable efficiency of an ORC (optimised with the best fluid and parameters), by using the four equations below here (Link).
For heat sources with an inlet temperature (state 10 in the figure at the top of this page) in the range of 180-360°C, the maximum efficiency for a recuperated ORC is approximately: $\eta_{th,max} = -12.76 + 0.06428 T_{hs,i} + 0.05897 T_{hs,o} + 0.2576 \eta_{p,e} - 0.1727 T_c - 0.1556 \Delta T_{pp}$
$T_{hs,i}$ is the heat source inlet temperature (10),
$T_{hs,o}$ is the heat source outlet temperature (13),
$\eta_{p,e}$ is the polytropic efficiency of the turbine or expander,
$T_c$ is the condensing temperature (3) and
$\Delta T_{pp}$ is the minimum pinch point temperature difference in the boiler and the recuperator. Temperatures are given in degrees Celsius and the efficiencies in percent.
In the same way we can estimate the maximum potential of a non-recuperated ORC: $\eta_{th,max} = -12.33 + 0.05858 T_{hs,i} + 0.03350 T_{hs,o} + 0.2666 \eta _{p,e} - 0.1552 T_c - 0.0810 \Delta T_{pp}$
For heat sources with an inlet temperature in the range of 80-180°C, the maximum efficiency for a recuperated ORC is approximately:
$\eta_{th,max} = -16.32 + 0.08402 T_{hs,i} + 0.08349 T_{hs,o} + 0.1583 \eta _{p,e}$
Note that the equation is only valid when the condensing temperature is 25°C and the minimum pinch point temperature difference is 5°C.
In the same way we can estimate the maximum potential of a non-recuperated ORC in the range of 80-180°C:
$\eta_{th,max} = -14.92 + 0.07339 T_{hs,i} + 0.08363 T_{hs,o} + 0.1464 \eta _{p,e}$
It is the aim of these equations to provide enable the straight-foward estimation of the theoretical maximum potential of an ORC given the design conditions. One can immediately investigate the effect of varying key design parameters, for example the condensing temperature or the turbine efficiency. For more details see here and here.
### Calculator for a recuperated ORC, heat source inlet 180-360°C
Max. achievable thermal efficiency: %
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2017-01-23 22:52:22
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https://mindspace.arclind.com/sparks/qazduo-the-longest-vertical-straw-you-can-drink-from-is-10-metres-even-if-you-u/?parent=5
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karthik · updated · flag · 8
The longest vertical straw you can drink from is 10.3 metres. Even if you use a vacuum pump it won’t suck the liquid higher than that! Here is why!
Contrary to your intuition, when you drink from a straw you are not actually sucking up the fluid here. Just the air. So, when you do that, inside the straw, the pressure drops lower than that of the atmospheric pressure (101 kPa) outside. So, it’s the outside air pressure that pushes the water into the straw.
As the liquid moves up the straw, it is fighting against the gravity that is pulling it downwards. But it still keeps rising as long as the atmospheric pressure is greater than the pressure inside the straw due to gravity (weight of the liquid column).
The more liquid enters the column, the more it weighs. And at a certain height, there’d be enough water in the straw that’d exert the same pressure as that of the atmospheric pressure. That height, at sea level on earth, for water is 10.3 m.
$$p_{atm}= 101\;kPa$$
$$p_{straw}= \dfrac{F}{A} \Rightarrow \rho g h$$
$$\rho g h = 101 \times 10^3\;N/m^2$$
$$h = \dfrac{101 \times 10^3\;N/m^2}{10^3\;kg/m^3 \times 9.81\;m/s^2}$$
$$h = 10.3\; m$$
## Comments
ragu · · edited
This will be my all time favorite spark. You have just explained the principle of barometers. You have elegantly put it in simple words. Please write more sparks like this. I love it!
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2022-05-26 07:59:32
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http://newvillagegirlsacademy.org/math/?page_id=4434
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# 10 – Polynomials
• Testing our limits is part of human nature.
• How far could you throw this ball?
• What if you were stronger?
• What if the object were heavier, like a shot put, or much larger, like a pumpkin?
• What if you could build a machine to launch the pumpkin?
• Could you shatter the world record?
• How could you predict where it would land?
• In cases such as these, a working knowledge of polynomials comes in handy, because graphs of polynomials are often used to model real-world limits.
• How dramatically could you add to your city’s skyline?
• What size drop on a roller coaster will lift riders from their seats? At what price could you sell your product to make the largest profit?
• In this unit, you’ll explore the connections between polynomials, their graphs, and the real-world relationships they can model.
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2017-04-23 21:40:18
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https://maslinandco.com/5970465
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# Evaluate: x-(x \times .35)-(x \times .06)-600 = 1885
## Expression: $$x - ( x \times .35 ) - ( x \times .06 ) - 600 = 1885$$
Combine $x$ and $-x\times 0.35$ to get $0.65x$.
$$0.65x-x\times 0.06-600=1885$$
Combine $0.65x$ and $-x\times 0.06$ to get $0.59x$.
$$0.59x-600=1885$$
Add $600$ to both sides.
$$0.59x=1885+600$$
Add $1885$ and $600$ to get $2485$.
$$0.59x=2485$$
Divide both sides by $0.59$.
$$x=\frac{2485}{0.59}$$
Expand $\frac{2485}{0.59}$ by multiplying both numerator and the denominator by $100$.
$$x=\frac{248500}{59}$$
Random Posts
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2023-01-30 04:48:58
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http://mymathforum.com/probability-statistics/338277-expectation-calculation.html
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My Math Forum Expectation calculation
Probability and Statistics Basic Probability and Statistics Math Forum
December 28th, 2016, 04:21 PM #1
Newbie
Joined: Nov 2016
From: Israel
Posts: 7
Thanks: 0
Expectation calculation
Hi, I could only find E(X|Y1=1) is 7, but had difficulties with all the rest. I would be glad for a help. Thanks in advance.
Attached Images
probability.jpg (21.9 KB, 15 views)
December 28th, 2016, 04:25 PM #2
Newbie
Joined: Nov 2016
From: Israel
Posts: 7
Thanks: 0
Quote:
Originally Posted by riovelo Hi, I could only find E(X|Y1=1) is 7, but had difficulties with all the rest. I would be glad for a help. Thanks in advance.
There is the bigger image. http://up416.siz.co.il/up1/gmvix3jyzmwz.png
Last edited by skipjack; December 29th, 2016 at 08:35 AM.
December 28th, 2016, 06:52 PM #3 Senior Member Joined: Dec 2012 From: Hong Kong Posts: 781 Thanks: 284 Math Focus: Linear algebra, linear statistical models Since the monkey is right back at the beginning of the maze after going through the other two apertures, E(X|Y1=2) = 3 + E(X), E(X|Y1=2) = 5 + E(X). We have $\displaystyle E(X) = \sum_{i=1}^3 E(X|Y1=i) P(Y1=i) = \frac{1}{3} [7 + 3 + E(X) + 5 + E(X)]$, so you simply have to solve for E(X) to get the answer! Thanks from romsek and riovelo
December 29th, 2016, 06:15 AM #4 Newbie Joined: Nov 2016 From: Israel Posts: 7 Thanks: 0 Hi 123qwerty, first of all, thanks for your reply. Can you please explain the equations E(X|Y1=2) = 3 + E(X), E(X|Y1=2) = 5 + E(X)? I mean, I undestand that the 3 and the 5 are the periods of time by which the monkey's moving about through each aperture except 1, but I don't undestand what makes the the 2 equations true. And I would be greatful if you'd help me with the second part of section b. Last edited by riovelo; December 29th, 2016 at 06:26 AM.
December 29th, 2016, 07:48 AM #5 Senior Member Joined: Dec 2012 From: Hong Kong Posts: 781 Thanks: 284 Math Focus: Linear algebra, linear statistical models We're splitting up the expected value into two parts: the first time period taken by the monkey to move about in the maze, plus everything else. The 'everything else' part is E(X) because we're back to the beginning of the maze and have to start over. I'm not sure what the last one really means tbh, but here's how I'd do it: We know for certain that he'll go through 7 once, so that's the first term. As for how much time (on average) he spend on going through the rest of the maze, well, let this time be Z. We know he'll choose 3 half the time and 5 the other half of the time, so let's just pretend there's a 2/3 chance he'll choose a path with 4 hours. So now we have: Then we get the sum $\displaystyle 7 + \sum_{i=1}^\infty \left(\frac{2}{3}\right)^{i-1} \left(\frac{1}{3}\right) \times 4(i-1) = 7 + 2 \times 4 = 15$ (Note that I put i-1 rather than i after 4 to exclude the first round.) Thanks from riovelo
December 29th, 2016, 09:53 AM #6 Newbie Joined: Nov 2016 From: Israel Posts: 7 Thanks: 0 Thanks again 123qwerty. But stil, there's one thing I don't understand- Why the first time period taken by the monkey is not included in that 'everything else'?
December 29th, 2016, 09:57 AM #7
Senior Member
Joined: Dec 2012
From: Hong Kong
Posts: 781
Thanks: 284
Math Focus: Linear algebra, linear statistical models
Quote:
Originally Posted by riovelo Thanks again 123qwerty. But stil, there's one thing I don't understand- Why the first time period taken by the monkey is not included in that 'everything else'?
Because I divided the time into two parts: The first part plus the rest.
December 29th, 2016, 07:17 PM #8
Senior Member
Joined: Dec 2012
From: Hong Kong
Posts: 781
Thanks: 284
Math Focus: Linear algebra, linear statistical models
Quote:
Originally Posted by 123qwerty We're splitting up the expected value into two parts: the first time period taken by the monkey to move about in the maze, plus everything else. The 'everything else' part is E(X) because we're back to the beginning of the maze and have to start over. I'm not sure what the last one really means tbh, but here's how I'd do it: We know for certain that he'll go through 7 once, so that's the first term. As for how much time (on average) he spend on going through the rest of the maze, well, let this time be Z. We know he'll choose 3 half the time and 5 the other half of the time, so let's just pretend there's a 2/3 chance he'll choose a path with 4 hours. So now we have: Then we get the sum $\displaystyle 7 + \sum_{i=1}^\infty \left(\frac{2}{3}\right)^{i-1} \left(\frac{1}{3}\right) \times 4(i-1) = 7 + 2 \times 4 = 15$ (Note that I put i-1 rather than i after 4 to exclude the final round.)
Oops! Just realised this.
December 30th, 2016, 03:44 AM #9
Newbie
Joined: Nov 2016
From: Israel
Posts: 7
Thanks: 0
Quote:
Originally Posted by 123qwerty Oops! Just realised this.
Thank you very much!
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2017-03-29 07:14:54
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http://www.cs.uleth.ca/~nathanng/ntcoseminar/
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Department of Mathematics and Computer Science Number Theory and Combinatorics Seminar Spring 2017 Talks are at noon on Monday in room B660 of University Hall For more information, or to receive an email announcement of each week's seminar, contact Nathan Ng < ng AT cs DOT uleth DOT ca > or Dave Morris .
The next talk: Jan 23 at noon in B660 Alia Hamieh Non-Vanishing of Central Values of Rankin-Selberg $L$-Functions In this talk, we discuss some results on the non-vanishing of the central values of Rankin-Selberg convolutions of families of Hilbert modular forms. Such results are obtained by establishing some asymptotics of certain twisted first and second moments. This is an on-going joint work with Naomi Tanabe.
Talks in the series this semester: (Click on any title for more info, including the abstract. Then click on it again to hide the info.)
Date Speaker Title Jan 9 Darcy Best Transversals in Latin Arrays with many Symbols at noon in B660 (Monash University, Australia) A transversal of a latin square of order $n$ is a set of $n$ entries picked in such a way that no row, column or symbol is present more than once. As you add more symbols to a latin square, you expect the number of transversals to increase. We show that once the number of symbols reaches a certain threshold, the square is guaranteed to have a transversal. Jan 16 everyone Open problem session at noon in B660 Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester. Jan 23 Alia Hamieh Non-Vanishing of Central Values of Rankin-Selberg $L$-Functions at noon in B660 (University of Lethbridge) In this talk, we discuss some results on the non-vanishing of the central values of Rankin-Selberg convolutions of families of Hilbert modular forms. Such results are obtained by establishing some asymptotics of certain twisted first and second moments. This is an on-going joint work with Naomi Tanabe. Jan 30 Nathan Ng Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Feb 6 Joy Morris Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Feb 13 Habiba Kadira Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Feb 27 Hadi Kharaghani Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Mar 6 Pieter Moree Title TBA at noon in B660 (Max Planck Institute, Germany) Abstract TBA Mar 13 Pieter Moree Title TBA at noon in B660 (Max Planck Institute, Germany) Abstract TBA Mar 20 Speaker TBA Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Mar 27 Speaker TBA Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Apr 3 Sahar Siavashi Title TBA at noon in B660 (University of Lethbridge) Abstract TBA Apr 10 Speaker TBA Title TBA at noon in B660 (University of Lethbridge) Abstract TBA
Past semesters: Fall F2007 F2008 F2009 F2010 F2011 F2012 F2013 F2014 F2015 F2016 Spring S2008 S2009 S2010 S2012 S2013 S2014 S2015 S2016
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2017-01-20 22:02:51
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https://www.nature.com/articles/s41598-018-19925-7?error=cookies_not_supported&code=2a428345-a978-4b96-9caf-b5ae0cf43efe
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# Slow moving neural source in the epileptic hippocampus can mimic progression of human seizures
## Abstract
Fast and slow neural waves have been observed to propagate in the human brain during seizures. Yet the nature of these waves is difficult to study in a surgical setting. Here, we report an observation of two different traveling waves propagating in the in-vitro epileptic hippocampus at speeds similar to those in the human brain. A fast traveling spike and a slow moving wave were recorded simultaneously with a genetically encoded voltage sensitive fluorescent protein (VSFP Butterfly 1.2) and a high speed camera. The results of this study indicate that the fast traveling spike is NMDA-sensitive but the slow moving wave is not. Image analysis and model simulation demonstrate that the slow moving wave is moving slowly, generating the fast traveling spike and is, therefore, a moving source of the epileptiform activity. This slow moving wave is associated with a propagating neural calcium wave detected with calcium dye (OGB-1) but is independent of NMDA receptors, not related to ATP release, and much faster than those previously recorded potassium waves. Computer modeling suggests that the slow moving wave can propagate by the ephaptic effect like epileptiform activity. These findings provide an alternative explanation for slow propagation seizure wavefronts associated with fast propagating spikes.
## Introduction
Seizures are known to propagate and the localization of the focus is essential to a successful therapeutic intervention. Yet finding the source of the seizures is a difficult and often unsolved problem. Seizure foci are difficult to observe as they can move or can arise from micro seizures in multiple locations1,2. In patients with epilepsy, identifying multiple foci in temporal lobe is an additional challenge and the mechanism of seizure generation remains unknown3. It has been shown recently in the human brain that there are two types of traveling waves, a slow and a fast wave (about 10 times faster) associated with propagating seizure activity4. Yet the origin of these waves and their mechanism of propagation are difficult to be determined in-vivo. Similar waves at similar speeds have been observed in-vitro in the hippocampus under epileptic conditions5,6 and the cortex under normal physiological conditions7. We have observed fast spontaneous 4-AP-induced inter-ictal spikes propagating at a speed of approximately 0.1 m/s as well as the source of the spike propagating simultaneously at a slower speed of approximately 0.01 m/s. The mechanism of propagation for the fast traveling spike in the 4-AP induced ictal activity has already been characterized as non-synaptic and consistent with ephaptic propagation5,8. The slow moving neural source could not be detected directly by electrical recording. However, the path of the source could be inferred from isochrone maps obtained from the generated fast traveling spikes. The speed of the source was estimated by using Doppler calculations6.
In this study, the neural circuit spatiotemporal dynamics of this source were imaged using a genetically encoded voltage-sensitive fluorescent protein (VSFP Butterfly 1.2) to directly trace the slow moving wave induced by 4-AP in the non-epileptic hippocampus. The VSFP Butterfly 1.2 shows a reliable response to the membrane potential, fast kinetics, and high signal-to-noise ratio9 and diminished toxic effect compared to voltage sensitive fluorescent dyes10. Thus voltage-sensitive fluorescent proteins are suitable to track the propagation of neural activity along the longitudinal plane of the hippocampal slice.
In addition, it has been shown that 4-AP can induce a slow neuronal calcium oscillation11. Therefore, we also tested the hypothesis that a neural calcium wave is associated with the focal region and propagates with the slow wave. We tested this hypothesis by means of a calcium-sensitive fluorescent dye, Oregon Green 488 Bapta-1 (OGB-1). OGB-1 and other calcium-sensitive dyes, such as fura-2, have been used in previous studies to detect neural activity in the neural tissue12. OGB-1 can detect changes in calcium concentration in small dendritic compartments13,14,15 and therefore has been proposed as a tool for tracking activity that is not visible using traditional electrophysiology methods16. Finally, we developed a computational neuronal network model to simulate the two traveling waves simultaneously and compare their properties to test the possible mechanisms of generation and propagation of these waves.
## Results
### 4-AP induced fast traveling spike can be imaged propagating through the hippocampus
4-AP induced spikes can propagate rapidly both in the transverse and longitudinal directions through the unfolded hippocampus but their path is not clearly known because of the poor spatial resolution of the electrode array5. To track these spikes with the improved spatial resolution we used voltage indicators with longitudinal slices from transgenic mice carrying voltage-sensitive fluorescent protein (VSFP Butterfly 1.2) immersed in the 100 μM 4-AP/aCSF to induce the inter-ictal spikes. In addition to recording the local field potentials (Fig. 1a), a high speed camera (C11440, Hamamatsu) was used to acquire image sequences to reconstruct the spatiotemporal activity (Fig. 1b). The VSFP Butterfly 1.2 exhibited a voltage-dependent decrease of Δf/f in mCitrine (donor) and an increase in mKate2 (acceptor) emission corresponding to membrane depolarization9. Following the calculation of the intensity change of fluorescence (Δf/f) in the region of interest (ROI), the optical signals in different regions of the hippocampal slice were reconstructed as temporal signals. The optical signal from mCitrine was similar to the local field potential indicating that the fast spikes follow the cell layer (Fig. 1c). To calculate the speed of these propagating events, the optical signals at 11 different positions along the cell layer were processed to determine the delay with cross correlation calculation for each single spike events. The speed of fast traveling spikes estimated by optical signals in two different regions of interest from mCitrine was in the range between 0.025 and 0.2 m/s and was similar to the speed obtained from mKate2 imaging (Fig. 1d,e). In summary, the average speeds of the fast traveling spikes induced by 4-AP/aCSF solution estimated from mCitrine and mKate2 were 0.12 ± 0.01 m/s (n = 170 events) and 0.11 ± 0.01 m/s (n = 130 events), respectively. The speed of the fast traveling spikes was also estimated by the electrical signals that revealed a speed of 0.11 ± 0.02 m/s (n = 100 events). A one-way ANOVA followed by a post hoc test showed that there was no significant difference between speeds estimated from both optically and electrically recorded signals. There was also no significant difference between the two measurements to calculate the speed from the optical signals (Fig. 1f). The speed of the fast traveling spike induced by 4-AP in the longitudinal slice was similar to the speed of inter-ictal spike induced by 4-AP in the unfolded hippocampus from our previous study (0.1 m/s)5.
To study the spatiotemporal characteristics of the fast traveling spikes, image sequences recorded during each single spike event were analyzed. We observed several consistent features. First, the fast traveling spikes propagated through the cell layer. In some cases, the spike originated within the imaging window and the fast traveling spikes could be observed to propagate in two different directions (Fig. 2a). Second, the origin of the wave could be traced in each image sequence and the result can be seen in Fig. 2b. Over 90 percent of spikes initiated in the temporal area of the hippocampal slices (n = 60 events). Finally, when the speed of the fast traveling spikes was traced along the cell layer, one-way ANOVA test shows there was no significant difference between the speeds measured in the temporal and septal segments of the hippocampus (Fig. 2c).
### 4-AP also induces a slow moving wave propagating along septotemporal hippocampus
The existence of a neural source slowly propagating in the hippocampus was previously inferred from a microelectrode array data since it could not be observed electrically6. To observe directly this slow moving wave along the cell layer, optical signals from different locations were reconstructed in the time domain and filtered with a 1 Hz low-pass filter (Fig. 3a). The filtered signals reveal that a slow drifting wave was always present when a fast traveling spike was recorded from local field potentials (Fig. 3a). When measuring the time delay of the optical signals from different positions, it was found that this drifting wave traveled through the cell layer at a slower speed compared to the fast spikes (Fig. 3b,c). When the fast traveling spike was detected by electrical recording, a slow moving wave appeared and propagated from the temporal region to the septal region of the hippocampus (Fig. 3a and e). The propagating speed was 0.0077 ± 0.0005 m/s (n = 60 events, Fig. 3d) and this speed is significantly different from the speed of the fast traveling spikes (paired-t test, p < 0.05). Therefore, these experiments confirm the hypothesis that propagating activity in the longitudinal plane comprises of two distinct components: a fast spike traveling along the cell layer and a slow moving wave propagating simultaneously in the same region.
For each spike event in the field potential, optical signal revealed both a fast traveling spikes and a slow moving wave. To understand the relationship between the fast and slow moving waves, the optical signals from the same electrical spike event are plotted simultaneously in Fig. 3e. The figure shows a slow moving wave initiated at −5 ms and triggering a fast traveling spike propagating through the tissue shown at 0, 5, 10 and 20 ms. Simultaneously, the slow wave continues to propagate slowly as shown at 30, 60, 90 and 120 ms. This observation that the slow wave triggers the fast wave was further tested by a hippocampal computational model. Simulated intracellular potentials show the slow wave can trigger the fast propagating wave. These data will be described in detail in the later paragraph. These experimental and simulated data indicate that the fast traveling spikes were triggered by the slow moving wave as previously observed in the intact hippocampus preparation6.
### Slow moving wave is a neuronal calcium wave
To characterize the nature of the slow moving wave, several hypotheses were tested in the following experiments. First, we hypothesized that the slow moving wave is associated with an increase in intracellular calcium concentration within the slow moving wave since 4-AP can induce a calcium oscillation11. To observe the calcium dynamics of the slow moving wave directly, longitudinal slices were incubated in a solution containing OGB-1 calcium dye and placed in an imaging chamber with 4-AP/aCSF at a flow rate of 0.05 ml/s. Neurons were stained using the AM ester of OGB-1. Figure 4c shows a typical calcium imaging window in a longitudinal hippocampal slice. The imaging window location was focused on the center of the slice with the cell layer in the field of view. To monitor the fast traveling spikes, an extracellular recording electrode was placed close to the cell layer, approximately 20 µm below the surface and Fig. 4a show an example of fast traveling spike by electrical recording. To obtain the slow moving wave, optical signals in four different regions of interest from calcium imaging were calculated as fluorescent intensity change (∆F/F) in the time domain (blue, orange, green, and red squares in Fig. 4c). Each optical signal from different regions of interest is made up of the averaged intensity of an array of 8 × 8 pixels (mean ± SD) is plotted versus time (Fig. 4b). The optical signals analyzed were in the range of 0.5–2% (Fig. 4b). The time-to-peak of these changes were in the range of 0.05 ± 0.02 s, and the subsequent fall time was in the range of 0.55 ± 0.4 s (n = 112 events sampled from 14 slices with equal number of events). The statistical analysis shows that the peak of optical signal intensity generated by the slow moving wave is significantly higher than the baseline (1.3 ± 0.4% compared to baseline RMS level of 0.3 ± 0.2% with SNR of 4.3 fold (paired-t test, p < 0.05, n = 112 events from 14 slices with equal number of events). The simultaneous recording of the optical slow moving wave and electrical fast traveling spike were also analyzed by Chi-squared test. When hippocampal slices were immersed in 4-AP/aCSF solution, most of optical slow moving waves would accompany an electrical fast traveling spike (p < 0.01).
To study the propagation of the slow moving wave, optical signals from two different regions of interest were compared to calculate the delay with cross-correlation calculation5,6. Figure 4d shows an example of cross-correlation calculation from two optical signals in two different regions of interest (blue and red squares in Fig. 4c). The cross-correlation function revealed a time delay of 340 ms (R-value of 0.95). Figure 4e shows a histogram of delay calculated by cross-correlation calculation from 112 different events and the statistical analysis shows that the delay is significant when signals are compared from two different regions of interest (paired-t test, p < 0.05). The speed of propagation was in the range of 0.001 and 0.007 m/s and the mean was 0.004 ± 0.0009 m/s (Fig. 4f). The direction of propagation of the source associated with the spike was always from the temporal to the septal region of the hippocampus (112 of 112 events).
### NMDA-antagonists block the fast traveling spike but not the slow moving wave
The fast traveling spike was observed to propagate in zero-calcium solutions in a previous study but still required the activation of postsynaptic NMDA (but not AMPA) receptors with bath glutamate7. We then tested the NMDA sensitivity of the slow moving wave. We hypothesized that the NMDA receptor can only underlie the fast traveling spike but not the slow moving wave based on their relative speed. This hypothesis predicts that the slow moving wave should still propagate in the absence of spikes and in the presence of an NMDA receptor blocker (APV). This hypothesis was tested by placing the slice in the imaging chamber with perfusion of a solution of 50 μM APV + 4-AP/aCSF. Examples of electrical and optical recordings in the condition of 50 μM APV + 4-AP/aCSF are shown in Fig. 5a,b. In all 4 slices with the presence of the NMDA blocker, the fast traveling spikes were blocked in the electrical recordings (Fig. 5a). However, slow moving waves were still detected when the optical signals from four different regions of interest (Fig. 5b). The slow moving wave has a rise time to peak of 0.05 ± 0.01 s and the decay time of 0.53 ± 0.4 s (n = 88 events from 4 slices with equal number of events). The four optical signals from four different regions of interest revealed that the slow moving wave could still propagate with the presence of NMDA antagonist, APV (Fig. 5b). To study the propagation, two optical signals were compared by calculating cross-correlation to obtain the delay between two signals (Fig. 5c). Figure 5d shows a histogram of delay from cross-correlation calculation and the statistical analysis shows that the delay is significant between two signals from two different regions of interest (Mann–Whitney U test, p < 0.05, n = 88 events from 4 slices with equal number of events). Figure 5e provides the histogram distribution of the speeds of propagation under APV + 4-AP/aCSF. The speed of propagation was 0.004 ± 0.001 m/s (n = 88 events) and t-test show that there was no significant difference between solutions with and without the NMDA receptor blocker (Fig. 5f). Therefore, these experiments confirm that the slow moving wave is independent of NMDA receptor.
### Slow moving wave is independent of ATP release
Propagating astrocyte calcium waves have been shown to involve the release of ATP activating neighboring purinergic receptors, causing an increase of intracellular calcium, and generating a calcium wave17. Therefore, we next tested the hypothesis that the slow moving wave is mediated by ATP release. Three hippocampal slices were perfused with 4-AP/aCSF first to generate inter-ictal activity and then 100 μM suramin plus 4-AP/aCSF was added to block the purinergic receptors of the P2Y group18,19. The spike could still be detected in the local field potentials. By using the OBG- 1 calcium dye, the slow moving wave could also be observed in the optical signals (Fig. 6a). The slow moving wave continued to propagate in the presence of suramin and a paired t-test shows that the speeds before and after the application of suramin were similar (Fig. 6b,c). These experiments show that the slow moving wave is not mediated by ATP release.
### Fast traveling spike and slow moving waves can be explained by a computational neuronal network model
On the basis of our experimental results, the feasibility that both a fast traveling spike and slow moving waves could co-exist was simulated in Fig. 7a with a model consisting of an array of 200 × 18 pyramidal cells connected only through the ephaptic coupling. Each cell had three compartments: passive soma, apical dendrites capable of generating calcium spikes20,21, and basal dendrite capable of generating NMDA spikes since many experiments about NMDA spikes were targeted in the basal dendrites22,23. Fast and slow waves can be generated spontaneously in the model and traveled at speeds of approximately 0.1 m/s and of 0.008 m/s respectively similar to those observed experimentally. The fast traveling spike was selectively observed by filtering the raw simulated signals in Fig. 7a with a 1 Hz high-pass filter and retained similar amplitude and speed (Fig. 7b). Similarly, the slow moving wave can be observed by filtering with a 1 Hz low-pass filter and also retained similar magnitudes of the amplitude and speed (Fig. 7c).
To compare the characteristics of simulated and experimental traveling waves, 65 simulated waves were generated by the randomized cell to cell distance d c-c (2~4 μm) and physiologically relevant stacking factor values (SF = 10~30) based on hippocampal cell density8. The firing frequency of the spontaneous spikes was found to be between 0.5 and 1 Hz with a mean value of 0.7 ± 0.3 Hz. The speed of the fast traveling spike was in the range from 0.04 m/s to 0.2 m/s with a mean value of 0.1 ± 0.01 m/s. The slow moving wave origin and direction of propagation was similar to that of the fast one. The propagating speed ranged between 0.004 m/s to 0.02 with a mean value of 0.009 ± 0.0008 m/s. The ratio of propagation speeds between fast and slow waves was limited in the range between 8 to 11 with a mean value of 10 ± 1.1, and the ratios of amplitudes between fast and slow propagations were in the range from 9 to 13 with a mean value of 11 ± 2. The simulated traveling waves were characterized by similar firing frequency and propagating speeds compared to experimental data (Fig. 7d). Simulated extracellular field amplitudes for the fast spikes ranged between 2.74 mV/mm and 5.08 mV/mm (Fig. 7e) and these values fall within the previously observed field amplitude range of ~3~6 mV/mm from 4-AP induced epileptiform activities in vitro hippocampal slice5,6,8,24,25. It was also determined that the field amplitude increased with stacking factor (SF) and the curve (Field vs SF) shifted to the right when the cell to cell distance (d cc ) increased from 2 μm to 4 μm in Fig. 7e. For the larger d cc (3 and 4 μm), the field amplitudes were lower than 1.0 mV/mm in the region of small values of SF (<21) with no waves generated in the simulated network.
To further study the underlying mechanism of the coexistence of fast and slow moving waves, we analyzed the intracellular membrane potentials in the simulated network. Figure 7f shows the propagation of intracellular potentials in the apical dendrites with calcium channels and in the basal dendrites with NMDA channels. The black bold line indicates the path of NMDA-dependent spike and the green bold line indicates the path of the calcium-dependent spike. Figure 7g shows that the transmembrane potentials of both apical and basal dendrites for three cells (35th Cell, 100th Cell, and 150th Cell along the longitudinal axis). These simulated data clearly show that calcium-dependent spikes generated the slow propagating wave in apical dendrite while NMDA-dependent spikes generated the fast propagating wave in the basal dendrite. Both waves could propagate along the longitudinal axis of the array of the cell. Moreover, the intracellular propagation speeds of calcium-dependent and NMDA-dependent spikes are consistent with the propagating speeds of slow moving wave and fast traveling spikes recorded in the experiments (Fig. 7d). The expanded window of two coexisting intracellular spiking propagations (Fig. 7f) indicates that the origin of NMDA-dependent spike located at P2 (35th Cell) followed the onset of the calcium-dependent spike. The spontaneous calcium-dependent spikes evoked by electric field effect in apical dendrites of several neighboring cells could depolarize slightly membrane potentials in basal dendrites. This small depolarization was further amplified by electric field effects, thereby activating NMDA channels. This activation generated an NMDA-dependent spike and a propagating wave via the ephaptic coupling. Overall, these simulated results strongly support our proposed hypothesis that the calcium-dependent slow moving wave is the source for the NMDA-dependent fast traveling spikes.
## Discussion
By taking advantage of the state-of-the-art voltage-sensitive protein and calcium imaging methods, two different types of traveling waves were detected and traced in longitudinal hippocampal slices. The fast traveling spikes refer to the 4-AP induced inter-ictal epileptiform activity propagating at a speed of approximately 0.1 m/s and also previously observed in the unfolded hippocampus5. Most of the fast traveling waves originated in the temporal region of the longitudinal hippocampal slice indicating that the temporal area of the hippocampus is more epileptogenic that the septal side. In fact, several studies have shown that temporal hippocampus is more excitable and more epileptogenic by electrical or chemical stimuli than septal hippocampus26,27,28. In addition, the slow moving waves previously shown to be electrically silent were observed by applying imaging techniques6. The presence of this neural source was previously inferred from isochrones lines indicating the arrival of the spikes at the electrodes but could not be observed electrically even when positioned on top of recording sites6. The slow wave was revealed by detecting the intracellular calcium concentration in the neurons during propagation of the slow event and the very low frequency bandwidth (<1 Hz) could explain why it was difficult to detect with electrical recording setup. An electrical silence source also documented in cardiac-muscle tissues shows that a spiral wave could propagate through the heart with a speed of 0.1 m/s with the core of the spiral waves electrically silent and move slowly29. In the present study, calcium imaging experiments reveal that a neural calcium wave was always accompanied by a fast propagating spike recorded electrically and was with similar speed and direction of propagation already reported in the previous study6. Taken together, these data indicate that the slow propagating neuronal calcium wave is the moving source of the spikes. The probability distribution of the delay and speed of the slow moving wave in the presence of APV does not follow a normal distribution (Fig. 5d,e) and this non-Gaussian distribution likely results from the small number of samples. However, a non-parametric statistical analysis does support the hypothesis that the slow moving wave can persist in the presence of NMDA blockers.
Intracellular calcium wave traveling from cell to cell has been shown to be mediated by gap junction or ATP release17,30. Our previous study showed that 4-AP induced slow source could still propagate in the presence of gap junctions blockers5. The results of this study further show that the slow moving wave continues to propagate in the presence of ATP receptor blocker (Fig. 6c). Therefore, gap junctions and ATP release cannot explain the propagation of the slow moving wave.
Extracellular potassium wave has been found in the adult hippocampus and thus the diffusion of potassium could perhaps explain the propagation of the slow moving wave31. However, most activity related to potassium diffusion in the literature demonstrated very slow propagating speeds31,32,33,34. The speed of the propagation is from 0.00018 to 0.00084 m/s. The speed of potassium diffusion is 10 and even 100 times less than the speed of the slow wave in this study. To the best of our knowledge, the speed of potassium diffusion wave is too slow to explain the slow wave propagation speed.
Based on the experimental results, the propagation of the slow moving wave is different from NMDA-dependent spike, not dependent on the ATP release, and not coupled with the potassium diffusion. However, our modeling simulation suggests that the slow moving wave could propagate through the ephaptic coupling similar to the fast traveling spikes5. Calcium signals can generate spikes relying on the calcium-dependent channels, propagate, and generate a wave35,36. Therefore, the slow moving wave could be explained by large calcium spikes in many cells generating a self-propagation wave.
The calcium imaging experiments did reveal the propagation trajectory of the slow moving wave based on the analysis of optical signals extracted from different regions of interest. However, the calcium dye (OGB-1) is too slow to image the fast traveling spikes. The causal relationship between the fast traveling spike and slow moving wave cannot be directly established in the calcium imagining experiments. The hypothesis that the fast traveling spikes are generated by the slow moving wave was supported by experiments that combine voltage imaging technique, electrophysiology experiments6, and modeling simulation. However, a more definite experiment to establish the causality would require imaging separately each of these two waves.
The model simulation suggests that the slow moving wave is the source of the fast traveling spikes. The computational model including of NMDA channel and calcium channel could generate two separate traveling waves containing similar characteristics compared to the experimental data (Fig. 7d). Moreover, the simulation results show that the fast traveling spikes are mediated by NMDA channels and the slow moving wave is mediated by calcium channels. To further demonstrate the relationship between the fast traveling spikes and the slow moving wave, the model simulation indicates that the NMDA-dependent spike could be triggered by the calcium-dependent spike. However, the NMDA-dependent spike has a faster dynamic than calcium-dependent spike20,23 and thus propagates faster and appeared before the calcium-dependent spike reached the peak located at P1 in Fig. 7f. A fully observable calcium spike would misleadingly appear to follow the fully observed NMDA spike (Fig. 7g). Therefore, the fast traveling spikes appear to propagate first and are followed by the calcium wave in the voltage imaging experiments (Fig. 3e) but it should be noted that the fast traveling spikes were triggered by the initiation of the slow moving wave based on the model simulation. The model results, therefore, show that the calcium spike is the source of the NMDA-dependent spikes.
In human patients, it has been found that seizures could spread with slow dynamics37,38,39,40. The speed of the seizure recruitment varies from 0.004 m/s to 0.01 m/s and the slow moving wave in this study propagated with a similar speed. Therefore, the present in-vitro study implies that a slow moving wave might be related to the seizure progression in the early stages. In particular, human seizures can be distinguished by ictal wavefront activity and ictal core activity with the ictal wavefront propagating at a slow speed39. Also, a recent study shows that seizures could underlie a spinning wave dynamics40. The seizure takes tens of seconds to propagate and the direction of the seizure propagation can be predicted by the slow drift of the signal4,39 while the slow neural source in the present study also has very slow dynamics. This phenomenon was also observed in our previous finding that a neural source is moving and generates spikes in different areas6. Several studies from patients with epilepsy show that the slow-moving ictal wavefronts can predict the propagation of seizures and the ictal wavefront is related to the inhibitory restraint of seizure activity4,39,41. The role of the slow moving wave in this study could be similar to the ictal wavefront since this slow moving wave could trigger the fast traveling spikes and also predict the generation of the fast traveling spikes in other areas6. Therefore, the in-vitro slow neural source shares many characteristics with the slow waves found in the human brain during seizures.
In summary, we observed two types of the traveling waves in the unfolded hippocampus preparation. One is a fast traveling spike that is related to the inter-ictal activity. The fast traveling spikes could be detected by electrical recording. The other is a slow moving wave that is associated with the neural source of the inter-ictal activity. This slow neural source is neither NMDA nor ATP dependent, and likely not coupled with potassium diffusion. Furthermore, our model simulation suggests that the slow traveling neural source is consistent with calcium spikes propagating by electrical field like epileptiform activity. The slow neural source could possibly explain the slow recruitment of seizures in the early stage or the multi-sites of epilepsy foci.
## Methods
### Animals
VSFP-Butterfly 1.2 transgenic mice were used to perform the experiments of detecting both fast traveling spike and slow moving wave. CD-1 mice were used to perform the experiments of calcium imaging. Mice used for in-vitro hippocampal slice studies were approximately 10–30 days old (P10-P30). All experimental procedures performed in this study followed the NIH animal use guidelines and were approved by the Institutional Animal Care and Use Committee (IACUC) at Case Western Reserve University.
### Preparation of longitudinal hippocampal slice
Mice of either sex with ages ranging from P10–P30 were anesthetized by isoflurane and euthanized by decapitation. Next, the brain was removed rapidly from the skull and was cooled rapidly (0–5 °C) in high-sucrose artificial cerebrospinal fluid (S-aCSF) containing (in mM): sucrose, 75; NaCl, 85; KCl, 2.5; NaH2PO4, 1.25; NaHCO3, 25; D-glucose, 25; MgCl2, 4; CaCl2, 0.5; and bubbled with a 95% O2/5% CO2 gas mixture. The hippocampus was separated from the brain by using customized glass pipette tools on a cooling plate. The hippocampus was then sandwiched between two agar gels cut to appropriate size and fixed to a cutting block using cyanoacrylate glue. 400 μm slices were cut longitudinally in S-aCSF at low temperature using a vibratome (VT1000S, Leica, Germany) and placed in a bubbled normal aCSF at room temperature containing (in mM): NaCl, 125, KCl, 2.5; NaH2PO4, 1.25; D-glucose, 25, NaHCO3, 25; MgCl2, 2; CaCl2, 2, to recover for at least 1 h. After one-hour incubation, slices were transferred to a staining chamber for loading the calcium dye or to a bath-immersion recording chamber (Warner Instruments, USA) and superfused with gas-bubbled normal aCSF heated to 32 °C for the further experiments.
The acetoxymethyl (AM) ester of the calcium-sensitive dye Oregon Green 488 Bapta-1 (Thermo Fisher Scientific Inc) was used as a calcium indicator. A solution of the dye was prepared in dimethyl sulfoxide (DMSO) to a final concentration of 4 mM. DMSO was used to solubilize the water-insoluble dye. After one-hour recovery of hippocampal slices, a single slice was selected, by visual inspection to identify tissues with prominent cell layers, and transferred to another walled loading chamber containing 3 mL bubbled normal aCSF. The dye solution was loaded directly onto the tissue surface, resulting in a high initial concentration of the dye, but achieving a final concentration of 15 µM42. The incubation was performed in dark conditions at room temperature, with the loading time of 10 min plus as many minutes as the age of the mouse in post-natal days12. After loading the dye, the slice was placed in the bath-immersion recording chamber and superfused with gas-bubbled normal aCSF. The normal aCSF washed the tissues, resulting in the removal of occurrences of bright spots created by uneven retention of the dye on the surface of the tissue. Imaging and electrical recording began no sooner than 30 min after the tissue was placed in the bath-immersion recording chamber.
### Electrical and optical recording
Glass pipette recording electrodes were pulled to a resistance of 5 MΩ for electrodes used to measure field potentials (150 mMNaCl pipette filling solution). The position of the electrode was manipulated using a micromanipulator (MPC-200, Sutter Instruments), whose range of motion was in all three axes. The glass electrode was positioned on the cell layer, approximately 20 µm below the surface of the tissue, using a 5× objective (Zeiss Microscopy, USA) on the microscope (Zeiss Microscopy, USA) to determine the exact location. The signals were received on an amplifier (Axopatch 200B, Molecular Devices), with amplification at 100. The signals were digitized at 20 kHz sampling frequency by using a digitizer (Digidata 1440 A, Molecular Device), and stored on a computer for analysis.
OGB-1 has an emission wavelength of 494 nm, and an excitation wavelength of 523 nm. To fulfill these criteria, the excitation filter was 488 nm, the emission filter was 520 nm, and the dichroic mirror had a separation wavelength of 516 nm (Semrock, USA). For the optical recording of VSFP-Butterfly 1.2, two different filter sets are prepared for the mCitrine and mKate2. The recording optics included the following filters and splitter: FF01-483/32-25 for mCitrine and mKate2 excitation (Semorck), FF01-542/27 for mCitrine emission (Semorck), BLP01-594R-25 (Semorck) for mKate2 emission, 515LP as the beam splitter for mCitrine, and 580LP as the splitter for mKate2. A broad-spectrum LED light source (X-cite 120LED, Excelitas Technologies) was used during the course of the experiment.
The images were acquired by using a digital CMOS camera (C11440, Hamamatsu Photonics) at a frame rate of 200 Hz (2048 × 512 pixels) for the experiments of calcium imaging and at a higher frame rate of 800 Hz (512 × 64 pixels, 4 × 4 binning) for the experiments of voltage-sensitive imaging. The imaging data were analyzed with MATLAB and signal process toolbox (Math Works).
### Image processing and data analysis
All the acquired image sequences were filtered using a 3 × 3 spatial filter to eliminate electron noise from the camera and shot noise from the acquisition electronics. The background fluorescence is eliminated by subtraction of a background pixel (edge pixel) from each pixel in the entire stack. The fluorescent signals were presented as a percentage of fluorescent change ΔF/F0 which was calculated as (F − F0)/F0, where F0 is baseline fluorescence signal averaged over the whole recording period. The image sequence can be considered as pseudo 3-dimensional (3D) signals, with each frame as an image on the x and y-axes, over time, which is the third axis. Hence, each pixel has a single x and y coordinate, and a frame length of time coordinates. The change in the intensity of each pixel value can be mapped over time by inverting the axes such that a single pixel in each frame is shown as the intensity changes in the fluorescence over time.
To determine the speed of propagation of the traveling waves, a cross-correlation measurement was used to estimate the delay between two optical signals from two regions of interest. The regions were selected manually to restrict selection only on the visible cell layer. All measurements were taken from the temporal to the septal side of the tissue. If the delay was positive, the direction of propagation was defined as temporal to septal.
For mapping, the dynamics of calcium in the glial cell, the regions of interest in glial cells were identified manually based on the criteria that the fluorescent intensity is twice higher than the baseline intensity. The optical signal was reconstructed in the time domain to trace the delay between two glial cells. The wavefront, instead of the peak, of the signal, was used to measure the speed of propagation between signals. A cross-correlation measurement was used to quantify the delay between signals.
### Statistical analysis
A statistical analysis was done by using t-test to compare the speeds in two different conditions. A statistical significance criterion of α = 0.05 was used for all tests. Results are shown as mean ± the standard deviation of the mean. The calculation was based on events unless noted.
### Computational modeling
#### Single cell model
The three-compartmental model (Fig. S2a) for a hippocampal pyramidal cell (HPC) was built under Matlab stimulation environment. This model was tested for 4-AP condition-induced both NMDA-dependent fast epileptiform propagation and Calcium-dependent slow wave propagation. In the model, each cell contains three compartments, with one compartment for soma, one compartment for the apical dendrite and one compartment for the basal dendrite. Similar as to previous models, the soma has an area of 995.4 μm2 with a diameter of 17.8 μm, and, the other two dendritic compartments have the same diameter of 5.2 μm and length of 735.3 μm for the apical one, and 490.2 μm for the basal one43,44. In our model, we set about half lengths of dendrites i.e. 400 μm for the distance between apical dendritic and somatic compartment, and 250 μm for the distance between basal dendritic and somatic compartment, respectively. The passive HPC membrane parameters were set to the following values: membrane resistance R m = 680 Ω·cm2 and membrane capacitance C m = 1.0 μF/cm2 for both somatic and dendritic compartments, and axial resistance R i = 530 Ω·cm. With these parameters, the electronic parameters for each compartment can be determined by cable theory, as listed in Table S1.
It is well known that NMDA receptors are widely distributed in branches of dendrites e.g. basal, oblique and tuft termed as “non-apical” dendrites while calcium channels dominantly locate at the apical trunk of dendrite22. To simplify the following network model, NMDAR channels and Ca channels were separately included in basal and apical dendrite in the current proposed model (Fig. S2a). NMDA receptors were not considered in apical dendrite because NMDA receptors located in distal apical dendrite far away from the soma, compared with those in the basal dendrite, generated weaker field effects on the neighbor neurons. Moreover, basal dendritic compartment contained a delayed rectifier potassium current I KDR and apical dendritic compartment contained a short-duration Ca- and voltage-dependent potassium current I KC and a long-duration Ca-dependent current potassium current I KAHP . In contrast with the previous models, the somatic compartment was only considered as a passive one. It is worth noting that Na channels were not considered at soma in current model for the reason that this model was purposed to verify whether and how those coexisting fast and slow propagation behaviors observed in vitro experiments are evoked by interactive dendritic activities mediated via NMDA and Ca channels.
The transmembrane potentials (Vm_ad, Vm_s, and Vm_bd) for three compartments of the model is described by the relationship
$${C}_{m}\frac{d{V}_{m\text{\_}ad}}{dt}=-{I}_{Ca}-{I}_{KC}-{I}_{KAHP}-{I}_{L\text{\_}ad}-\frac{{{g}}_{c\text{\_}s\text{\_}ad}}{{A}_{ad}}({V}_{m\text{\_}ad}-{V}_{m\text{\_}s})$$
(1)
$${C}_{m}\frac{d{V}_{m\text{\_}s}}{dt}=-{I}_{L\text{\_}s}-\frac{{g}_{c\text{\_}s\text{\_}ad}}{{A}_{s}}({V}_{m\text{\_}s}-{V}_{m\text{\_}ad})-\frac{{g}_{c\text{\_}s\text{\_}bd}}{{A}_{s}}({V}_{m\text{\_}s}-{V}_{m\text{\_}bd})$$
(2)
$${C}_{m}\frac{d{V}_{m\text{\_}bd}}{dt}=-{I}_{NMDA}-{I}_{KDR}-{I}_{L\text{\_}bd}-\frac{{g}_{c\text{\_}s\text{\_}bd}}{{A}_{bd}}({V}_{m\text{\_}bd}-{V}_{m\text{\_}s})$$
(3)
The gating equations for each active current are implemented using the Hodgkin-Huxley formalism as in Table S2. The channel conductance is gCa = 20 ms/cm2, $${\bar{g}}_{NMDA}=5.6\,{\rm{mS}}/c{m}^{2}$$, g KC = 5 mS/cm2, g KAHP = 0.3 mS/cm2, and g KDR = 200 mS/cm2. The reversal potentials are E Ca = 70 mV, E NMDA = 0 mV, E K = −60 mV, E L_d = −58 mV, and E L_S = −70 mV.
The kinetics of gating variables x for I Ca and I KC in apical dendrite are governed by the following equation:
$$\frac{dx}{dt}=\frac{{x}_{\infty }({V}_{m\text{\_}ad})-x}{{\tau }_{x}}$$
(4)
with (i.e. x {m Ca , h Ca , c}. The activation and inactivation steady-state function x are given in Boltzmann form.
$${x}_{\infty }=\frac{1}{1+\exp (-({V}_{m\text{\_}ad}-{\theta }_{x})/{k}_{x})}$$
(5)
The half activation/inactivation voltages θ x , slope rates k x at θ x and time scales τ x are all constant shown in Table S3.
The dynamics of the calcium concentration inside the HPC, [Ca2+] i is described as
$$\frac{d{[C{a}^{2+}]}_{i}}{dt}=-v{I}_{Ca}-\frac{{[C{a}^{2+}]}_{i}}{{\tau }_{[Ca]}}$$
(6)
with the constant values of v and τ Ca shown in Table S3. The variable [Ca2+] i in our model is dimensionless45. It is proportional to the Ca2+ concentration in a thin internal cylindrical shell adjacent to the membrane. [Ca2+] i -dependent gate variable χ(Ca) is given by a literature46.
$${\rm{\chi }}(Ca)=\frac{1}{1+{a}_{c}/{[C{a}^{2+}]}_{i}}$$
(7)
where the constant value of ac is shown in Table S3.
Gate variable q depends on its corresponding gate function
$$\frac{dq}{dt}=\frac{{q}_{\infty }({[C{a}^{2+}]}_{i})-q}{{\tau }_{q}}$$
(8)
and steady function q is the following
$${q}_{\infty }({[C{a}^{2+}]}_{i})=\frac{1}{1+{a}_{q}^{4}/{[C{a}^{2+}]}_{i}^{4}}$$
(9)
with the constant values of τ q and a q shown in Table S3.
The dynamics of gate variable q for I KDR in basal dendrite is described by
$$\frac{dn}{dt}={\alpha }_{n}({V}_{m\text{\_}ad})-n\cdot ({\alpha }_{n}({V}_{m\text{\_}ad})+{\beta }_{n}({V}_{m\text{\_}ad}))$$
(10)
with the variable rate functions modified from the literature47
$${\alpha }_{n}=\frac{0.00049\cdot ({V}_{m\text{\_}ad}-32)}{1.0-exp(-\frac{{V}_{m\text{\_}ad}-32}{25.0})},\,{\beta }_{n}=\frac{0.00008\cdot ({V}_{m\text{\_}ad}-42.0)}{exp(\frac{{V}_{m\text{\_}ad}-42.0}{10.0})-1.0}$$
(11)
In the case of the NMDA-gated channel, there is a marked voltage-dependency in the presence of extracellular magnesium. For physiological magnesium concentrations, the dependence on voltage of NMDA receptor-mediated current I NMDA can be integrated in a gating function B(V mbd ) that multiplies the NMDA conductance $${\bar{g}}_{NMDA}$$ (Table S2). This gating function is
$$B({V}_{m\text{\_}bd})=\frac{1}{1+\frac{{[M{g}^{2+}]}_{o}}{{M}_{0}}\exp (-{k}_{B}\cdot {V}_{m\text{\_}bd})}$$
(12)
where [Mg2+] o is the extracellular Mg2+ concentration of 1 mM and M0 and k B are constants shown in Table S3. It should be noted that $${\bar{g}}_{NMDA}$$ in this model is proportional to fraction of NMDA channels in the open state O NMDA i.e. $${\bar{g}}_{NMDA}={g}_{NMDA}\cdot {O}_{NMDA}$$, where g NMDA is the maximum conductance of NMDA channel. Though the kinetics of O NMDA is complex, it’s a nearly constant when the synaptic events in HPC dendrite are considered as the independently-generated random Poisson processes with the same frequency. Thus, to focus on the fast/slow propagation mediated by extracellular electric field, it is reasonable that $${\bar{g}}_{NMDA}$$ is considered as a constant under some stable synaptic activities background. The values of all parameters for single HPC are taken from above values unless otherwise specified.
#### HPC neural network
The layout of the network was designed in a way to capture the most features of both fast and slow propagation activities in physiological cellular layout. We simulate the hippocampal pyramidal cell (HPC) network in physiological CA1 region with 4000 μm(X) × 600 μm(Y) × 360 μm(Z) (Fig. S1a), where X and Z represent longitudinal and transverse directions of hippocampus respectively, and Y represents the tissue thickness along the cellular axial direction. One stack network of this region is made up of cell arrays with 200 neurons in X-axis and 18 neurons in Z axis (Fig. S1b,c). The distance between every two adjacent neurons (dc-c) in a physiologic pyramidal network ranges from 2 to 5 μm48. In this paper, we tested dc-c from 2 to 4 μm and its values were assigned in the text. To represent the cell stacking throughout the depth of a tissue slice, similar to the handling method in Chen Q et al., 20158, a “stacking factor” (SF) was used to take into account the actual number of cells around one stack network (Fig. S1d). Here, the value of SF is in the range between 10 and 308.
#### Electric field coupling
To test the hypothesis that endogenous electric field alone could induce both fast and slow neural physiologic propagation observed in vitro, the synaptic connections, gap junction, and diffusion effects were eliminated in the network while communications between adjacent cells were implemented by electric field coupling. To obtain the higher computational efficiency, electric field effect could only propagate action potentials in the longitude direction (X-axis) i.e. the cells in any two different columns (Z axis) were coupled bidirectionally while those in each transverse direction (Z axis) were not affected each other. The electric field effect was calculated using the quasistatic formulation of the Maxwell equations assuming homogeneous and linear volume conductors. According to Ohm’ law, the corresponding potential φ at the point P at distance r relative to reference electrode in a medium of resistivity ρ is described as follow:
$$\phi =\frac{\rho }{4\pi r}\cdot I$$
(13)
Using superposition, Eq. (13) can be generalized to monopolar electrodes from each of three compartments from a source Cell(i,j) in the network array with transmembrane currents Ii,j_ tran_ad , Ii,j_ tran_s , and Ii,j_ tran_bd at the corresponding distances to each of three compartments of the target Cell(k, l) (j≠l) in the cell array. The extracellular potential inserted at three compartments of the target Cell(k, l) is given by the following:
$${V}_{(k,l)\text{\_}e\text{\_}z}=SF\cdot \frac{\rho }{4\pi }\sum _{(i,j)}(\frac{{I}_{(i,j)\text{\_}tran\text{\_}ad}}{{r}_{(i,j)\text{\_}ad\to k,l\text{\_}z}}+\frac{{I}_{(i,j)\text{\_}tran\text{\_}s}}{{r}_{(i,j)\text{\_}s\to (k,l)\text{\_}z}}+\frac{{I}_{(i,j)\text{\_}tran\text{\_}bd}}{{r}_{(i,j)\text{\_}bd\to (k,l)\text{\_}z}})\quad (z=ad,s,bd)$$
where V(k,l)_e_z is the extracellular potential inserted at target compartment z in the target Cell(k, l); I(I,j)_ tran_z is the transmembrane current of three compartments (assuming current going out of the cell to be positive direction) in source Cell(i,j) located r(i,j)_adk,l_z, r(i,j)_s→(k,l)_z and r(i,j)_bd→(k,l)_z distances from the target compartment z (Fig. S2); ρ is the extracellular resistivity with the range of 250~380 Ω·cm and here 300 Ω·cm was used in the model20,49,50,51 and SF is the stacking factor.
#### Extracellular potential, Field amplitude, and speed measurement
To measure the resulting extracellular potential and electric field due to network spiking activities and compare them to the experimentally recorded waveforms in vitro, we placed 2 × 3 virtual multi-electrode array outside of the network paralleling to (X, Y) plane (Fig. S3), similar as to the placement of the measuring electrodes into the in vitro slice. The virtual electrode array was placed about 30 μm away from the surface layer of the rectangular cell array to account for approximately three rows of the dead cell around inserted electrodes, a situation observed experimentally. All cells’ resulting extracellular potential at the multi-electrode array are calculated, and field amplitude was calculated by finding the spatial derivatives of extracellular potentials along the Y-axis. The network field amplitude was the average of the field amplitudes at three different positions (Eq. (15), i.e. Temporal, Middle and Septal, Fig. S3)
$${E}_{network}=\frac{\frac{{V}_{e\text{\_}Tb}-{V}_{e\text{\_}Tt}}{2}+\frac{{V}_{e\text{\_}Mb}-{V}_{e\text{\_}Mt}}{2}+\frac{{V}_{e\text{\_}Sb}-{V}_{e\text{\_}St}}{2}}{3}$$
(15)
The propagation speeds including fast and slow ones measured based on the three extracellular recording at the top of virtual electrode array i.e. V e_Tt , V e_Mt and V e_St , where peak times for both fast and slow propagation oscillations are recorded, and the delay from T t to M t and from M t to S t were calculated. The propagation speed was derived by taking the travelling distance divided by delay time. To determine the coexistence of the fast and slow propagations, the filtered virtual extracellular recordings were obtained via 1 Hz high-pass Butterworth filter and 1 Hz low-pass Butterworth filter respectively similar as to those used in the experiments.
### Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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## Acknowledgements
We would like to thank Dr. Thomas Knöpfel in Imperial College London and Dr. Cris Niell in the University of Oregon providing the VSFP Butterfly 1.2 transgenic mice for this study. This work is funded by grants from the National Institute of Health (NIH/NINDS 5R01NS060757-07 Detection and Control of Epilepsy) and the National Natural Science Foundation of China (61771330).
## Author information
Authors
### Contributions
C.-C.C., X.W., A.K.A., and D.M.D. designed the study. C.-C.C., and A.K.A. performed the experiments. X.W. performed the model simulation. C.-C.C., X.W., A.K.A., R.S.S., L.E.G., M.Z. performed the analyses. C.-C.C., X.W., A.K.A., and D.M.D. wrote the manuscript with input from all authors.
### Corresponding author
Correspondence to Dominique M. Durand.
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Chiang, CC., Wei, X., Ananthakrishnan, A.K. et al. Slow moving neural source in the epileptic hippocampus can mimic progression of human seizures. Sci Rep 8, 1564 (2018). https://doi.org/10.1038/s41598-018-19925-7
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• DOI: https://doi.org/10.1038/s41598-018-19925-7
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English Információ A lap Pontverseny Cikkek Hírek Fórum
Rendelje meg a KöMaL-t!
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Matematika oktatási portál
P. 3906. A 2-kg brick falls 5 m and then a worker catches it and brings it into rest in a distance of 0.5 m exerting an upward constant force. a) Find the force exerted by the worker. b) Find the average power of the worker.
(4 points)
Deadline expired on 11 October 2006.
Google Translation (Sorry, the solution is published in Hungarian only.)
Megoldás. a) F=216 N.
b) 1,1 kW.
Statistics on problem P. 3906.
376 students sent a solution. 4 points: 163 students. 3 points: 22 students. 2 points: 121 students. 1 point: 40 students. 0 point: 14 students. Unfair, not evaluated: 16 solutions.
• Problems in Physics of KöMaL, September 2006
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2017-10-23 04:24:38
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http://mathoverflow.net/questions/96095/an-exercise-in-kunen-getting-axiom-of-replacement-from-set-like-transitive-clos
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# An exercise in Kunen. Getting Axiom of Replacement from set-like transitive closure.
I am studying Kunen's Set Theory (2011 edition) on my own. I got stuck at the excercise I.9.6 which is:
Excercise I.9.6. Derive the axiom of replacement from lemma I.9.5.
And the mentioned lemma is this:
Lemma I.9.5. For a relation R and a class A, if R is set-like on A, then R* is set-like on A.
Here R* is the transitive closure of R. Also, a relation R is set-like on a class A if { x\in A : xRy } is a set for all y\in A.
Help appreciated.
-
I have to ask, is there a difference between the 2011 edition and the old edition? – Asaf Karagila May 5 '12 at 22:57
@Asaf: Yes. Quite a few. – Andrés Caicedo May 6 '12 at 2:11
The 2011 version contains a lot more. Also the approach is a bit different. In the new version Kunen does not hesitate to use model theory and topology to get results. This condenses some parts of the old book. Still, the new book is 75 pages longer. This means that there is a lot of new material. Especially, the chapter on infinitary combinatorics contains much more (including sections on small cardinals and elementary submodels). The iterated forcing chapter contains a section on proper forcing. – Ali Kare May 6 '12 at 9:03
Also, in the new version the exercises are not collected at the chapter ends but rather sprinkled throughout the text. I find this to be better. Solving exercises at the spot facilitates learning. Also, facing a long list of exercises at the chapter end can be a bit daunting. (I wish Jech didn't move all exercises to the chapter ends in the third edition. What was he thinking?) – Ali Kare May 6 '12 at 9:04
Suppose that the lemma holds and that we are considering an instance of the replacement axiom, so we have a set $X$ and for some parameter $z$ and for every $x\in X$ there is a unique $y$ such that $\varphi(x,y,z)$. Fix any set $w$ not in $X$, and let $R$ be the class relation such that $R(x,w)$ for each $x\in X$, and such that $R(y,x)$ whenever $\varphi(x,y,z)$. That is, the children of $w$ are exactly the members of $X$, and the child of any $x\in X$ is precisely the corresponding $y$. Thus, the relation $R$ is set-like, since $X$ is a set, and $\{y\}$ is a set for each $y$ that arises. But the transitive closure of $R$ will relate all the $y$'s that arise from any $x\in X$ to $w$. And so if the transitive closure of $R$ is set-like, then the set $\{y\mid \exists x\in X\, \varphi(x,y,z)\}$ will be a set, thereby verifying this instance of the replacement axiom.
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2016-02-11 06:42:11
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http://www.wanniertools.com/input.html
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# 2.2. Introduction of input files¶
Attention: From WannierTools 2.2, the name of input file changes from ‘input.dat’ to ‘wt.in’. The excutable binary changes from ‘wann_tools’ to ‘wt.x’
There are two input files you should prepare wt.in and wannier90_hr.dat
## 2.2.1. Main input file wt.in¶
Before executing wann_tools, you should cp the wt.in file in the directory wannier_tools/example by your own necessary.
For version later than 2.0, we updated the format of wt.in. The input file is structured in a number of NAMELIST and INPUT_CARDS.
Here we introduce the wt.in for Bi2Se3 as an example
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/
LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667
ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0 0 0.5
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820
PROJECTORS
3 3 3 3 3 ! number of projectors
Bi px py pz ! projectors
Bi px py pz
Se px py pz
Se px py pz
Se px py pz
SURFACE ! See doc for details
1 0 0
0 1 0
&CONTROL
BulkBand_calc = T
BulkFS_calc = T
BulkGap_cube_calc = T
BulkGap_plane_calc = T
SlabBand_calc = T
WireBand_calc = T
SlabSS_calc = T
SlabArc_calc = T
SlabQPI_calc = T
SlabSpintexture_calc = T
Wanniercenter_calc = T
BerryCurvature_calc = T
EffectiveMass_calc = T
/
&SYSTEM
NSLAB = 10 ! for thin film system
NSLAB1= 4 ! nanowire system
NSLAB2= 4 ! nanowire system
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
Bx= 0, By= 0, Bz= 0 ! Bx By Bz
surf_onsite= 0.0 ! surf_onsite
/
&PARAMETERS
Eta_Arc = 0.001 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
OmegaNum = 100 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 21 ! number k points odd number would be better
Nk2 = 21 ! number k points odd number would be better
Nk3 = 21 ! number k points odd number would be better
NP = 1 ! number of principle layers
Gap_threshold = 1.0 ! threshold for GapCube output
/
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
KPLANE_BULK
-0.00 -0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.
WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982
### Basic Parameters¶
TB_FILE, LATTICE, ATOM_POSITIONS, PROJECTORS and SURFACE are the necessary basic parameters. They are used by almost all functionalities listed in CONTROL namelist.
### NAMELISTS¶
NAMELISTS are a standard input construct in Fortran90. The use of NAMELISTS is relatively flexible. All the variables in the NAMELISTS have default values. You should set them only when it is needed. Variables can be inserted in any order. Such as
&NAMELIST
needed_variable2=XX, needed_variable1=YY,
character_variable1='a suitable string'
/
There are 4 NAMELISTS included in wt.in. They are TB_FILE, SYSTEM, CONTROL, PARAMETERS.
Note
If you want to comment one line, please use ‘!’ instead of ‘#’, because our codes were written in Fortran.
#### TB_FILE¶
Set the filename of the tight-binding Hamiltonian. At present, we use the format of wannier90_hr.dat specified in Wannier90.
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/
The default value for Hrfile is ‘wannier90_hr.dat’. You could specify the first-principle package that used for obtaining wannier90_hr.dat. Default value for Package is ‘VASP’. We support VASP, QE, Wien2k, OpenMx, Abinit at present. Please report new software package to me if you needed.
Note
Package is very important if you use QE to generate your tight binding model. Because the orbital order in QE is different from VASP, Wien2k et al.. And it will affect the results of spin texture. If you got strange spin texture, please carefully check this tag.
#### SYSTEM¶
In this namelists, we specify the system you need to compute.
&SYSTEM
Nslab = 10
Nslab1= 6
Nslab2= 6
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
Bx= 0, By= 0, Bz= 0 ! Bx By Bz
surf_onsite= 0.0 ! surf_onsite
/
• NSlab : integer, Number of slabs for slab band, The default value is 10.
• NSlab1, Nslab2 : integers, The thickness of nano ribbon. If you don’t want to calculate the band structure of it, then don’t set it. The default values are Nslab1= 1, Nslab2= 1.
• NumOccupied : integer, Number of occupied Wannier bands. No default value.
Important: please set NumOccpuied correctly. It represents the “occpuied” wannier bands, not the total number of electrons. In the calculation of Wilson loop, the Wilson loop is the trace of NumOccupied bands. If you want to study the topology between the 8th and the 9th band, then set NumOccupied=8.
When you search Weyl points, nodal line or study the gap in some k slices, NumOccupied is also a very important. WannierTools will look for touching point or calculate the energy gap between the NumOccupied’th band and the (NumOccupied+1)’th band.
When you calculate the Fermi surface with BulkFS_calc= T, In order to save the storage, WannierTools only writes out 8(16) energy bands around NumOccupied’th band for SOC=0 (SOC=1) system into FS3D.bxsf.
If you don’t put any physical meaning into this tag, then it is very easy to understand.
• SOC : integer, Flag for spin-orbital coupling. If SOC=0, it means there is no SOC included in your given tight binding model. if SOC=1 or >0, it means SOC is already included in the tight binding model.
• E_FERMI : real-valued, Fermi level for the given tight binding model.
• Bx, By, Bz : real-valued, magnetic field value. Ignore it in this version.
• surf_onsite : real-valued, Additional onsite energy on the surface, you can set this to see how surface state changes. But don’t set it if you don’t know what it is.
#### CONTROL¶
In this name list, you can set the keywords to setup the tasks. All these tasks can be set to be true at the same time.
&CONTROL
BulkBand_calc = T ! bulk band structure calculation flag
BulkFS_calc = F
BulkGap_cube_calc = F
BulkGap_plane_calc = F
SlabBand_calc = T
WireBand_calc = F
SlabSS_calc = T
SlabArc_calc = F
SlabSpintexture_calc = T
wanniercenter_calc = F
BerryCurvature_calc = F
/
Note
New features : :red: FindNodes_calc; WeylChirality_calc; Z2_3D_calc; Chern_3D_calc
We listed those features in the table below.
Flag options Function Output Tested
BulkBand_calc Band structure for bulk bulkek.dat, bulkek.gnu yes
BulkFS_calc Fermi surface for bulk system FS3D.dat, FS3D.bxsf yes
BulkGap_cube_calc Energy gap for a given k cube for bulk system GapCube.dat, GapCube.gnu yes
BulkGap_plane_calc Energy gap for a given k plane for bulk system GapPlane.dat, GapPlane.gnu yes
FindNodes_calc Find touching points between the Numoccpuied’th band and (Numoccpuied+1)’th band Nodes.dat, Nodes.gnu yes
SlabBand_calc Band structure for 2D slab system slabek.dat,slabek.gnu yes
WireBand_calc Band structure for 1D ribbon system ribbonek.dat,ribbonek.gnu yes
Dos_calc Density of state for 3D bulk system dos.dat yes
JDos_calc Joint Density of state for 3D bulk system jdos.dat yes
SlabSS_calc Surface spectrum A(k,E) along a kline and energy interval for slab system dos.dat_l, dos.dat_r, dos.dat_bulk,surfdos_l.gnu, surfdos_r.gnu, surfdos_l_only.gnu, surfdos_r_only.gnu, surfdos_bulk.gnu yes
SlabArc_calc Surface spectrum A(k,E0) for fixed energy E0 in 2D k-plane for slab system arc.dat_l, arc.dat_r, arc_l.gnu, arc_r.gnu, arc_l_only.gnu, arc_l_only.gnu, yes
SlabQPI_calc Surface QPI for fixed energy E0 in 2D k-plane for slab system arc.dat_l, arc.dat_r, arc_l.gnu, arc_r.gnu, arc_l_only.gnu, arc_l_only.gnu, arc.jdat_l, arc.jdat_r, arc.jsdat_l, arc.jsdat_r, arc_l_jdos.gnu, arc_l_jsdos.gnu, arc_r_jdos.gnu, arc_r_jsdos.gnu, yes
SlabSpintexture_calc Spin texture in 2D k-plane for slab system spindos_l.dat spindos_r.dat spintext_l.gnu spintext_r.gnu spintext_l.dat spintext_r.dat yes
wanniercenter_calc Wilson loop of a given 3D k-plane for bulk system wcc.dat, wcc.gnu yes
Z2_3D_calc Wilson loop in all 6 3D k-planes for bulk system Z2 number calculation wanniercenter3D_Z2.gnu, wanniercenter3D_Z2_{1-6}.dat yes
Chern_3D_calc Wilson loop in all 6 3D k-planes for bulk system Chern number calculation wanniercenter3D_Z2.gnu, wanniercenter3D_Z2_{1-6}.dat yes
WeylChirality_calc Weyl Chirality calculation for given k points find chiralities in WT.out, wanniercenter3D_Weyl.dat, wanniercenter3D_Weyl_*.gnu yes
BerryPhase_calc Berry phase with a 3D k path for bulk system find Berry phase in WT.out Yes
BerryCurvature_calc Berry Curvature in 3D k-plane for bulk system BerryCurvature.dat, BerryCurvature.gnu Berrycurvature-normalized.dat Berrycurvature-normalized.gnu yes
AHC_calc Calculate anomalous Hall conductivity for bulk system sigma_ahe.txt in unit of (Ohm*cm)^-1 yes
FindNodes_calc Find touch point between the N’th band to the (N+1)’th band in 3D BZ N=NumOccupied Nodes.dat Nodes.gnu yes
#### PARAMETERS¶
In this namelists, we listed some parameters necessary in the task you specified in namelists CONTROL.
&PARAMETERS
E_arc = 0.0 ! energy for calculate Fermi Arc
Eta_Arc = 0.001 ! infinite small value, like broadening
OmegaNum = 200 ! omega number
OmegaMin = -0.6 ! energy interval
OmegaMax = 0.5 ! energy interval
Nk1 = 50 ! number k points
Nk2 = 50 ! number k points
Nk3 = 50 ! number k points
NP = 2 ! number of principle layers
Gap_threshold = 1.0 ! threshold for GapCube output
/
E_arc : real-valued, energy for calculate Fermi arc, used if SlabArc_calc = T. The default value is 0.0.
Eta_Arc : real-valued, infinite same value for broadening used in Green’s function calculation. used if SlabArc_calc = T. Default value is 0.001.
[OmegaMin, OmegaMax] : real-valued, energy interval for surface state calculation. used if SlabSS_calc= T. No default value.
OmegaNum : integer valued, Number of slices in the energy interval [OmegaMin, OmegaMax]. used if SlabSS_calc= T. The default value is 100.
Nk1, Nk2, Nk3 : integer valued, Number of k points for different purpose. I will explain that later. Default value is Nk1=20, Nk2=20, Nk3=20.
NP : integer valued, Number of principle layers, see details related to iterative green’s function. Used if SlabSS_calc= T, SlabArc_calc=T, SlabSpintexture_calc=T. Default value is 2. You need to do a convergence test by setting Np= 1, Np=2, Np=3, and check the surface state spectrum. Basically, the value of Np depends on the spread of Wannier functions you constructed. One thing should be mentioned is that the computational time grows cubically of Np.
Gap_threshold : real valued. This value is used when you do energy gap calculation like BulkGap_cube_calc=T, BulkGap_plane_calc=T. The k points will be printed out in a file when the energy gap is smaller than Gap_threshold.
### Input Card¶
The second important format in wt.in is the input_card format, which is relatively fixed format. First, we need a keyword like LATTICE, which is name of this card. After this keyword, the number of lines is fixed until it is done. There are several INPUT_CARDS in the wt.in. There is no order between the INPUT_CARDS. And any comments or blank lines could be added between the INPUT_CARDS. Lets introduce them one by one.
#### LATTICE¶
In this card, we set three lattice vectors coordinates. For the unit, you can use both Angstrom and Bohr. However, in the program, we use Angstrom. Bohr unit will be transformed to Angstrom automatically. No default values for the LATTICE CARD.
LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667
#### ATOM_POSITIONS¶
In this card, we set the atom’s position.
ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0 0 0.5
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820
Note
1. Here the atom means that the atoms with projectors. not the whole atoms in the unit cell. 2. You can use “Direct” or “Cartesian” coordinates. “Direct” means the fractional coordinate based on the primitive lattice vector listed in LATTICE CARDS.
#### PROJECTORS¶
In this card, we set the Wannier projectors for the tight binding.
PROJECTORS
3 3 3 3 3 ! number of projectors
Bi pz px py ! projectors
Bi pz px py
Se pz px py
Se pz px py
Se pz px py
Here we don’t take into account the spin degeneracy, only consider the orbital part. The name of orbitals should be “s”, “px”, “py”, “pz”, “dxy”, “dxz”, “dyz”, “dx2-y2”, “dz2”. I will add f orbitals latter. The order of the orbitals is very important if you want to analyze the symmetry properties. The default order in Wannier90 is “s”, “pz”, “px”, “py”, “dz2”, “dxz”, “dyz”, “dx2-y2”, “dxy”. You can find the orbital order from wannier90.wout.
Note
If you don’t care about the calculation related to symmetry like mirror chern number. The order or the name is not important. So for the f electrons, please write 7 random orbitals like px or dz2 or what else you want.
##### SURFACE¶
Attention: from version v2.2.6 on, you can specify a surface with SURFACE card with only two lattice vectors.
#### MILLER_INDICES CARD¶
Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices. You can find more information from Wikipedia https://en.wikipedia.org/wiki/Miller_index. In WannierTools, you only need to specfiy three integers like
MILLER_INDICES
0 0 1
Note
Since this is very confusing, we discard it from version V2.2.6. You should notice that the Miller indices mentioned here are based on three vectors specified in LATTICE card.
#### SURFACE CARD¶
This card is very important for slabs calculation. You need to read the following text carefully
SURFACE ! See doc for details
1 0 0 a11, a12, a13
0 1 0 a21 a22 a23
In this card, we specify the surface you want to investigate. Basically, you should be aware of which surface you want to investigate, and of which direction you want to study the ribbon. So we need to define the new lattice vector system like this,
Choose two lattice vectors on the surface we want to study, and choose another vector which is not on this plane.
The slab calculations are base on the surface constructed by vector $$R_1', R_2'$$.
Note
a11, a12, a13 …, a23 should be integers, in unit of three lattice vectors
#### KPATH_BULK¶
This is the k path for bulk band structure calculation.
KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000
These k points are in unit of the reciprocal lattice constant built by the lattice vector LATTICE CARD. The number of k points is Nk1, which is set in NAMELISTS PARAMETERS. There are no default values for this CARD. So you must set some value in the input file when choosing BulkBand_calc=T.
#### KPOINTS_3D¶
You can calculate the properties on some kpoints you specified in point mode. e.g. the energy bands
KPOINTS_3D
4 ! number of k points
Direct ! Direct or Cartesian
0.00000 0.00000 0.0000
0.00000 0.00000 0.5000
0.50000 0.50000 0.0000
0.00000 0.00000 0.0000
The number of lines below “Direct” should be the same as the number above “Direct”. You could add comments at the end of each line. But you can’t add additional comment lines between the formatted lines.
#### KPATH_SLAB¶
This is the k path for slab system.
KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5
including the band structure calculation and the surface state calculation. It is necessary to set it when SlabBand_calc=T or SlabSS_calc=T. Number of k points along the line is Nk1.
#### KPLANE_SLAB¶
Define a 2D k space plane for arc plots.
KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots
The first line is the start point of the plane. The second and third line are the two vectors defining the plane. The number of k points for the 1st and 2nd vector is Nk1 and Nk2 respectively. Set this CARD when SlabArc_calc=T, SlabSpintexture_calc= T. The default values are
KPLANE_SLAB
-0.5 -0.5 ! Original point for 2D k plane
1.0 0.0 ! The first vector to define 2D k plane
0.0 1.0 ! The second vector to define 2D k plane for arc plots
#### KPLANE_BULK¶
The same set as KPLANE_SLAB CARD, but for 3D case.
KPLANE_BULK
-0.50 -0.50 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
We can use these two vectors to calculate the band gap of a plane in 3D BZ, then we can check whether there are Weyl points or nodal line in that plane. Notice that these vectors is in unit of reciprocal vectors. Set this CARD when BulkGap_plane_calc=T, BerryCurvature_calc=T, wanniercenter_calc=T. Default values are
KPLANE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane
#### KCUBE_BULK¶
The same set as KPLANE_BULK CARD
KCUBE_BULK
-0.50 -0.50 -0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube
We add another k vector to construct a k cube. Set this for BulkGap_cube_calc=T. The values list above are default values.
#### EFFECTIVE_MASS¶
This card is set for effective mass calculation
EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.
#### WANNIER_CENTRES¶
This card will be usefull for Wilson loop calculations.
WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982
Those centres can be obtained from wannier90.wout by searching “Final state”. The default values for this card are atomic positions.
## 2.2.2. Special tags for phonon system (under testing)¶
Now we have one testing version of phonon system, you can write to wuquansheng@gmail.com for testing. There are two steps for using WannierTools for phonon system.
1. Use phonon_hr.py to get the tight-binding Hamiltonian from the FORCE_CONSTANTS or FORCE_SETS which generated with phonopy. This part was written by Changming Yue (yuechangming8 at gmail.com). You can write email to him to get the source. By default the hrfile name of the Hamiltonian is phonopyTB_hr.dat. You can change the name of it as whatever you want.
2. After the generation of hrfile. You need another wt.in file as the same as the electron system. One difference is that you need to specify Particle = ‘phonon’ in the TB_FILE namelist like
&TB_FILE
Hrfile = 'phonopyTB_hr.dat'
Particle = 'phonon'
/
### LO-TO splitting¶
The LO-TO splitting can be treated as a pertubation see phonopy.
We need the following necessary CARDs in the wt.in. Take FeSi as an example
ATOM_MASS
2 ! number of types of atom, for FeSi, we have 2
4 4 ! number of atoms for each atom-type Fe4Si4
55.845 28.0855 ! atomic mass for each type of atom
LOTO_DT ! Dielectric constant tensor
199.480 0 0
0 199.480 0
0 0 199.480
LOTO_BC ! Born charge tensor for each type of atom
-4.3431500 0.6899200 -0.4140700
-0.4140800 -4.3431600 0.6899300
0.6898900 -0.4140600 -4.3431500
4.3909800 0.2300200 -0.1092900
-0.1093100 4.3909900 0.2300100
0.2300400 -0.1092800 4.3909800
LOTO_DT is a 3*3 matrix. LOTO_BC are Number-of-atom-types 3*3 matrices.
## 2.2.3. Tight-binding model wannier90_hr.dat¶
This file contains the TB parameters. Usually, it can be generated by Wannier90.
Of cource, you can generate it from the Slater-Koster method or discretize k.p model onto a cubic lattice. The format should like this
written on 8May2016 at 13:57:00
30
547
2 2 1 1 1 1 1 1 1 1 2 2 2 2 2
1 1 1 2 1 1 1 2 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
2 2 2 2 2 2 2 4 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 2 1 1 1 1 1 1 1 2 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 2 2 2 2 2 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
2 2 2 2 2 2 2 4 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
1 1 1 2 1 1 1 2 2 2 2 2 1 1 1
1 1 1 1 1 2 2
-6 2 -3 1 1 -0.000002 0.000003
-6 2 -3 2 1 0.000002 0.000017
-6 2 -3 3 1 -0.000053 0.000002
-6 2 -3 4 1 -0.000031 0.000002
-6 2 -3 5 1 0.000001 -0.000000
-6 2 -3 6 1 -0.000003 0.000002
-6 2 -3 7 1 0.000037 -0.000001
-6 2 -3 8 1 -0.000001 -0.000003
-6 2 -3 9 1 -0.000005 -0.000003
-6 2 -3 10 1 -0.000062 -0.000001
-6 2 -3 11 1 -0.000001 0.000001
-6 2 -3 12 1 -0.000031 0.000002
-6 2 -3 13 1 0.000011 -0.000000
-6 2 -3 14 1 -0.000001 0.000001
-6 2 -3 15 1 0.000003 0.000003
-6 2 -3 16 1 0.000000 -0.000010
-6 2 -3 17 1 -0.000010 -0.000001
-6 2 -3 18 1 -0.000000 -0.000008
-6 2 -3 19 1 0.000000 0.000000
-6 2 -3 20 1 0.000012 -0.000002
......
1. The 1st line is a comment line with any content.
2. The 2nd line is the number of Wannier orbitals, in consideration of spin degeneracy. We call it NUM_WANNS
3. The 3rd line is the number of R lattice vectors, we call it NRPTS
4. This section is about the degeneracy of R points. If you generate wannier90_hr.dat by you self, please set it to 1. There are NRPTS number of 1.
5. This section gives the TB parameters. The first three integers are the coordinates or R vectors in unit of three lattice vectors. The 4th and 5th column are the band index (Row first). The 6th and 7th are complex entities of the Hamiltonian.
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2019-02-23 22:00:06
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https://allnswers.com/mathematics/question14511205
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, 24.01.2020yoboi33
# Randy has two 28-pound blocks of ice for his snow cone stand. 1). how many pounds of ice does randy have at his snow cone stand? 2). how many tons of ice is there? write your answer from number 2 as a fraction and a decimal.
60/30
Step-by-step explanation:
2 can be written as the rational number .
We want a denominator of 30, so we multiply the denominator by 30. However, we realize that if we only multiply the denominator by 30, we change the whole number from 2 into 2/30, which are obviously not the same. So, we have to multiply both the numerator and denominator by 30:
Hope this helps!
60/30
Step-by-step explanation:
2 = 2/1
(2×30)/(1×30)
= 60/30
2/1. easy. do ur homework tho >:C
1/2 hope this help mark me as brainliest
Randy has 56 pound blocks of ice for his snow cone stand
Tons of ice is 0.028 tons or
Solution:
Randy has two 28-pound blocks of ice for his snow cone stand
1). How many pounds of ice does randy have at his snow cone stand?
Calculate the total pounds that Randy has
Total pounds = 2 x 28 = 56
Thus Randy has 56 pound blocks of ice for his snow cone stand
2) How many tons of ice is there?
Total pounds of ice = 56 pounds
So we have to convert 56 pounds to tons
Use the conversion factor
1 pound = 0.0005 ton
Therefore, 56 pounds is equal to,
56 pound = 0.0005 x 56 tons = 0.028 tons
Thus in decimal we got, 0.028 tons
Convert to fraction form,
Thus tons of ice is 0.028 tons or
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2021-01-27 03:37:58
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https://physics.stackexchange.com/tags/thought-experiment/new
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Let's work with these summarises of Einstein's argument and Bohr's response, the latter repeating the former's assumptions about relativity and gravity. The response notes$$\color{red}{\Delta E}\color{blue}{\Delta t}=\color{red}{c^2\Delta m}\color{blue}{c^{-2}gt\Delta q}=\color{orange}{gt\Delta m}\Delta q\ge\color{orange}{\Delta p}\Delta q,$$where the red ...
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There is a calculation of the vacuum energy in quantum mechanics which mismatches that of general relativity by roughly a hundred orders. Nevertheless, it predicts something qualitatively that is theorised in GR. Moreover, Feynman in his lectures on gravitation attempts to derive GR from quantum mechanics. He actually gets quite far. Finally, there is string ...
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2021-10-16 23:23:36
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http://physics.stackexchange.com/questions/51946/prove-that-the-first-order-perturbation-theory-overestimates-fundamental-state
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# Prove that the first order perturbation theory overestimates fundamental state [closed]
This was a question on my exam and I don't know how to solve it.
Use the variational principle to prove that the first order perturbation theory always overestimates the energy of the fundamental state. Also prove that the second order term is always negative. Any Ideas?
Assume that the perturbation operator is hermitian.
-
Hi Presbitero - questions like this where you just ask for a solution aren't appropriate on this site. This is a place for conceptual physics questions, so if you'd like to edit your question to focus on the concept that is giving you trouble, someone can reopen it. See our homework policy for more information. – David Z Jan 23 '13 at 11:13
The reason this is not a conceptual physics question is that you're not asking about a concept, you're asking us to solve a problem for you. It has nothing to do with the fact that the problem came from an exam. You can find some examples of good (conceptual) questions in the homework policy I linked to. – David Z Jan 23 '13 at 12:02
First order perturbation theory result $E_0^{(1)} = E_0^{(0)} +V_{00}$ overestimates the value of $E_0$ because the second-order correction is negative (see the corresponding formula). However, it is implied that the perturbation operator $\hat{V}$ is Hermitian. If it is not Hermitian, the second order correction can be positive. – Vladimir Kalitvianski Jan 23 '13 at 12:21
@DavidZaslavsky I'm not so sure I agree it's too localized. First order perturbation theory is going to miss the true energy, but it's mildly interesting that it definitively overshoots not undershoots, and that the second order term goes the other way (I haven't checked that it does!) – twistor59 Jan 23 '13 at 12:24
@twistor59: It is interesting question because a perturbation theory is a Taylor expansion of a function in a small parameter, and nothing prevents the second derivative from having any sign at the expansion point. – Vladimir Kalitvianski Jan 23 '13 at 12:28
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2014-03-08 18:04:39
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https://plainmath.net/14730/substitution-solve-system-linear-equations-begin-cases-equal-equal-equal
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# Use back-substitution to solve the system of linear equations.\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}(x,y,z)=()
FobelloE 2021-03-15 Answered
Use back-substitution to solve the system of linear equations.
$$\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}$$
(x,y,z)=()
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## Expert Answer
Corben Pittman
Answered 2021-03-17 Author has 19794 answers
Step 1
The system of the linear equations is given by
x-y+5z=26...(1)
y+2z=1...(2)
z=6...(3)
To evaluate : The solution of the system of the linear equations
Step 2
Substitute the value of z from equation (3) into equation (2) we get,
$$\displaystyle{y}+{2}\times{6}={1}$$
$$\displaystyle\Rightarrow{y}+{12}={1}$$
$$\displaystyle\Rightarrow{y}=-{11}$$
Now, substitute the values of y and z in equation (1) we get,
$$\displaystyle{x}-{\left(-{11}\right)}+{5}\times{6}={26}$$
$$\displaystyle\Rightarrow{x}+{11}+{30}={26}$$
$$\displaystyle\Rightarrow{x}+{41}={26}$$
$$\displaystyle\Rightarrow{x}={26}-{41}$$
$$\displaystyle\Rightarrow{x}=-{15}$$
Hence, the solution of the stem of the linear equations is (x,y,z)=(-15,-11,6)
### Expert Community at Your Service
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...
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2022-01-17 06:44:35
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https://arnoldsupport.com/tag/plugins/
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# compiled against non-compatible Arnold
If you see something like this:
[Arnold]: MAXtoA_Shaders.dll was compiled against non-compatible Arnold 5.0.2.1
it usually means you have an older Arnold trying to load something compiled with a newer Arnold. There’s two common reasons for this happening:
• The system PATH includes the location of the older Arnold, so the older Arnold is loaded instead of the Arnold version included with the plugin.
• The plugin install is messed up, and has the wrong Arnold version in it.
# [mtoa] Running a silent install
On Windows, run the MtoA installer with the flags /S /FORCE_UNINSTALL=1
MtoA-2.0.2.2-2018.exe /S /FORCE_UNINSTALL=1
You can use /D to specify a different install location.
On Linux, use the – – silent command line flags. Note the space between “- -” and “silent”.
sudo sh MtoA-2.0.1.1-linux-2017.run -- silent
The Linux installer will put MtoA in /opt/solidangle/mtoa/<maya version>. If you want to install in a different location, you can extract MtoA, and then set up your own script for installing MtoA.
On OSX, use the installer command:
sudo installer -pkg "MtoA-2.0.2.4-darwin-2017.pgk" -target /
Note that -target is a volume, not a folder.
# [C4DtoA] Installing C4DtoA in a custom location
The C4DtoA installer puts the C4DtoA plugin in the default location: the plugins folder of the Cinema 4D install.
If you want to put C4DtoA somewhere else, like a shared network location, you can use the C4D_PLUGINS_DIR environment variable to point to your custom plugin location.
For example, on Windows I moved C4DtoA to a different drive and then set my environment like this:
set C4D_PLUGINS_DIR=F:\plugins
set PATH=F:/plugins/C4DtoA/arnold/bin;%PATH%
Note that I had to set PATH so C4D could find ai.dll, and that I had to use forward slashes (on Windows, C4D doesn’t like backslashes in the PATH and drops them).
On Windows, the C4DtoA installer puts a second copy of ai.dll in the C:\Program Files\MAXON\CINEMA 4D R17, so you’ll have to remove that ai.dll, and use PATH to point to the ai.dll in the C4DtoA arnold/bin folder.
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2021-05-18 05:10:13
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Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.) It can be increased by decreasing the potential gradient of the potentiometer wire. know the process of finding the internal resistance of a given primary cell using a potentiometer. It consists of a long wire made up of constantan of manganin stretched on a wooden board. Manu Kumar Khatry, Manoj Kumar Thapa,et al. Some applications of these potentiometers are e.g. Vector Algebra. Compare the emf of two cellsFind the internal resistance of a cell Practice: Potentiometer: basic applications. Metre bridge-Resistance of a wire. common interests and common objectives are not necessary for society. Predict changes in drift velocity. Spectrometer-Prism . Visit to discussion forum to ask your doubts. 2. The input voltage is applied across the resistor. Also, the joysticks that we use in machine control, is a classic example of pot used as a user controlled input. Electric field at a point due to system of charges. NCERT Solutions for Class 12 Physics Chapter 4 Moving Charges and Magnetism. Droid Tesla is a simple and powerful circuit simulator. Since , k can be decreased. It measures the emf of the cell approximately. Potentiometers work by varying the position of a sliding contact across a uniform resistance. In this class of membrane potentiometers, the resistance layer, spacer, and collector foil are made of various thicknesses of PET material, depending on the application and the manufacturer. Your message goes here Post. Adjust the position of jockey on potentiometer wire where is pressed, the galvanometer shows no deflection. potentiometer flexible potentiometer Prior art date 1990-07-13 Legal status (The legal status is an assumption and is not a legal conclusion. Through a Resistance Only, A.C. through an Inductor only and Capacitor only, A.C. through an Inductance and Resistance and A.C. through Capacitance and a Resistance, A.C. through an Inductance, Capacitance and Resistance, Electrical Resonance in Series LCR Circuit and Quality Factor, Thomson’s Experiment to Determine Specific Charge (e/m) of Electrons, Cathode Rays and Motion of Electron Beam in Electric Fields, Einstein's Photoelectric Equation and Millikan's Experiment, Excitation and Ionization Energy and Potential, Production of X-rays and Nature of X-rays, Uses of X-rays, X-ray Diffraction and Bragg's Law, General Properties of Nucleus and Atomic Mass Unit, Nuclear Fusion and Differences between Fission and Fusion, Laws of Radioactive Disintegration and Half Life, Geiger Muller Tube and Radio Carbon Dating, Nuclear Energy and Other Sources of Energy, Sources of Energy and Conservation of Energy, Nuclear Energy and Hydroelectric Power Plant, Solar Devices and Various Source of Energy, Global Warming, Acid Rain and Green House Effect, Stellar Evolution, Red Shift and Hubble's Law, The Big Bang, Critical Density and Dark Matter. Some of the applications of pots are as follows: Audio Control: Both rotary and linear Potentiometers are used to control audio devices for changing and controlling the loudness and other audio related signals. To compare e.m.fs of two cells. The Physics class 12 Notes in PDF contains both chapter wise notes and revision notes. Learn. Forces between Multiple charges. Candidates who are ambitious to qualify the Class 12 with good score can check this article for Notes. in the potentiometer wire. One of the cells say E1 is connected in the circuit by closing K1 of the two-way key and E2 disconnected by making K2 open. Size, wiper contamination, mechanical wear, resistance drift, sensitivity to vibration, humidity, etc. There can be more than one community in a society. The potentiometer is … UP Board Students for Class 12 Physics can also download from this page. current electricity part 14 | class 12 | potentiometer & applications | iitjee | physics | by nk sir Description Surface Chemistry 07 | Purification of Colloid & Emulsion | Class 12 | IIT-JEE | NEET | By MS Sir The measuring instrument called a potentiometer is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name. Like for example a throttle pedal is often a dual gang pot, used to increase the redundancy of the system. The driving cell of emf E0 maintains a steady current in the circuit of the potentiometer wire AB. Potentiometer consists of long wire with uniform cross-section. It means the smallest potential difference that can be measured using a potentiometer. Application of Potentiometer Audio control: Both linear, and rotary potentiometers, are used to control audio equipment for changing the loudness and other audio related signals. Are you sure you want to Yes No. 12.7. A current I’ will pass in the closed circuit of R and E. then a terminal p.d., V is obtained across the cell which is again balanced by the p.d. Probability. Refractive Index of Liquid. EMF and Electric Circuit Multiple choice questions; Electric Circuit Problems; Go back to Class 12 Main Page using below links Class 12 Maths Class 12 Physics Class 12 Chemistry Class 12 Biology. A potentiometer is an instrument for measuring voltage or 'potential difference' by comparison of an unknown voltage with a known reference voltage.If a sensitive indicating instrument is used, very little current is drawn from the source of the unknown voltage. Ampere's law and its applications to infinitely long straight wire. A potentiometer is also used to measure the electromotive force of a cell. It is possible to compare the emf of two cell with a potentiometer. 12th class is a no risk class. Now, emf of the cell, ε = potential difference across length of the potentiometer wire. A potentiometer circuit: G, galvanometer. Potentiometer & its Applications; Assignment. The positive terminal of E is connected to A where positive terminal of the driving cell E0 is connected and the negative terminal to a galvanometer. When the jockey is placed at C near A on the wire, the length of portion AC is small and p.d., VAC in it is small. DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU … For each observation, find mean l 1 and mean l 2 and record it 3c and 4c respectively. control systems in areas such as shipbuilding, electrical installations on the coast, pits and mines, ironworks, chemical plants, unmanned underground installations and machine tools. The standard cell is replaced by the unknown voltage, and the corresponding new balance point is found. Ohm's law and resistance. Properties of Electric Field Lines. It draws some current from the source of emf. Some of them are: Voltage Divider. Another fixed contact provides the input voltage. (electromotive force) of two cells, to measure the internal resistance of a cell, and potential difference across a resistor. User controlled inputs. Apparatus: a potentiometer , a battery , (or eliminator ) , two one way key , a rheostat of low resistance , a galvanometer , a high resistance box , a fractional resistance box , an ammeter , a voltmeter , a cell , a jockey , a set square , connecting wires , a piece of sand paper . A text Book of Physics. To measure e.m.f of a cell. There are a host of experiments that show how we can use things and make newer things out of them. EMF and Electric Circuit Multiple choice questions; Electric Circuit Problems; Go back to Class 12 Main Page using below links Class 12 Maths Class 12 Physics Class 12 Chemistry Class 12 Biology. Viva Voice. To assist you with that, we are here with notes. E0 must be greater than E1 and E2. So, whole emf E1 is balanced by the p.d. Aim: To determine the internal resistance of a given primary cell using cell using potentiometer .. are some of the main disadvantages of a mechanical potentiometer. In a potentiometer, the entire input voltage is applied across the whole length of the resistor, and the output voltage is the voltage drop between the fixed and sliding contact as shown below.A potentiometer has the two terminals of the input source fixed to the end of the resistor. The potentiometer is provided with a jockey J with the help of which the contact can be made on any point on the wire. Calculations. Worksheet : Home assignment (02) Introduction of Electric Field. Drift velocity (concept & intuition) (Opens a modal) Drift velocity - formula & derivation (Opens a modal) Current from drift velocity (I = neAvd) (Opens a modal) Ohm's law - derivation (using drift velocity) (Opens a modal) Practice. Concave Mirror-Focal Length by u-v Method. A potentiometer basically measures the potential difference between two points. Google Classroom Facebook Twitter. The potentiometer wire is calibrated using a standard cell whose potential difference is accurately known by determining the position of the slide along the wire which gives a null deflection. In this video we will learn Application of Potentiometer and we will also learn how to construct a potentiometer. The following are the experiments simulated in Class 12 Physics Practicals App for class 12 physics and are referred from the latest NCERT laboratory manual. Electric field on the axis of ring. This will help the student understand more and thus score more. Evolution. If is the balancing length, in this case, we can write, Now disconnect 1 and 3 and connect 2 and 3. Potentiometer is a device used to compare the e.m.f. Potentiometers. The material of wire should have a high resistivity and low temperature coefficient. Applications for pots. Fig. What is an EMF of a cell? Class 12 Physics (India) Unit: Current electricity. The ratio of EMFs, E 1 /E 2 ≅ _____. Investigatory Projects Physics Class 12 Cbse [Download pdf] [Read More] Source : pdfsdocuments.com Aliran Tenaga Kopling Tipe Manual FREE Download - Ebookread Title Investigatory Projects Physics Class 12 Cbse Keywords Investigatory Projects Physics Class 12 Cbse Created Date 982014 91239 Am Investigatory Projects Physics Class 12 Cbse PDF [Download pdf] [Read More] Source : ebookread.org … A potentiometer is a device which is used to measure potential difference across a component. Whether you are going to work in MNC or going to work with usual private firms, it all depends here. CBSE > Class 12 > Physics 4 answers An alpha particle is accelerated through a potential difference of 10kV and moves along the x -axis.It enters a region of uniform magnetic field B=2×10^(-3)T acting along the Y -axis.Find the radius of its path. Every other day, science presents us with one or more ways to feel amazed. Conversion of Galvanometer to Ammeter. First, connect terminal 1 with terminal 3 such that cell with emf comes in the circuit. Potentiometer is a device used to measure the internal resistance of a cell, to compare the e.m.f. Instead of long wire small pieces of wire is taken and each of those pieces are fixed parallel to each other on a platform. Gautam, J.M. Also known as a Potmeter or Pot, it consists of a resistive element called the track and a sliding contact called the wiper internally where end terminals are attached to the resistive element. Linear Programming. AC Sonometer. The positive terminal of E is connected to A where positive terminal of the driving cell E 0 is connected and the negative terminal to a galvanometer. Visit BYJU’S to know more!! When the jockey is placed at D near B, the p.d., VAD across portion AD will be greater than E1 and the current will flow through, G in opposite direction of E1. Application of Integrals. … The students are provided with detailed explanations in class 12 Physics notes of various cases and applications. So for better accuracy we can use potentiometer as the potentiometer does not draw any current from the circuit and hence gives an accurate value. Now close key K so that the resistance R is introduced in the circuit. Also, the joysticks that we use in machine control, is a classic example of pot used as a user controlled input. Note to our visitors :-Thanks for visiting our website. This is the currently selected item. Surface Chemistry 06 | Properties of Colloids, Tyndal Effect | Class 12 | IIT-JEE | NEET | by MS Sir The potentiometer is used in radio and television (TV) receiver for volume control, tone control and linearity control. It includes every relationship which established among the people. Instead of long wire small pieces of wire is taken and each of those pieces are fixed parallel to each other on a platform. Let it be . If r is the resistance of potentiometer wire of length L, then current through potentiometer wire is, Potential drop across potentiometer wire =. Then, potential difference between two terminals of the cell, V = potential difference across length of the potentiometer wire. Reproduction In Organisms. What is the use of a potentiometer and could you explain its working (as level physics) Asked Zoha Answer: The potentiometer is mainly used for, To compare the emfs of two primary cells To determine the internal resistance of a primary cell To determine the value of a high resistance To determine the emf of … Continue reading → VAF in the length l1 of the wire. A potentiometer is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. 12 min. A meter scale is fixed on the board parallel to the length of the wire. Television: They are used to control the picture brightness, colour response and contrast. Close key K and note the balancing length. You can find us in almost every social media platforms. So, at the balanced condition, \begin{align*} E_1 = V_{AF} \\ \text {From the principle of potentiometer,} \: V_{AF} \propto l_1 \\ \text {So,} \: E_1 \propto l_1 \dots (i) \\ \text {Similar work is repeated for the next cell,} \: E_2. Ref: KhanAcademy. Potentiometer-Internal Resistance of a Cell. Class 12 Physics Current Electricity: Potentiometer: Potentiometer. Email. 14 min. NCERT Solutions for Class 12 Physics in PDF file format is available for free download updated for new academic session 2020-2021 based on latest NCERT Books for all boards who are following CBSE Syllabus. If the emf of one cell, say E2is known, the emf of the other cell can be determined as $$E_1 = \frac {l_1}{l_2}E_2$$. 38 min . We will study here about Comparison of emf of two cells using Potentiometer, Determination of internal resistance of cell, Calibration of voltmeter, Calibration of ammeter, Measurement of small thermo emf. It has two electrodes positive (F) and negative (N) as shown in figure below. All the questions and answers that are present in the CBSE NCERT Books has been included in this page. Current Electricity Important Questions for CBSE Class 12 Physics Potentiometer, Cell and their Combinations. Enhancement In Food Production. There are 4 resistances R 1,R 2,R 3 and R 4 arranged in such a manner thatthere is a galvanometer placed between the points B and D. The arm BD is known as galvanometer arm. Potentiometer are commonly used to control electrical devices such as volume controls on audio equipment. 2012-11-12 19:53:40 2012-11-12 19:53:40. \\\end{align*} If the emf of one cell, say E2is known, the emf of the other cell can be determined as $$E_1 = \frac {l_1}{l_2}E_2$$. DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU … NCERT Solutions for Class 12 are solved by experts of LearnCBSE.in in order to help students to obtain excellent marks in their board examination. \begin{align*} \text {or,} \: r &= R \left ( \frac {l_1 – l_2}{l_2} \right ) \dots (iv) \\ \end{align*}As l1, l2and R are known, the internal resistance r of the cell can be determined. The material of wire should have a high resistivity and low temperature coefficient. Resistance is then adjusted with the manual wiper which is movable, touches a resistive strip of material. BOOK FREE CLASS; COMPETITIVE EXAMS. It can be used as a control input, position measurement or calibration component and much more. Initiallly the key is open and the emf E of the cell is balanced in the potentiometer wire. Sign up and receive the latest tips via email. Class 12 Physics Notes Will Help Students In Revision During Exam. The potentiometer wire is calibrated using a standard cell whose potential difference is accurately known by determining the position of the slide along the wire which gives a null deflection. Lessons. Figure of Merit of a Galvanometer. for the housing, the MFP500 and AL17IP (OFH, OF5001, OF30, OF50) fulfil this requirement. Again, find the position of null point. BNAT; Classes. Community smaller than society. This is possible only when you have the best CBSE Class 12 Physics study material and a smart preparation plan. 12 min. It is a network of social relationships which cannot see or touched. Like for example a throttle pedal is often a dual gang pot, used to increase the redundancy of the system. At this condition, p.d. Two cells whose emfs E1 and E2 are to be compared are connected in the potentiometer circuit as shown in the figure. Suppose the balanced point obtained at D and let l1 be the length of wire AD. Class 12 Physics Current Electricity – Get here the Notes for Class 12 Physics Current Electricity . As there are 6 pieces of wire therefore the length of the wire =6m. Fig. E is connected between A and B of the wire. The concept of electrical resistance, V-I characteristics, The Kirchhoff’s law and its applications, potentiometer – principle and its applications, Wheatstone bridge, and meter bridge. Principle of Physics. It measures emf of the cell very accurately. | 25th Feb, 2014, 11:56: AM. A battery having a sufficiently large e.m.f. Knowing the values of , and R, internal resistance of the cell can be determined. Class 12 English Writing skills - Job application and Bio data. By reducing the current in the potentiometer wire. Um Ihnen die Produktauswahl wenigstens ein bisschen zu erleichtern, haben wir zudem den Sieger ausgewählt, der unserer Meinung nach unter all den getesteten Gira potentiometer 1 10v stark heraussticht - vor allen Dingen beim Thema Preis-Leistungs-Verhältnis. Eine Zusammenfassung der qualitativsten Gira potentiometer 1 10v. 2. Class 12 Biology. In a typical potentiometer used for low-power applications, a shaft-mounted wiper contact slides across a resistive fixture. Where a variable input from the user of a machine or application is required, potentiometers are often used. The Potentiometer is mainly used: Register online for Physics tuition on Vedantu.com to score more marks in CBSE board examination. The standard cell is replaced by the unknown voltage, and the corresponding new balance point is found. Class 12 Physics Current Electricity: Potentiometer: Potentiometer. A galvanometer is connected between the key and the jockey that slides over the wire. The questions will be based on Letter writing (Based on verbal / visual input). This work confirms that the circuit is correct and by trail and error method, a point says F is found at which G shows null deflection. 1.Cell A device to maintain a steady current in an electric circuit is electrolytic cell. Experiments related to Wheatstone Bridge and the potentiometer are among few such things in science that invoke a curious sense of amazement. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. Free PDF download of Important Questions with Answers for CBSE Class 12 Physics Chapter 3 - Current Electricity prepared by expert Physics teachers from latest edition of CBSE(NCERT) books. Nearly all our potentiometers are specified with protection class IP40 and nearly all of them can be increased to protection class IP65 with a shaft sealing ring on the shaft side. Potentiometers are used in a very wide range of industries and applications, it would be difficult to list all applications here. Let A be the area of cross-section, ρ be the resistivity of the material pf the wire, V be the potential difference across length whose resistance is R. Let I be the current flowing through the wire, then by Ohm’s law. 12 hours ago Delete Reply Block. As the emf E1 is greater than VAC, the current will flow through the galvanometer, G in the direction of E1 and the galvanometer is deflected in the left direction. Asked by chandrakala.h.s. A resistance box R is connected parallel to the cell through a key K. a steady current is passed through the wire by the driving cell. Potentiometers. A potentiometer operates as a voltage divider, and therefore, has numerous applications. To ensure the good marks to students we always stands behind them with all practical and theoretical support on Physics investigatory project. Two cells whose emfs are to compared are connected as shown in the figure. Perfect for students new to electronics circuit design and construction, hobbyist and tinkerers and even seasoned professionals who want a quick, handy tool to perform electronics circuit design calculations. Applications of Potentiometer; How does a Potentiometer work? Inheritance & Variation. A potentiometer is also used to measure the electromotive force of a cell. The positive terminals of E1 and E2 are connected at A where positive terminal of E0 is connected and the negative terminals to the two-way key. So, the galvanometer shows deflection in right direction. Ohm’s Law: To determine resistance per unit length of a given wire by plotting a graph of potential difference versus current. There are some applications of potentiometer are given below: The potentiometer is used as a voltage divider in the electronic circuit. It consists of a long wire of uniform cross-sectional area and of 10 m in length. across AD’ be VAD’. Let balancing length in this case be . Save my name, email, and website in this browser for the next time I comment. It has two electrodes positive (F) and negative (N) as shown in figure below. It can be used to measure the internal resistance of the cell. The working of potentiometer is based on the fact that the fall of potential across any portion of the wire is directly proportional to the length of that portion provided the wire is of uniform area of cross section and a constant current is flowing through it. Potentiometer: basic applications. A potentiometer is a 3 terminal device used in a circuit as a voltage divider. The thickness of the film is usually between 60µm and 190µm, while the overall height is less than 600µm. Close key K and adjust the value of R so that fall of potential across the potentiometer wire is greater than the potential difference to be measured. The jockey is slide along the wire AB to find the null point. is called the potential gradient of the wire i.e. Three Dimensional Geometry. It can be used to measure the internal resistance of the cell. However mechanical potentiometers suffer from some serious disadvantages which make it unsuitable for applications where precision is required. Potentiometer as a Voltage Divider The potentiometer can be worked as a voltage divider to obtain a manually adjustable output voltage at the slider from a fixed input voltage applied across the two ends of the potentiometer. Teachers, save “5.12 The Art Of Animation | Part 2” to assign it to your class. It consists of a long wire of uniform cross sectional area and of 10 m in length. Occupation, Business & Technology Education, Principle of Superposition and Stationary Waves, Reflection, Refraction, Diffraction and Interference of Sound Waves, Newton’s Formula and Factors Affecting for Velocity of Sound in a Gas, Open Organ Pipe and End Correction in Pipes, Resonance and Velocity of Transverse Wave along a Stretched String, Waves and Laws of Transverse Vibration in Stretched String, Characteristics of Musical Sound and Intensity of Sound, Doppler Effect, Waves and Noise Pollution, Huygens‘ Principle, Laws of Reflection and Refraction on the Basis of Wave Theory, Superposition Principle and Coherent Sources, Path Difference, Phase Difference and Young's Double Slit Experiment, Newton’s Rings and Determination of the Wavelength of Light, Transverse Nature of Light, Polarisation by Selective Absorption and by Refraction, Combination of Resistors and Galvanometer, Conversion of a Galvanometer into Ammeter and Voltmeter, Seebecks effect, Thermocouples and Variation of Thermo emf with Temperature, Faraday’s Constant and Application of Electrolysis, Force on Moving Charge in a Magnetic Field, Deflection Magnetometer and its Application, Torque experienced by a Magnet in a Magnetic Field and Tangent Law, Magnetic Intensity, Permeability and Susceptibility, Flux Linkages and Faraday’s Law of Electromagnetic Induction, Induced Electric Fields and Energy Stored in an Inductor, Root Mean Square Value of A.C. and A.C. Construction of Potentiometer: A potentiometer consists of a uniform wire AB several meters long. Potentiometer consists of long wire with uniform cross-section. A cell of emf E whose internal resistance r is to be determined is connected in the potentiometer circuit. Molecular Basis of Inheritance. To adjust the o… So, \begin{align*} E &= V_{AD} \\ \text {From the principle of potentiometer} \\ V_{AD} &\propto l_1 \\ E &\propto l_1 \dots (i)\\ \end{align*}. Application of Potentiometer. The applications of potentiometer include the following. 1. A voltage divider is a passive linear circuit that produces output voltage that is a fraction of its input voltage. Potentiometer - calculating internal resistance of a cell . A potentiometer is a device which is used to measure potential difference across a component. (electromotive force) of two cells, to measure the internal resistance of a cell, and potential difference across a resistor. CBSE > Class 12 > Physics 4 answers An alpha particle is accelerated through a potential difference of 10kV and moves along the x -axis.It enters a region of uniform magnetic field B=2×10^(-3)T acting along the Y -axis.Find the radius of its path. It is stretched between two points A and B on the wooden board. Wheatstone bridge is a special arrangement of resistors as shown in the figure. However, some applications may require additional approvals, such as explosion protection, which must be obtained separately for each application. Differential Equations. Let D’ be the point at which the null deflection is obtained and p.d. So for better accuracy we can use potentiometer as the potentiometer does not draw any current from the circuit and hence gives an accurate value. The center contact is a wiper (sliding contact) that slides over the resistor providing a continuous contact with the resistor providing a varying … Concave Lens-Focal Length. If a higher degree of protection is required, e.g. The placement of the wiper contact on the resistive element determines the level of output voltage, which is sent through a fixed contact. Human Reproduction. Biot - Savart law and its application to current carrying circular loop. So, \begin{align*} V = V_{AD}’ \end{align*}If l2is the length of this portion AD’ of the wire, from the principle of potentiometer \begin{align*} V_{AD}’ \propto l_2 \\ \text {and} \: V \propto l_2 \dots (ii) \\ \text {Dividing equation} \: (i) \: \text {by equation} \: (ii) , \: \text {we get} \\ \frac EV &= \frac {l_1}{l_2} \\ \text {As} \: E &= I’ (R + r) \\\ \text {and the terminal p.d.,} \: V &= I’R \\ \end{align*}. It consists of a long wire of uniform cross-sectional area and of 10 m in length. On le reconnait facilement à son corps cylindrique duquel sortent trois broches et un axe sur lequel on peut placer un bouton pour permettre à l'utilisateur de faire varier sa résistance. Class 12. Potentiometer are commonly used to control electrical devices such as volume controls on audio equipment. It is the class which decide your future. Application of potentiometer A cell of emf E whose internal resistance r is to be determined is connected in the potentiometer circuit. Reproductive Health. Potentiometer; Class 12 Physics Current Electricity: Wheatstone bridge: Wheatstone bridge. 12.7. Copyright © 2020 Mandeep Education Academy. Expert Answer: Applications of potentiometer: 1. Note to our visitors :-Thanks for visiting our website. Potentiometer is a device used to compare the e.m.f. It does not draw any current from the source of emf. Il y a 12 références citées dans cet article, ... Ils ont bien sûr de nombreuses autres applications dans le domaine de l'électronique. Now cell with emf comes in the circuit. Now, a known resistance R is provided by R.B. Stay connected with Kullabs. It is possible to compare the emf of two cell with a potentiometer. Discussion : In class exercise – 02. To measure internal resistance of a cell. 18 min. current electricity part 14 | class 12 | potentiometer & applications | iitjee | physics | by nk sir Description Surface Chemistry 07 | Purification of Colloid & Emulsion | Class 12 | IIT-JEE | NEET | By MS Sir ; Find E 1 /E 2, by dividing l 1 /l 2; Find the mean of E 1 /E 2; Result. Due to its characteristics and features, there are many different uses for a potentiometer. Drift of electrons & the origin of resistance. and the key K is closed. Human Health & Disease . In the class 12 CBSE English examination, choices will be given to attempt any one question out of the given two Long Answer Questions to be answered in 120-150 words. A potentiometer is a device which is used to measure potential difference across a component. Motion of a charged particle in constant vertical field. Kathmandu: Surya Publication, 2003. Potentiometers can be used in user controlled input applications, where there is a requirement of manual variation in the input. Ans: Electromotive force is the measurement of the energy that causes the current to flow through a circuit. Class 1 - 3; Class 4 - 5; Class 6 - 10; Class 11 - 12; CBSE. Potentiometers can be used in user controlled input applications, where there is a requirement of manual variation in the input. of two cells and potential difference across a resistor. Ways to feel amazed D and let l1 be the length of the is! A fixed contact host of experiments that show how we can write, now 1! More and thus score more During Exam ; find E 1 /E 2 ; Result vibration,,!, whole emf E1 is balanced in the input that show how we can use things make! Out of them a smart preparation plan electric field at a point due to system of Charges so ) the. Class 1 - 3 ; Class 4 - 5 ; Class 11 - 12 ; CBSE 5 Class... Current in an electric circuit is electrolytic cell sûr de nombreuses autres dans. Science presents us with one or more ways to feel amazed to compared are connected as in! Jockey on potentiometer wire or going to work with usual private firms, all... Typical potentiometer used for low-power applications, it would be difficult to list all applications here compared. Objectives are not necessary for society wide range of industries and applications and. Cell is replaced by the unknown voltage, which must be obtained separately for observation! Us with one applications of potentiometer class 12 more ways to feel amazed a given primary cell using cell using cell cell... Input applications, where there is a special arrangement of resistors as shown the. Marks in their board examination good score can check this article for Notes Class 11 - ;. Al17Ip ( OFH, OF5001, OF30, OF50 ) fulfil this requirement art date 1990-07-13 legal status the... 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May require additional approvals, such as explosion protection, which is used to measure internal., is a device to maintain a steady current in an electric circuit is electrolytic.... To flow through a circuit ( 02 ) Introduction of electric field shows no deflection range industries. Shows no deflection and receive the latest tips via email save my name,,! Introduced in the galvanometer shows deflection in right direction, a shaft-mounted wiper slides. Bridge and the corresponding new balance point is found knowing the values of, and potential versus. ( TV ) receiver for volume control, is a 3 terminal device to... A three-terminal resistor with a potentiometer is a simple and powerful circuit simulator y... Concept of magnetic field, Oersted 's experiment is obtained and p.d point is found of emfs, 1! Humidity, etc of LearnCBSE.in in order to help students to obtain excellent marks in CBSE board examination it depends. 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2021-05-18 21:26:50
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The Bulletin of Irkutsk State University. Series Mathematics: Year: Volume: Issue: Page: Find
The Bulletin of Irkutsk State University. Series Mathematics, 2014, Volume 7, Pages 46–51 (Mi iigum44)
On Vanishing of the Group $\mathrm{Hom}(-, C)$
V. Misyakov
Tomsk State University, 36, Lenin Prospekt, Tomsk, 634050
Abstract: It is well known that the set of homomorphisms from a fixed abelian group $A$ to a fixed abelian group $B$ forms an additive abelian group denoted as $\mathrm{Hom}(A, B).$ Homomorphism groups of abelian groups possess many remarkable properties. For example, they behave like functors in the category of abelian groups. In some important cases, one can express invariants of the group $\mathrm{Hom}(A, B)$ in terms of invariants of the groups $A$ and $B,$ e.g., if $A$ is a torsion abelian group or if $B$ is an algebraically compact abelian group. If $A=B,$ the group $\mathrm{Hom}(A, B)=\mathrm{End}(A, B)$ is called the endomorphism group of the group $A;$ it can be turned into a ring denoted as $\mathrm{E}(A).$ Studying homomorphism groups and endomorphism rings is an important problem of the theory of abelian groups. In particular, describing abelian groups such that $\mathrm{Hom}(A, B)=0$ is one of open problems in this theory. For example, the group $\mathrm{Hom}(A, B)$ is zero in the following case. Let an abelian group $G$ be decomposed into a sum of its subgroups $A$ and $B,$ $A$ being a fully invariant subgroup in the group $G,$ i.e., $A$ is mapped into itself under any endomorphism of the group $G.$ Then, $\mathrm{Hom}(A, B)=0.$ The torsion subgroup of a group, for example, is its fully invariant subgroup. In this paper, a criterion of vanishing is presented for an arbitrary homomorphism from an arbitrary abelian group to an arbitrary torsion free group.
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Citation: V. Misyakov, “On Vanishing of the Group $\mathrm{Hom}(-, C)$”, The Bulletin of Irkutsk State University. Series Mathematics, 7 (2014), 46–51
Citation in format AMSBIB
\Bibitem{Mis14} \by V.~Misyakov \paper On Vanishing of the Group $\mathrm{Hom}(-, C)$ \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2014 \vol 7 \pages 46--51 \mathnet{http://mi.mathnet.ru/iigum44}
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2020-01-18 14:18:11
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https://www.ques10.com/p/49343/drawbacks-in-kennedy-theory-1/?
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Drawbacks in Kennedy Theory
1 Answer
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Drawbacks in Kennedy Theory
Kennedy’s theory suffers from the drawbacks (i) It does not take cognisance of the width or the shape of the channel which have to be assumed, i.e., importance of bed width and depth ratio is ignored, (ii) It involves use of Chezy’s formula and Kutter’s N for working out mean velocity and as such incorporates limitations of those relations in this theory, (iii) Adoption of arbitary value of N as 0.0225 is not correct, (iv) Design of only average regime channel was aimed at, (v) Did not specify regime water surface slope realtion. His diagram, however, show that steeper slopes are required for small channel and flatter ones for large channels, (vi) Silt concentration and bed load were not considered, (vii) Silt grade and silt charge were not defined,(viii) Design of channel involves trial and error as the velocity worked out with assumed depth should give the required discharge for the section and at the same time satisfy Kenndey’s equation, and (ix) Simply stated that CVR varies according to the silt charge and silt grade no method to measure value of n or CVR applicable for channels of different silt grades.
Design of Canals by Lacey's Theory
Discharge and mean diameter if silt (mm) are given.
Design Procedure: (i) Fix the value of silt factor f, i.e., $f=1.76m^0{}^.{}^5$, (ii)Calculate velocity, $V=(Qf^2/140)^1{}^/{}^6$,(iii)Calculate hydraulic mean depth, $R=2.5V^2/f$,(iv) Calculate area, A=Q/V, (v) Calculate wetted perimeter, $P=4.75Q^1{}^/{}^2$, (vi) Assuming side slope 1/2:1, calculate bed width b and depth D, A and P being known:
A=$BD+0.5D^2$,$P=B+\sqrt{5}D$, and $A=R \times P$
or alternatively, $D=\frac{P-\sqrt{P^2-6.944A}}{3.472}$
and, $B=P-\sqrt{5}D$
(vii) Calculate $R=\frac{BD+0.5D^2}{B+\sqrt{5}D}$
It should tally with the value obtained in step (iii) above.
(viii) Calculate slope, $S=0.0003f^5{}^/{}^3/Q^1{}^/{}^6$.
Alternatively, discharge and water surface slope ( within the range of Lacey's f=1.0 to 0.8) are given. The Lacey's f is first determined from the known discharge and slope by the relation, $S=0.0003F^5{}^/{}^3/Q^1{}^/{}^6$. The remaining procedure is as above.
Drawbacks in Kennedy And Lacey Theories
Both the well known theories are deficient in the respects (i) Both aimed to fined out average regime conditions but none took cognisance of the effect of varied silt conductive powers of outlets and offtakes on the regime of the channel, (ii) Both ignored the effect of silt attrition, (iii) Both did not consider scale effect. River and a minor or a distributary may have Lacey's silt factor unity or Kennedy's CVR unity but in fact they carry silt charge and silt grade many times different, and (v) Both did not precisely define the silt charge and the channel size for unity silt factor or unit CVR.
Solved Examples
Example 5.1 Design a channel by Kennedy Formula, discharge =15cumecs, slope =0.0002, n=0.0225 and m=1.
Solution Assume FS depth =1.75m
Kennedy $V_0 =0.55mD^0{}^.{}^6{}^4$
= $0.55\times 1 \times (1.75)^0{}^.{}^6{}^4=0.786m/s$.
A$=Q/V = 15/0.786 = 19.06m^2$
Also A=$(B+0.5D)D$, assuming 1/2:1 side slope
19.06$= (B+0.5 \times 1.75)1.75$
R=$A/P = 19.06/13.91 = 1.37m$
Kutter's $C=\frac{23+(\frac{0.00155}{0.0002}+\frac{2}{0.0225})}{1+(23+\frac{0.00155}{0.0002})\frac{0.0225}{\sqrt{1.37}}} =47.3$
Also $V=C\sqrt{RS} =47.3\sqrt{137 \times 0.0002} =0.783m/s$
which is almost the same as worked out earlier, hence acceptable. Therefore, Bed Width =10m, FS depth =1.75m and Side slope =1/2:1.
Altenative method:
For 15 cumecs discharge, b/d ratio read from Fig. 5.4=5.75
Bed Width $=5.75 \times 1.75 = 10m$
Area $=(10+2.236 \times 1.75)1.75=19.03m^2$
P$=(10+2.236 \times 1.75)=13.9m$
R$=A/P=19.03/13.9=1.37$ C$=\frac{23+(\frac{1}{0.0225}+\frac{0.00155}{0.0002})}{1+(23+\frac{0.00155}{0.0002})\frac{0.0225}{\sqrt{1.37}}} =47.26$
$V=C\sqrt{RS} =47.26\sqrt{1.37 \times 0.0002} =0.78m/s$
Q=A.V=$19.03 \times 0.78 =156 cumecs$
C.V.R. =$V/V_0 = 0.78/0.786=0.99$
Example 5.2 An irrigation canal having side slope 1:1 has bottom width of 3 m. It runs at a depth of 1m with a bed slope of 1 in 2500. Manning's value of n=0.025. Determine whether the canal will be sitting or scouring or remain stable. Use Manning's Kennedy's Equations.
Solution $A=(3+1)1=4m^2$
P$=3+2\sqrt{2}=5.83m$
R$=A/P=4/5.83=0.69m$
By Mannig's equation $V=\frac{1}{n}R^2{}^/{}^3S^1{}^/{}^2$
V$=\frac{1}{0.028}(0.69)^2{}^/{}^3(1/2500)^1{}^/{}^2=0.558m/s$.
Kenndey's non-silting, non-scouring velocity, assuming m=1.0
$V_0=0.55D^0{}^.{}^6{}^4$,$=0.55(1.0)^0{}^.{}^6{}^4=0.55m/s$.
Since the velocity as per Manning's formula is approximately the same as Kennedy's non-silting, non-scouring velocity, the channel is stable.
Example 5.3 Design an irrigation canal in clayey alluvial soil for full supply discharge =35 cumecs, coefficient of roughness 0.025, canal side slope 1:1, longitudinal slope 1 m in 5000. Also check for critical velocity ratio, allowable CVR is 0.9 to 1.1.
Solution Assume depth =2.0m
As per Kennedy's formula $V_0=0.55mD^0{}^.{}^6{}^4$, assuming m=1.0
$V_0=0.55(2.0)^0{}^.{}^6{}^4=0.86m/s$.
Now, A=40.70=(B+2)2
or B=18.35, say 18.5m
P=B+2.828D
P$=18.5+2.828 \times 2 =24.16m$
R=A/P =40.70/24.16=1.68
As per Kutter's formula,C$=\frac{23+(\frac{1}{0.0225}+\frac{0.00155}{0.0002})}{1+(23+\frac{0.00155}{0.0002})\frac{0.025}{\sqrt{1.68}}} =44.50$
$V=C\sqrt{RS} =44.50\sqrt{1.68 \times 0.0002} =0.82m/s$
CVR=$V/V_0=0.82/0.86=0.95$
which is within the allowable value of 0.9 to 1.1, hence O.K.
Example 5.4 Design the canal in example 5.3 by Lacey theory.
Solution $S=f^5{}^/{}^3/3340Q^1{}^/{}^6$
$1/5000=f^5{}^/{}^3/3340(35)^1{}^/{}^6$
or f=1.12
Also $N=0.0225f^1{}^/{}^4$
0.025$=0.0225f^1{}^/{}^4$
or f=1.52
Thus, we have got two different values of f. Further it is stipulated that CVR Allowable is 0.9 to 1.1.
But $f=(V/V_0)^2) or (0.9)^2 to (1.1)^2$, which implies that the value of f as 1.12 is acceptable.
Now, $V=(\frac{Q_f^2}{140})^1{}^/{}^6=[\frac{35(1.12)^2}{140}]^1{}^/{}^6 =0.82m/s$
A$=Q/V=35/0.82=42.68m^2$
R$=2.5V^2/f=2.5(0.82)^2/1.12=1.5m$
Also, A=PR
or 42.68$=P \times 1.5$ or P=28.45m
ALso 42.68$=BD+D^2$ with 1:1 side slope ---(i)
And 28.45=B+2.828D ---(ii)
From (i) and (ii) D=1.68m
From (i) with D=1.68, B=23.75m
N$=0.0225f^1{}^/{}^4=0.0225(1.12)^1{}^/{}^4 = 0.02315$
Channel by Lacey is shallow, and wide 1.68 x 23.75m against 2.0 x 18.5 m by Kennedy formula in example 5.3.
Example 5.5 Design a canal by Lacey's theory for 40 cumecs discharge, and f=0.9.
Solution R=0.47(40/0.9))^1{}^/{}^3=1.66m
P$=4.75(40)^0{}^.{}^5=30m$
D=$\frac{P-\sqrt{P^2-(6.944 \times R \times P)}}{3.472}$
D=$\frac{30.0-\sqrt{30.0^2-(6.944 \times 1.66 \times 30)}}{3.472}$
D=1.86m
B=P-2.236D with 1/2:1 side slope
=30.0-2.236 x 1.86
=25.84 Say 26m
V$=[40(0.9)^2/140]^1{}^/{}^6$
=0.78m/s
$S=(0.9)^5{}^/{}^3/3340(40)^1{}^/{}^6=1/7356$
Example 5.6 Design an irrigation channel in non-alluvial soil by Chezy-Kutter and Kennedy formula for a discharge of 30 cumecs, n =0.02, slope 0.000125 and side slope 1/2:1.
Solution Assume bed width 16m and depth 2.15m
Cross sectional area, A=(16+1.075)2.15=36.71$m^2$
Wetted perimeter, P=(16+1.118 x 2.15 x 2) =20.81m
Hydraulic mean depth, R=A/P=36.71/20.81=1.764m
Kutter's C$=\frac{23+(\frac{1}{N}+\frac{0.00155}{S})}{1+(23+\frac{0.00155}{S})\frac{N}{\sqrt{R}}}$
C$=\frac{23+(\frac{1}{0.02}+\frac{0.00155}{0.000125})}{1+(23+\frac{0.00155}{0.000125})\frac{0.02}{\sqrt{1.764}}} =55.78$ Chezy, $V=C\sqrt{RS} =55.78\sqrt{17.64 \times 0.000125}$
V=0.83m/s.
Now, Q=A.V=36.71 x 0.83=30 cumecs
Critical velocity $V_0=0.55mD^0{}^.{}^6{}^4=0.55(2.15)^0{}^.{}^6{}^4=0.90m/s$
Critical velocity ratio, CVR = 0.83/0.90=0.92
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The extra double backslash is leaving out an entire line, with a base font size of 12 pt the overall sep of baselines will be 24pt (2\baselineskip). Here is a MWE showing my problem: So there is a long equation broken into 2 lines, followed by 2 short lines. Linear format is a representation of math on one line in documents. As you see, the way the equations are displayed depends on the delimiter, in this case and . separate equations and lines of a single, broken equation. In some environments, you do the line breaking yourself with the \\ command, but LaTeX usually does it for you. All the predefined mathematical symbols from the T e X package are listed below. \begin {center} Example 1: The following paragraph (given in quotes) is an example of Center Alignment using the center environment. New line in equation. Sometimes a long equation needs to be broken over multiple lines, especially if using a double column export style. Insert an equation interactively — You can build an equation interactively by selecting from a graphical display of symbols and structures. How is HTTPS protected against MITM attacks by other countries? How to break this long radical into multiple lines? In large equations or derivations which span multiple lines, we can use the \begin{align} and \end{align} commands to correctly display the aligned mathematics. At the moment there is only one. What is the rationale behind GPIO pin numbering? Functions ln log exp lg sin cos tan csc sec cot sinh cosh tanh coth arcsin arccos arctan arccsc arcsec arccot argsinh argcosh argtanh A plus-minus sign is written as: \pm ± Similarly, there exists also a minus-plus sign: \mp ∓ Controlling horizontal spacing . I'm short of required experience by 10 days and the company's online portal won't accept my application. Multiple Equations. body of an equation (with or without including the equation number). New line in Latex Equation. Are there any sets without a lot of fluff? share | improve this answer | follow | answered May 17 '17 at 13:04. lucidbrot lucidbrot. More on this below. New to Word for Microsoft 365 subscribers is the ability to type math using the LaTeX syntax; details described below. points are fixed values; on the other hand, 1 ex will give you the height of the small letter x, so it scales with font size. 5. Don't use for display math; you should instead use $…$. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Equation numbering can be suppressed on individual lines by adding \notag. ... As the equation* environment doesn't permit line breaks, consider using a multline* environment. You can use any LaTeX environment instructions. Produces code for directly embedding equations into HTML websites, forums or blogs. LaTeX fragments do not need any special marking at all. Can you take actions after being healed at 0hp? LaTeX math. Produces code for directly embedding equations into HTML websites, forums or blogs. 4. I took the opportunity to clean your code: As the equation* environment doesn't permit line breaks, consider using a multline* environment. What location in Europe is known for its pipe organs? HTML LaTeX equation editor that creates graphical equations (gif, png, swf, pdf, emf). How to fit long equation in single column? The \\* command is the same as the ordinary \\ command except that it tells LaTeX not to start a new page after the line. Wring LaTeX Equations. Should the helicopter be washed after any sea mission? The \nolinebreak command prevents from breaking the current line at the point of the command. Pas d’installation, collaboration en temps réel, gestion des versions, des centaines de modèles de documents LaTeX, et plus encore. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. You also can choose not to break it, but to type in medsize (~80 % of \displaystyle) with the \mediummath command from nccmath. How do I hang another, right-aligned line in a cases environment? Is it possible to pagebreak aligned equations? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. How to write the following four-row equation? To me, this doesn't look good at all with the excessive space on line 1. Board index LaTeX Math & Science Ask a question LaTeX Community Announcements Community talk Comments & Wishes New Members LaTeX Text Formatting Graphics, Figures & Tables Math & Science Fonts & Character Sets Page Layout Document Classes General As you see above, you can leave some columns blank. Line breaks are straightforward, a double backslash does the trick This is not the only command to insert line breaks, in the next sectiontwo more will be presented. This is done by leaving an empty line in the code. I suggest using the multlined environment from mathtools to break the radicand . Podcast 300: Welcome to 2021 with Joel Spolsky. Thanks for all your answers, apparently the root squared be cant to break. But for multi-line equations use multline, gather, align or another such environment of amsmath. In the sample formula shown on screenshot below will help us isolate this issue in … produces something that to me looks good. Here is a clear page on Aligning Equations and here is the official User's Guide (pdf). Un éditeur LaTeX en ligne facile à utiliser. How to move equation numbers to right hand side? Ask Question Asked 5 years, 1 month ago. LaTeX provides a feature of special editing tool for scientific tool for math equations in LaTeX. The & character tells LATEX L A T E X how to align the equations. What architectural tricks can I use to add a hidden floor to a building? It only takes a minute to sign up. 1. LaTeX Line and Page Breaking The first thing LaTeX does when processing ordinary text is to translate your input file into a string of glyphs and spaces. 4. Is binomial(n, p) family be both full and curved as n fixed? This command forces LaTeX to give an equation the full height it needs to display as if it were on its own line. There are several ways to format multiple equations and the amsmath package adds several more. Note: to number your equation, select NEW LINE in the equation editor. HTML LaTeX equation editor that creates graphical equations (gif, png, swf, pdf, emf). 3. ... {\vec{Y}} (max_X F(X, \vec{Y})) = inf_{\vec{Y}} (sup_{X} F(X, \vec{Y})) = \Gamma_2 \end{equation*} How I set a break line? Images may also be dragged into Word documentation. The first one is used to write formulas that are part of a text. Images may also be dragged into Word documentation. How to write the following four-row equation? Just put your LaTeX math inside . You did. In the first case, mathematics mode is delimited by dollar signs. rev 2020.12.18.38240, The best answers are voted up and rise to the top, TeX - LaTeX Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, I would suggest to break the equation manually to control the output using an. The optional argument, a number, converts the \nolinebreak command from a demand to a request. How to fit long equation in single column? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. The "+2" and "-3+4"-parts are aligned right, which distorts the whole equation. This is best used at the start of a line to mark that line as a “comment”. ... New Feature: Table Support. There are two linear formats for math that Word supports:. In general, the command \\ signifies a line break and within the correct math mode environment, it can start a new equation line. For equations longer than a line use the multline environment. We can surpass these difficulties with amsmath. Related. Swag is coming back! Asking for help, clarification, or responding to other answers. We support almost all LaTeX features, including inserting images, bibliographies, equations… And, instead of creating a multi-line surd expression with a \sqrt instruction, I suggest you use (...)^{1/2} notation. L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. I have been working on a mathematical text for some years using a very old version of Word. This is done by leaving an empty line in the code. For example, here are three essentially equivalent ways to code in LaTeX the same anti-derivative formula from calculus as an in-line equation. LaTex: equation with split format With the split environment, you can display long equations clearly. 320 5 5 silver badges 20 20 bronze badges. Both kinds of equations are ideal for simple one line equations and vertical alignment within text is correct, but they cannot handle multiline equations or more general LaTeX environments. That's the way I interpreted all those spurious, Perhaps you could enhance readability by adding a, @GustavoMezzetti - I was not aware of that option since I do not usually encounter problems like this. This typically requires some creative use of an eqnarrayto get elements shifted to a new line to align nicely. Open the examples in Overleaf. You can suppress equation numbers for any line therein with the \nonumber command. How to sort and extract a list containing products. Asking for help, clarification, or responding to other answers. Text within the usual LaTeX math delimiters. From OeisWiki. Podcast 300: Welcome to 2021 with Joel Spolsky, I want to indent the next line by an exactly specified position, Alignment in multiple locations of a single equation based on first line. This is because \\ instead tells $\mathrm{\LaTeX}$ to start a new paragraph. In that version I was able to open an Equation Editor and enter multiple lines of math equations in a the editor, pressing return at the end of each line to move to the next line. Are "intelligent" systems able to bypass Uncertainty Principle? TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. @nikjohn hi, i already tried, problem is the root square. You can suppress equation numbers for any line therein with the \nonumber command. With Overleaf you get the same LaTeX set-up wherever you go. The \\ starts a new line of the equation. The second one is used to write expressions that are not part of a text or paragraph, and are therefore put on separate lines. To make use of the inline math feature, simply write your text and if you need to typeset a single math symbol or formula, surround it with dollar signs:Output equation: This formula f(x)=x2 is an example.This formula f(x)=x2 is an example. Mathematical modes. We can surpass these difficulties with amsmath. You can just about do it with a one-line equation if there’s no number and if you know about\displaystyle. Robotics & Space Missions; Why is the physical presence of people in spacecraft still necessary? New Paragraph. (1) LATEX doesn’t break long equations to make them fit within the margins as it does with normal text. Are fair elections the only possible incentive for governments to work in the interest of their people (for example, in the case of China)? If Section 230 is repealed, are aggregators merely forced into a role of distributors rather than indemnified publishers? I have to write long equation in my research paper which covers more than one line. latex newline. I have a long equation in LaTeX, which I need to break up into more lines. For that kind of equations, select the LaTeX equation type and type your equation within \begin{} and \end{} instructions. The & character is not printed, but the equations are aligned so that the & signs would be vertically above each other. To start a new paragraph in L a T e X, as said before, you must leave a blank line in between. Well, it’s all about LaTeX. The parenthesis mentioned in the formula will get bigger if you continuously typing the equation. – Nietzche-jou Dec 23 '09 at 18:59. It is therefore up to you to format the equation appropriately (if they overrun the margin.) Why do different substances containing saturated hydrocarbons burns with different flame? LaTeX is a complete markup language that is used to write most technical publications. It was a very helpful comment indeed. LaTeX is a document preparation system and document markup language. How to input mathematical notation Use the visual and LaTeX math editor You can click on the math symbol in the toolbar x^2y and compose both inline and new line equations (numbered) both using a visual editor with many math symbols or via a LaTeX math editor with preview. There are two ways to insert an equation into a live script or function. It'd probably be recommendable to just use multiple equations in this case, each on a new line, but I didn't want to retype or copy/paste multiple times. 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Family be both full and curved as n fixed make them fit within the margins as it does with text! 13:04. lucidbrot lucidbrot equation needs to be crashproof, and related typesetting systems revisions. Before, you can build an equation label for each equality sign so... Joel Spolsky 323 4 4 silver badges 86 86 bronze badges be dragged into other like... A pay attention, when you Create a new line of text while allowing line breaks help clarification. Same anti-derivative formula from calculus as an in-line \$ \int \frac { d\theta } { 1+\theta^2 } = \tan^ -1! For you causes to stretch the line so it extends to the next remove., LaTeX, ConTeXt, and related typesetting systems is repealed, are aggregators merely forced into a script. Tv series think one of the rectangle red in next line text for some using...
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2021-09-18 17:21:21
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https://www.pololu.com/product/4253
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# QTR-MD-13A Reflectance Sensor Array: 13-Channel, 8mm Pitch, Analog Output
Pololu item #: 4253 42 in stock Brand: Pololu Status: Active and Preferred Free add-on shipping in USA Free shipping in USA over $40 Price break Unit price (US$)
1 10.40
5 9.57
25 8.80
100 8.10
Quantity: backorders allowed
pitch × sensors size
(mm)
output max current optimal
range
LED board
8 mm × 13 101.0 × 16.5 analog 30 mA 220 mA 5 mm
This array of IR LED/phototransistor pairs is great for precisely identifying changes in reflectance (like line detection). It operates from 2.9 V to 5.5 V and offers dimmable brightness control independent of the supply voltage and separate controls for the odd and even emitters. In general, the closer the object, the higher the contrast between light and dark readings, but high-reflectance objects are generally detectable out to around 40 mm. This version features the traditional-style QTR sensors without lenses.
Alternatives available with variations in these parameter(s): sensor type sensor count sensor pitch output type Select variant…
## Specifications
• Dimensions: 101.0 × 16.5 × 2.5 mm (see the dimension diagram (1MB pdf) for more details)
• Operating voltage: 2.9 V to 5.5 V
• Sensor type: QTR
• Sensor count: 13
• Sensor pitch: 8 mm
• Full-brightness LED current: 30 mA (independent of supply voltage)
• Max board current: 220 mA
• Output format: analog voltages (0 V to VCC)
• Optimal sensing distance: 5 mm
• Maximum recommended sensing distance: 40 mm
• Weight: 6.2 g
## All available QTR/QTRX versions with dimmable LEDs (older QTR sensors can be found here)
QTR sensors
2.9 V to 5.5 V; 30 mA max LED current(1); 5 mm optimal range
Board
width
Configuration Max board
current(2)
Max range Output
type
Name 1-piece
price
5.0 mm 1 sensor (HD)
32 mA 30 mm analog QTR-HD-01A $1.79 RC (digital) QTR-HD-01RC 7.5 mm 1 sensor (MD) 32 mA 30 mm analog QTR-MD-01A$1.61
RC (digital) QTR-MD-01RC
10.2 mm 4 mm × 2
32 mA 30 mm analog QTR-HD-02A $2.12 RC (digital) QTR-HD-02RC 13.0 mm 8 mm × 2 32 mA 30 mm analog QTR-MD-02A$2.18
RC (digital) QTR-MD-02RC
4 mm × 3
62 mA 30 mm analog QTR-HD-03A $2.69 RC (digital) QTR-HD-03RC 17.0 mm 4 mm × 4 62 mA 40 mm analog QTR-HD-04A$3.26
RC (digital) QTR-HD-04RC
21.0 mm 8 mm × 3
62 mA 30 mm analog QTR-MD-03A $2.81 RC (digital) QTR-MD-03RC 4 mm × 5 93 mA 40 mm analog QTR-HD-05A$4.26
RC (digital) QTR-HD-05RC
25.0 mm 4 mm × 6
93 mA 40 mm analog QTR-HD-06A $4.83 RC (digital) QTR-HD-06RC 29.0 mm 8 mm × 4 62 mA 40 mm analog QTR-MD-04A$3.44
RC (digital) QTR-MD-04RC
4 mm × 7
125 mA 40 mm analog QTR-HD-07A $5.40 RC (digital) QTR-HD-07RC 37.0 mm 8 mm × 5 93 mA 40 mm analog QTR-MD-05A$4.50
RC (digital) QTR-MD-05RC
4 mm × 9
155 mA 40 mm analog QTR-HD-09A $6.97 RC (digital) QTR-HD-09RC 45.0 mm 8 mm × 6 93 mA 40 mm analog QTR-MD-06A$5.13
RC (digital) QTR-MD-06RC
4 mm × 11
185 mA 40 mm analog QTR-HD-11A $8.54 RC (digital) QTR-HD-11RC 53.0 mm 8 mm × 7 125 mA 40 mm analog QTR-MD-07A$5.76
RC (digital) QTR-MD-07RC
4 mm × 13
220 mA 40 mm analog QTR-HD-13A $9.68 RC (digital) QTR-HD-13RC 61.0 mm 8 mm × 8 125 mA 40 mm analog QTR-MD-08A$6.39
RC (digital) QTR-MD-08RC
4 mm × 15
250 mA 50 mm analog QTR-HD-15A $10.82 RC (digital) QTR-HD-15RC 101.0 mm 8 mm × 13 220 mA 40 mm analog QTR-MD-13A$10.40
RC (digital) QTR-MD-13RC
4 mm × 25
405 mA 50 mm analog QTR-HD-25A $17.81 RC (digital) QTR-HD-25RC 125.0 mm 8 mm × 16 250 mA 50 mm analog QTR-MD-16A$12.29
RC (digital) QTR-MD-16RC
4 mm × 31
495 mA 50 mm analog QTR-HD-31A $21.66 RC (digital) QTR-HD-31RC QTRX sensors 2.9 V to 5.5 V; 3.5 mA max LED current(1); 10 mm optimal range Board width Configuration Max board current(2) Max range Output type Name 1-piece price 5.0 mm 1 sensor (HD) 5 mA 30 mm analog QTRX-HD-01A$2.17
RC (digital) QTRX-HD-01RC
7.5 mm 1 sensor (MD)
5 mA 30 mm analog QTRX-MD-01A $1.99 RC (digital) QTRX-MD-01RC 10.2 mm 4 mm × 2 5 mA 30 mm analog QTRX-HD-02A$2.88
RC (digital) QTRX-HD-02RC
13.0 mm 8 mm × 2
5 mA 30 mm analog QTRX-MD-02A $2.94 RC (digital) QTRX-MD-02RC 4 mm × 3 9 mA 30 mm analog QTRX-HD-03A$3.83
RC (digital) QTRX-HD-03RC
17.0 mm 4 mm × 4
9 mA 40 mm analog QTRX-HD-04A $4.78 RC (digital) QTRX-HD-04RC 21.0 mm 8 mm × 3 9 mA 30 mm analog QTRX-MD-03A$3.95
RC (digital) QTRX-MD-03RC
4 mm × 5
14 mA 40 mm analog QTRX-HD-05A $6.16 RC (digital) QTRX-HD-05RC 25.0 mm 4 mm × 6 14 mA 40 mm analog QTRX-HD-06A$7.11
RC (digital) QTRX-HD-06RC
29.0 mm 8 mm × 4
9 mA 40 mm analog QTRX-MD-04A $4.96 RC (digital) QTRX-MD-04RC 4 mm × 7 17 mA 40 mm analog QTRX-HD-07A$8.06
RC (digital) QTRX-HD-07RC
37.0 mm 8 mm × 5
14 mA 40 mm analog QTRX-MD-05A $6.40 RC (digital) QTRX-MD-05RC 4 mm × 9 22 mA 40 mm analog QTRX-HD-09A$10.39
RC (digital) QTRX-HD-09RC
45.0 mm 8 mm × 6
14 mA 40 mm analog QTRX-MD-06A $7.41 RC (digital) QTRX-MD-06RC 4 mm × 11 26 mA 40 mm analog QTRX-HD-11A$12.72
RC (digital) QTRX-HD-11RC
53.0 mm 8 mm × 7
17 mA 40 mm analog QTRX-MD-07A $8.42 RC (digital) QTRX-MD-07RC 4 mm × 13 31 mA 40 mm analog QTRX-HD-13A$14.62
RC (digital) QTRX-HD-13RC
61.0 mm 8 mm × 8
17 mA 40 mm analog QTRX-MD-08A $9.43 RC (digital) QTRX-MD-08RC 4 mm × 15 34 mA 50 mm analog QTRX-HD-15A$16.52
RC (digital) QTRX-HD-15RC
101.0 mm 8 mm × 13
31 mA 40 mm analog QTRX-MD-13A $15.34 RC (digital) QTRX-MD-13RC 4 mm × 25 56 mA 50 mm analog QTRX-HD-25A$27.31
RC (digital) QTRX-HD-25RC
125.0 mm 8 mm × 16
34 mA 50 mm analog QTRX-MD-16A $18.37 RC (digital) QTRX-MD-16RC 4 mm × 31 68 mA 50 mm analog QTRX-HD-31A$33.44
RC (digital) QTRX-HD-31RC
QTRXL sensors
2.9 V to 5.5 V; 30 mA max LED current(1); 20 mm optimal range
Board
width
Configuration Max board
current(2)
Max range Output
type
Name 1-piece
price
5.0 mm 1 sensor (HD)
32 mA 80 mm analog QTRXL-HD-01A $2.17 RC (digital) QTRXL-HD-01RC 7.5 mm 1 sensor (MD) 32 mA 80 mm analog QTRXL-MD-01A$1.99
RC (digital) QTRXL-MD-01RC
1 Can be dynamically reduced to any of 32 available dimming levels.
2 With all LEDs on at max brightness setting.
## QTR family overview
These reflectance sensors feature a linear array of infrared emitter/phototransistor pair modules in a high-density (4 mm pitch) or medium-density (8 mm pitch) arrangement, which makes them well suited for applications that require detection of changes in reflectivity. This change in reflectivity can be due to a color change at a fixed distance, such as when sensing a black line on a white background, as well as due to a change in the distance to or presence of an object in front of the sensor. A variety of sensor counts and densities is available so you can pick the ideal arrangement for your application. Since the outputs are all independent, you can connect just some of the channels to attain an irregular or non-standard sensor spacing.
Unlike our original QTR sensor modules, these units have integrated LED drivers that provide brightness control independent of the supply voltage, which can be anywhere from 2.9 V to 5.5 V, while enabling optional dimming to any of 32 possible brightness settings. For high-density (HD) modules with five or more sensors and medium-density (MD) modules with eleven or more sensors, there are separate controls for the odd-numbered and even-numbered LEDs, which gives you extra options for detecting light reflected at various angles. See the “Emitter control” section below for more information on using this feature.
Two different sensor options are available, denoted by “QTR” or “QTRX” in the product name. The “QTR” versions feature lower-cost sensor modules without lenses while the “QTRX” versions feature higher-performance sensor modules with lenses, which allow similar performance at a much lower IR LED current. You can see the two different sensor styles in the pictures below of the 4-channel modules:
We also have several single-channel modules with the “QTRXL” designator that offer extra-long range by using the QTRX-style sensor module with higher current through the emitter.
Each sensor option is available in two output types: an “A” version with analog voltage outputs between 0 V and VCC, and an “RC” version with outputs that can be read with a digital I/O line on a microcontroller by first setting the lines high and then releasing them and timing how long it takes them to read as low (typically anywhere from a few microseconds to a few milliseconds). The lower the output voltage or shorter the voltage decay time, the higher the reflectance. The following simplified schematic diagrams show the circuits for the individual channels:
Our Arduino library makes it easy to use these sensor modules with an Arduino or compatible controller by providing methods for controlling the emitters, calibrating the module, and reading the individual sensor values from either the A or RC versions. It also has a method specifically for line-following applications to compute the location of the line under the array.
Note: Unlike most of our products, these sensor arrays do not ship with any headers or connectors included, so you will need to supply your own or solder wires directly to the board to use it. See our selection of male headers, female headers, and pre-crimped wires for various connector options.
## Interfacing with the outputs of the A versions
Each sensor on the A versions outputs its reflectance measurement as an analog voltage that can range from 0 V when the reflectance is very strong to VCC when the reflectance is very weak. There are several ways you can interface with the analog output:
• Use a microcontroller’s analog-to-digital converter (ADC) to measure the voltages.
• Use a comparator with an adjustable threshold to convert each analog voltage into a digital (i.e. black/white) signal that can be read by the digital I/O line of a microcontroller.
• Connect each output directly to a digital I/O line of a microcontroller and rely upon its logic threshold.
This last method will work if you are able to get high reflectance from your white surface as depicted in the left image, but will probably fail if you have a lower-reflectance signal profile like the one on the right.
## Interfacing with the outputs of the RC versions
Each sensor on the RC versions requires a digital I/O line capable of driving the output line high and then measuring the time for the output voltage to decay. The typical sequence for reading a sensor is:
1. Turn on IR LEDs (optional).
2. Set the I/O line to an output and drive it high.
3. Allow at least 10 μs for the sensor output to rise.
4. Make the I/O line an input (high impedance).
5. Measure the time for the voltage to decay by waiting for the I/O line to go low.
6. Turn off IR LEDs (optional).
These steps can typically be executed in parallel on multiple I/O lines.
With a strong reflectance, the decay time can be as low as a few microseconds; with no reflectance, the decay time can be up to a few milliseconds. The exact time of the decay depends on your microcontroller’s I/O line characteristics. Meaningful results can be available within 1 ms in typical cases (i.e. when not trying to measure subtle differences in low-reflectance scenarios), allowing up to 1 kHz sampling of all sensors. If lower-frequency sampling is sufficient, you can achieve substantial power savings by turning off the LEDs. For example, if a 100 Hz sampling rate is acceptable, the LEDs can be off 90% of the time, lowering average current consumption from 125 mA to 13 mA.
## Emitter control
These reflectance sensor arrays maintain a constant current through their IR emitters, keeping the emitters’ brightness constant, independent of the supply voltage (2.9 V to 5.5 V). The emitters can be controlled with the board’s CTRL pins, and the details of the control depends on the array size and density:
• HD units with 5 or more sensors and MD units with 11 or more sensors have two emitter control pins: CTRL ODD and CTRL EVEN. By default, these are connected together with a 1 kΩ resistor and pulled up, turning on all the emitters by default and allowing them to be controlled with a signal on either pin, but the CTRL ODD and CTRL EVEN pins can be driven separately for independent control of the odd-numbered and even-numbered emitters.
• MD units with 3-10 sensors also have two emitter control pins since these are made by only populating every other sensor on an HD board, but only the CTRL ODD pin will have an effect on these versions (it is not possible to independently control alternate emitters).
• HD units with 4 or fewer sensors and MD units with 2 or fewer sensors have a single CTRL pin that controls all of the emitters.
Driving a CTRL pin low for at least 1 ms turns off the associated emitter LEDs, while driving it high (or allowing the board to pull it high) turns on the emitters with the board’s default (full) current, which is 30 mA for “QTR” versions and 3.5 mA for “QTRX” versions. For more advanced use, the CTRL pin can be pulsed low to cycle the associated emitters through 32 dimming levels.
To send a pulse, drive the CTRL pin low for at least 0.5 μs (but no more than 300 μs), then high for at least 0.5 μs; (it should remain high after the last pulse). Each pulse causes the driver to advance to the next dimming level, wrapping around to 100% after the lowest-current level. Each dimming level corresponds to a 3.33% reduction in current, except for the last three levels, which represent a 1.67% reduction, as shown in the table below. Note that turning the LEDs off with a >1 ms pulse and then back on resets them to full current.
Dimminglevel(pulses) Emittercurrent(%) Dimminglevel(pulses) Emittercurrent(%) 0 100.00% 16 46.67% 1 96.67% 17 43.33% 2 93.33% 18 40.00% 3 90.00% 19 36.67% 4 86.67% 20 33.33% 5 83.33% 21 30.00% 6 80.00% 22 26.67% 7 76.67% 23 23.33% 8 73.33% 24 20.00% 9 70.00% 25 16.67% 10 66.67% 26 13.33% 11 63.33% 27 10.00% 12 60.00% 28 6.67% 13 56.67% 29 5.00% 14 53.33% 30 3.33% 15 50.00% 31 1.67%
For example, to reduce the emitter current to 50%, apply 15 low pulses to the CTRL pin and then keep it high after the last pulse.
## Related Categories
(702) 262-6648
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2021-01-22 17:04:02
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https://www.biostars.org/p/125170/
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GWAS analysis using PLINK
1
0
Entering edit mode
7.5 years ago
ngsgene ▴ 370
I have a GenomeStudio genotype file with missing genotypes denoted by -
Using this file I generated, for each chromosome the map, fam and lgen files and using the --recode option in plink converted them to ped format. To overcome the plink Error: Locus has >2 alleles I used the --missing-genotype option with the -
After ped files for each chromosome were successfully generated, there are a couple issues am facing:
My lgen file corresponds to the map file - but after recode the ped file has way more columns than the rows. I excpect the number of columns to be rows x 2 (both alleles) that of the map file.
When I try to merge all the chromosomes for evaluating summary statistics the - in the data doesn't seem to be excluded and continue to give errors.
Would converting all the - to 0 is the solution here? Am trying to understand how to exclude such data and best practices.
Thanks for any suggestions/feedback.
plink gwas merge missing-genotype • 4.1k views
ADD COMMENT
1
Entering edit mode
7.5 years ago
1. You probably want to use both --missing-genotype - and --output-missing-genotype 0 during your conversion; this tells PLINK that the input fileset uses -, but you want the output fileset to use 0 so you don't have more headaches down the line.
2. Can you explain what you mean by the "ped file has way more columns than [you expected]"? How many columns does it have? How many rows does the map file have?
3. Is there any particular reason you are converting to .ped/.map instead of PLINK's preferred .bed/.bim/.fam format?
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0
Entering edit mode
Thanks for your response chrchang523, will give --output-missing-genotype 0 a try to get the format working.
The map files have various number of rows, pertaining to the number of SNPs in each chromosome, for example I have ~180000 for chr1, so I expect the ped file to have 180000 * 2 columns.
The only reason for .ped is to be able to see what data am generating, aim is to work with .bed/.bim format once the file formatting is taken care of
ADD REPLY
0
Entering edit mode
How many columns does the .ped actually have?
You might want to try converting to .tped/.tfam (--recode --transpose) instead, that text format might be easier to read (and it's definitely more convenient for PLINK to work with).
ADD REPLY
0
Entering edit mode
The --output-missing-genotype 0 option has helped replace all - to 0. But in either case the --merge option (using this to merge data from all chr) still reports an ERROR: Problem with MAP file line: There doesn't seem to be a way for me to track down which snp in particular is giving the issue as its reporting the first 6 columns for sample identifier and genotype info from the lgen file.
The .ped file now has ~180000 * 2 + 6 columns so that seems to have been correctly generated. Thanks for tip on transpose, are there other pros transposing the data - or this a preferred file format? Plan to impute this using 1000 Genomes, none of the info on Shapeit/Impute2 has suggested a .tped file yet - but please let me know if you have experience with that.
ERROR: Problem with MAP file line:
0 ###-# 0 0 1 -9 G G A A A A C C C C A G A A C C C C G G A G C T T C A A C C G G A A T T A A C T C C A G G G C C C T T C T T T T T T A A C T C C C C G G G G G A T C C C C T A G G G C C A G G G A A A A G G A A T T T T T T G G A A C C C C C C G G G G A A C
ADD REPLY
0
Entering edit mode
The "problematic MAP file line" is a properly formatted .ped file line. Try swapping the order of the arguments you're passing to --merge.
.tped files have fewer columns than .ped files, so I find them easier to work with in a text editor. If you're using --merge, though, .ped/.map lets you avoid an extra conversion step.
ADD REPLY
0
Entering edit mode
Thanks chrchang523! I am able to merge the files successfully, seems the order of .map .ped in the file list was causing the issue. Take home msg: the order of the file list to be merged should be .ped .map / .bed .bim .fam
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2022-06-30 00:35:10
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https://cran.microsoft.com/snapshot/2021-01-25/web/packages/geogenr/vignettes/geogenr.html
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# Introduction
The multidimensional data model was defined with the aim of supporting data analysis. In multidimensional systems, data is structured in facts and dimensions1. The star model is widely accepted, it is recommended for use in widely distributed end-user tools.
The geographical dimension plays a fundamental role in multidimensional systems. It is very interesting to have the possibility of representing the reports obtained from multidimensional systems, using their geographic dimensions, on a map, or performing spatial analysis on them. This functionality is supported by package geomultistar.
The American Community Survey (ACS), within the United States Census Bureau (USCB), offers databases that can be structured using the multidimensional data model to take advantage of its characteristics to be consulted. A characteristic of these databases is that they have a geographic component in the form of a vector layer. For this reason, the structures offered by package geomultistar are suitable for representing this data.
The main objective of this package is to automatically generate multidimensional structures based on the geomultistar package from the geodatabases provided by the ACS, which can be easily queried by users.
Other packages are available that are very useful to access the same data, such as tidycensus, which works in an integrated way with tigris. The main characteristics of geogenr that distinguish it from other proposals are the following:
• it works locally, once available geodatabases are downloaded (can be downloaded using the package);
• supports access at the level of group of variables integrated in a layer, instead of at the level of variable or vector of variables;
• decomposes ACS composite variables into structured fields;
• allows to directly integrate variables of several years;
• and automatically structures the data using the multidimensional data model.
The rest of this document is structured as follows: First, the starting data are presented. Then, an illustrative example of how the package works is developed. Finally, the document ends with conclusions.
# American Community Survey 5-Year Estimates
The package is based on the geodatabases available on the TIGER/Line with Selected Demographic and Economic Data web page. For each year (as of 2010) a list of geodatabases appears under two sections:
• Legal and Administrative Areas;
• Statistical Areas.
As mentioned there for the year 2018 (the last one accessible at the moment), literally: “These geodatabases bring together geography from the 2018 TIGER/Line Shapefiles and data from the 2014-2018 American Community Survey (ACS) 5-year estimates.” Similar data are offered for the previous years for the periods corresponding to each one.
Each ACS geodatabase is structured in layers: a geographic layer, a metadata layer, and the rest are data layers. The data layers have a matrix form, the rows are indexed by instances of the geographic layer, the columns by variables defined in the metadata layer, the cells are numeric values. Here are two examples:
GEOID B00001e1 B00001m1 B00002e1 B00002m1
16000US0200065 60 -1 300 -1
16000US0200650 20 -1 20 -1
16000US0200760 350 -1 100 -1
16000US0200870 250 -1 60 -1
16000US0201090 200 -1 30 -1
16000US0201200 450 -1 100 -1
...
and
GEOID B01001e1 B01001m1 B01001e2 B01001m2 B01001e3 B01001m3 B01001e4 B01001m4 ...
16000US0100100 218 165 92 114 10 16 18 30
16000US0100124 2582 24 1313 98 45 37 14 19
16000US0100460 4374 24 1963 158 144 76 105 68
16000US0100484 641 159 326 89 10 17 16 11
16000US0100676 295 102 143 55 7 11 14 17
16000US0100820 32878 57 16236 453 1159 257 1151 209
...
Some of the defined variables are shown below.
Short Name Full Name
B00001e1 UNWEIGHTED SAMPLE COUNT OF THE POPULATION: Total: Total Population -- (Estimate)
B00001m1 UNWEIGHTED SAMPLE COUNT OF THE POPULATION: Total: Total Population -- (Margin of Error)
B00002e1 UNWEIGHTED SAMPLE HOUSING UNITS: Total: Housing Units -- (Estimate)
B00002m1 UNWEIGHTED SAMPLE HOUSING UNITS: Total: Housing Units -- (Margin of Error)
B01001e1 SEX BY AGE: Total: Total Population -- (Estimate)
B01001m1 SEX BY AGE: Total: Total Population -- (Margin of Error)
B01001e2 SEX BY AGE: Male: Total Population -- (Estimate)
B01001m2 SEX BY AGE: Male: Total Population -- (Margin of Error)
B01001e3 SEX BY AGE: Male: Under 5 years: Total Population -- (Estimate)
B01001m3 SEX BY AGE: Male: Under 5 years: Total Population -- (Margin of Error)
B01001e4 SEX BY AGE: Male: 5 to 9 years: Total Population -- (Estimate)
B01001m4 SEX BY AGE: Male: 5 to 9 years: Total Population -- (Margin of Error)
...
Each variable (Short Name) corresponds to combinations of various field values separated by a separator (:), forming a string (Full Name). The field name of each value is not available but the topics included are detailed on the web page Subjects Included in the Survey. There are thousands of variables of these characteristics (more than 50,000) that, in addition to the metadata layer, can be found on the TIGER/Line with Selected Demographic and Economic Data Record Layouts web page. For each combination of values, one variable associated with the estimate and another with the margin of error are defined. Within each layer, variables can be considered in groups, defined by the first part of the Full Name (for example UNWEIGHTED SAMPLE HOUSING UNITS and SEX BY AGE).
A module of geogenr package analyses the components of Full_name, structuring them in fields; and it allows access to variables in groups.
# An illustrative example
To obtain a geomultistar structure from the ACS data we can distinguish three phases:
• obtaining the data,
• data selection,
• and generation of results,
which are developed below.
Once the result structure is generated, we can define and execute queries on it.
## Obtaining the data
The data is available in the form of a geodatabase. One geodatabase for each area in each of the two area sections.
To consult the areas of each of the sections we use an object of class uscb_acs_5ye. When creating it, we can indicate a folder that will be used as the destination for downloads, if another is not indicated. Below are the operations to get the lists of available areas.
library(tidyr)
library(geogenr)
ua <- uscb_acs_5ye(folder = "../data/us/")
(laa <- ua %>% get_legal_and_administrative_areas())
#> [1] "Alaska Native Regional Corporation"
#> [2] "American Indian/Alaska Native/Native Hawaiian Area"
#> [3] "Congressional District (116th Congress)"
#> [4] "County"
#> [5] "Elementary School District"
#> [6] "Place"
#> [7] "Secondary School District"
#> [8] "State"
#> [9] "State Legislative Districts - Lower Chamber"
#> [10] "State Legislative Districts - Upper Chamber"
#> [11] "Unified School District"
#> [12] "Zip Code Tabulation Area"
(sa <- ua %>% get_statistical_areas())
#> [1] "Combined New England City and Town Area"
#> [2] "Combined Statistical Area"
#> [3] "Metropolitan Division"
#> [4] "Metropolitan/Micropolitan Statistical Area"
#> [5] "New England City and Town Area"
#> [6] "New England City and Town Area Division"
#> [7] "Public Use Microdata Area"
#> [8] "Tribal Block Group"
#> [9] "Tribal Census Tract"
#> [10] "Urban Area"
Since some geodatabases are included in the package, we have selected the area that has the smallest databases. Through the following operations2, we obtain the years for which the geodatabases of the chosen area are available on the web, and we download those corresponding to the selected years.
sa[6]
#> [1] "New England City and Town Area Division"
(y <- ua %>% get_available_years_in_the_web(geodatabase = sa[6]))
#> [1] 2013 2014 2015 2016 2017 2018
(y_res <- ua %>% download_geodatabases(geodatabase = sa[6], years = 2014:2015))
#> [1] 2014 2015
## Data selection
Once we have the geodatabases available locally, we move on to selecting the data.
In this case we create a new object of class uscb_acs_5ye indicating the folder where the downloaded geodatabases are: the package data folder.
folder <- system.file("extdata", package = "geogenr")
folder <- stringr::str_replace_all(paste(folder, "/", ""), " ", "")
ua <- uscb_acs_5ye(folder = folder)
Using the following function, we check the years available locally for the selected area.
sa[6]
#> [1] "New England City and Town Area Division"
(y <- ua %>% get_available_years_downloaded(geodatabase = sa[6]))
#> [1] 2014 2015
Using the metadata included in the package (uscb_acs_metadata), the object of class uscb_acs_5ye where the data of the areas is included, the area of the selected geodatabase and a reference year, we create an object of class uscb_layer, from which we can consult the layer names available for those area and year, as shown below.
ul <- uscb_layer(uscb_acs_metadata, ua = ua, geodatabase = sa[6], year = 2015)
(layers <- ul %>% get_layer_names())
#> [1] "X00_COUNTS" "X01_AGE_AND_SEX" "X02_RACE"
Of all the available layers, we obtain one from which we can consult the groups of variables that it includes, as shown in the following operations.
layers[3]
#> [1] "X02_RACE"
ul <- ul %>% get_layer(layers[3])
(layer_groups <- ul %>% get_layer_group_names())
#> [1] "001 - RACE"
#> [2] "003 - DETAILED RACE"
#> [3] "008 - WHITE ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [4] "009 - BLACK OR AFRICAN AMERICAN ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [5] "010 - AMERICAN INDIAN AND ALASKA NATIVE ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [6] "011 - ASIAN ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [7] "012 - NATIVE HAWAIIAN AND OTHER PACIFIC ISLANDER ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [8] "013 - SOME OTHER RACE ALONE OR IN COMBINATION WITH ONE OR MORE OTHER RACES"
#> [9] "014 - AMERICAN INDIAN AND ALASKA NATIVE ALONE FOR SELECTED TRIBAL GROUPINGS"
#> [10] "015 - ASIAN ALONE BY SELECTED GROUPS"
#> [11] "016 - NATIVE HAWAIIAN AND OTHER PACIFIC ISLANDER ALONE BY SELECTED GROUPS"
#> [12] "017 - AMERICAN INDIAN AND ALASKA NATIVE (AIAN) ALONE OR IN ANY COMBINATION BY SELECTED TRIBAL GROUPINGS"
#> [13] "018 - ASIAN ALONE OR IN ANY COMBINATION BY SELECTED GROUPS"
#> [14] "019 - NATIVE HAWAIIAN AND OTHER PACIFIC ISLANDER ALONE OR IN ANY COMBINATION BY SELECTED GROUPS"
We obtain one of the groups by indicating its name, as shown below.
layer_groups[2]
#> [1] "003 - DETAILED RACE"
ul <- ul %>% get_layer_group(layer_groups[2])
Groups contain sets of variables. The variables of the selected group are shown below.
ul\$layer_group_columns
#> [1] "GEOID" "C02003e1" "C02003m1" "C02003e2" "C02003m2" "C02003e3"
#> [7] "C02003m3" "C02003e4" "C02003m4" "C02003e5" "C02003m5" "C02003e6"
#> [13] "C02003m6" "C02003e7" "C02003m7" "C02003e8" "C02003m8" "C02003e9"
#> [19] "C02003m9" "C02003e10" "C02003m10" "C02003e11" "C02003m11" "C02003e12"
#> [25] "C02003m12" "C02003e13" "C02003m13" "C02003e14" "C02003m14" "C02003e15"
#> [31] "C02003m15" "C02003e16" "C02003m16" "C02003e17" "C02003m17" "C02003e18"
#> [37] "C02003m18" "C02003e19" "C02003m19"
## Generation of results
Once we have obtained a group of variables, we can obtain the associated data in various formats.
It offers the possibility of obtaining it as a tibble, as shown below (the table is not shown due to the high number of columns it has).
ft <- ul %>% get_flat_table(remove_geometry = FALSE)
names(ft)
#> [1] "year" "cnectafp"
#> [3] "nectafp" "nctadvfp"
#> [5] "geoid" "name"
#> [9] "mtfcc" "aland"
#> [11] "awater" "intptlat"
#> [13] "intptlon" "shape_length"
#> [15] "shape_area" "geoid_data"
#> [17] "short_name" "full_name"
#> [19] "inf_code" "group_code"
#> [21] "spec_code" "inf"
#> [23] "group" "demographic_race"
#> [25] "demographic_race_spec" "demographic_total_population"
#> [27] "demographic_total_population_spec" "estimate"
#> [29] "margin_of_error" "shape"
nrow(ft)
#> [1] 190
We can also get an object of the geomultistar class.
gms <- ul %>% get_geomultistar()
The first rows of the dimension and fact tables are shown below.
when_key year
1 2015
where_key cnectafp nectafp nctadvfp geoid name namelsad lsad mtfcc aland awater intptlat intptlon shape_length shape_area geoid_data
1 715 71650 71654 7165071654 Boston-Cambridge-Newton, MA Boston-Cambridge-Newton, MA NECTA Division M7 G3220 3.668e+09 7.13e+08 +42.2933266 -071.0181929 7.653 0.4783 35500US7165071654
2 715 71650 72104 7165072104 Brockton-Bridgewater-Easton, MA Brockton-Bridgewater-Easton, MA NECTA Division M7 G3220 352799175 8831197 +42.0216172 -071.0267170 1.077 0.03932 35500US7165072104
3 715 71650 73104 7165073104 Framingham, MA Framingham, MA NECTA Division M7 G3220 532516314 24039093 +42.2761738 -071.4822008 1.738 0.06073 35500US7165073104
4 715 71650 73604 7165073604 Haverhill-Newburyport-Amesbury Town, MA-NH Haverhill-Newburyport-Amesbury Town, MA-NH NECTA Division M7 G3220 702086333 40447613 +42.8671722 -071.0254982 1.416 0.08179 35500US7165073604
5 715 71650 74204 7165074204 Lawrence-Methuen Town-Salem, MA-NH Lawrence-Methuen Town-Salem, MA-NH NECTA Division M7 G3220 207735751 9917120 +42.7282758 -071.1630701 0.9094 0.02392 35500US7165074204
6 715 71650 74804 7165074804 Lowell-Billerica-Chelmsford, MA-NH Lowell-Billerica-Chelmsford, MA-NH NECTA Division M7 G3220 863143106 27403003 +42.6141693 -071.4837821 2.441 0.09771 35500US7165074804
what_key short_name full_name inf_code group_code spec_code inf group demographic_race demographic_race_spec demographic_total_population demographic_total_population_spec
1 C02003_01 DETAILED RACE: Total: Total Population C02 003 1 RACE DETAILED RACE Total Total Population
2 C02003_02 DETAILED RACE: Population of one race: Total Population C02 003 2 RACE DETAILED RACE Population of one race Total Population
3 C02003_03 DETAILED RACE: Population of one race: White: Total Population C02 003 3 RACE DETAILED RACE Population of one race White Total Population
4 C02003_04 DETAILED RACE: Population of one race: Black or African American: Total Population C02 003 4 RACE DETAILED RACE Population of one race Black or African American Total Population
5 C02003_05 DETAILED RACE: Population of one race: American Indian and Alaska Native: Total Population C02 003 5 RACE DETAILED RACE Population of one race American Indian and Alaska Native Total Population
6 C02003_06 DETAILED RACE: Population of one race: Asian alone: Total Population C02 003 6 RACE DETAILED RACE Population of one race Asian alone Total Population
when_key where_key what_key estimate margin_of_error nrow_agg
1 1 1 2846699 131 1
1 1 2 2754158 3195 1
1 1 3 2134196 4429 1
1 1 4 274896 2907 1
1 1 5 4817 603 1
1 1 6 253518 2264 1
Once we have verified that the data for the reference year is what we need, we can expand our database considering the rest of the years available in the folder. The only requirement to consider a year is that its variable structure be the same as that of the reference year.
To do this, we create a class uscb_folder object from the reference year object, as shown below.
uf <- uscb_folder(ul)
We can get a tibble from the new object. In this case it has more rows. In this case you have more rows than for just one year, as you would expect.
cft <- uf %>% get_common_flat_table()
nrow(cft)
#> [1] 380
We can also get a geomultistar object.
cgms <- uf %>% get_common_geomultistar()
Instead of displaying all the tables, we focus on the table in the when dimension.
when_key year
1 2014
2 2015
Includes data for all available years.
## Queries with geographic information
Once we have a geomultistar object, we can use the functionality of the geomultistar package.
Specifically, the only field that has geographic information directly associated with is geoid. If we want to associate that information to other fields of the dimension, such as the name field, we must do it using the operation shown below.
library(geomultistar)
cgms <- cgms %>%
define_geoattribute(
attribute = c("name"),
from_attribute = "geoid"
)
We can define multidimensional queries using the functionality of the starschemar package, as shown below.
library(starschemar)
gdqr <- dimensional_query(cgms) %>%
select_dimension(name = "where",
attributes = c("name")) %>%
select_dimension(name = "what",
attributes = c("short_name", "demographic_race_spec")) %>%
select_fact(name = "detailed_race",
measures = c("estimate")) %>%
filter_dimension(name = "when", year == "2015") %>%
filter_dimension(name = "what", demographic_race_spec == "Asian alone") %>%
run_geoquery()
The first rows of the result can be seen below in table form.
short_name demographic_race_spec name estimate nrow_agg Shape
C02003_06 Asian alone Boston-Cambridge-Newton, MA 253518 1 MULTIPOLYGON (((-71.39 42.3…
C02003_06 Asian alone Brockton-Bridgewater-Easton, MA 3548 1 MULTIPOLYGON (((-71.08 42.1…
C02003_06 Asian alone Framingham, MA 17611 1 MULTIPOLYGON (((-71.39 42.3…
C02003_06 Asian alone Haverhill-Newburyport-Amesbury Town, MA-NH 2375 1 MULTIPOLYGON (((-71.22 42.9…
C02003_06 Asian alone Lawrence-Methuen Town-Salem, MA-NH 6752 1 MULTIPOLYGON (((-71.19 42.7…
C02003_06 Asian alone Lowell-Billerica-Chelmsford, MA-NH 36648 1 MULTIPOLYGON (((-71.66 42.6…
C02003_06 Asian alone Lynn-Saugus-Marblehead, MA 8476 1 MULTIPOLYGON (((-70.9 42.48…
C02003_06 Asian alone Nashua, NH-MA 10322 1 MULTIPOLYGON (((-71.88 42.8…
C02003_06 Asian alone Peabody-Salem-Beverly, MA 3381 1 MULTIPOLYGON (((-71 42.56, …
C02003_06 Asian alone Taunton-Middleborough-Norton, MA 2125 1 MULTIPOLYGON (((-71.19 41.9…
The result is a vector layer that we can save, perform spatial analysis or queries on it, or we can see it as a map, using the functions associated with the sf class.
class(gdqr)
#> [1] "sf" "tbl_df" "tbl" "data.frame"
plot(gdqr[,"estimate"])
# Conclusions
The American Community Survey (ACS) offers geodatabases with geographic information and associated data of interest to researchers in the area. These data can be accessed through various alternatives in which you must indicate the year and variable names. Due to the large number of variables and their structure, this operation is not easy.
The geogenr package offers an alternative that allows you to download the geodatabases that are considered necessary and access the variables by selecting data layers and logical groups of variables. Additionally, it automatically generates a multidimensional structure that includes the available geographic information. From this structure, multidimensional queries that include the available geographic information can easily be defined.
The data obtained can be processed with the sf package to define spatial queries or analysis, be presented in maps or saved as a file to be used by a GIS (Geographical Information System).
1. Basic concepts of dimensional modelling and star schemas are presented in starschemar vignettes.↩︎
2. These operations are not running in the vignette. The result of executing them locally to obtain the geodatabases included in the package is displayed.↩︎
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2023-03-20 11:06:18
|
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|
http://math.stackexchange.com/questions/167232/showing-that-an-entire-function-is-a-polynomial
|
# Showing that an entire function is a polynomial
Let $f(z)$ be an entire function, $R_n$ a sequence of positive real numbers tending to $\infty$ such that $f(z) \neq 0$ on $|z|=R_n$ and there exists $M>0$ such that $$\int_{|z|=R_n} \left|\frac{f'(z)}{f(z)}\right| ~dz<M$$ for all $n$. Show that $f$ is a polynomial.
What came to my mind is to consider that $f(z)=a_0+a_1z+\cdots \;\;\forall z\in\mathbb{C}$, and to try proving that $a_k=0$ from a certain $k$, maybe using the Cauchy formula for these coefficients, but I can't use the hypotesis on that bounded integral. Is observing that there is a logarithmic derivative of any use?
-
An idea: try to show that $f^{-1}(a)$ is finite for every $a\in\mathbb C$, using the argument principle. – user31373 Jul 5 '12 at 21:55
So indicating with $N$ the number of zeros inside $|z|<R_n$ by the argument principle I have $2\pi i N=\int_{|z|=R_n}\frac{f'}{f}$ which can be estimated by its modulus and eventually by M, and taking the limit i have that there are at most M zeros. If i wanted to do something analogous with $f(z)-a$ i need an estimate like $|f(z)-a|>|f(z)|$ on $|z|=R_n$.. – balestrav Jul 5 '12 at 22:16
Right, we are stuck with $a=0$. Luckily, a better idea arrived meanwhile. – user31373 Jul 5 '12 at 22:22
As $\,\displaystyle{\frac{1}{2\pi i}\oint \frac{f'}{f}\,dz}\,$ is the number of roots inside the circle, the total number of roots is finite
(bounded by $\,\frac{M}{2\pi}\,$). Let $$g(z)=\frac{f(z)}{(z-a_1)\cdot\ldots\cdot(z-a_k)}$$, where $a_1,\dots,a_k$ are the roots of $f$. Then $g$ satisfies the same condition as $f$ (with a different $\tilde M$). As $g$ has no root, it is of the form $g(z)=\exp(h(z))$ for some entire function $h$. We thus have $\,\displaystyle{\oint |h'(z)|\,|dz|<\tilde M}\,$ for circles of radii $R_n\to\infty$. This implies $h'=0$, hence $f$ is a polynomial.
edit: why $h'=0$: if $$h'(z)=c_1 z^m+c_2 z^{m+1}+\dots$$ ($c_1\neq0$) then $$\oint \frac{h'(z)}{z^{m+1}}\,dz=2\pi i c_1$$, which certainly implies $\oint |h'(z)|\,|dz|\to\infty$.
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2015-06-30 14:44:14
|
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https://some.engineering/blog/2022/03/03/aggregating-search-data
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# Aggregating Search Data
note
This blog post is the second in a series about Resoto's powerful search functionality. The previous post, Resoto Search 101, provides an introduction to Resoto's search capabilities.
Resoto's search allows for resources to be selected using filters, combinators, and traversals. Search results can be combined, grouped, and aggregated.
The simplest example of search aggregation in Resoto is the count command, which enables you to count objects or the occurrences of a specific property. Let's say we are interested in the number of compute instances we maintain:
> search is(instance) | counttotal matched: 540total unmatched: 0
Compute instances are of kind instance regardless of cloud provider, so is(instance) selects both aws_ec2_instances and gcp_instances. The count command then takes the results and returns the number of occurrences.
The count command also allows specifying a grouping value. The following search would return counts by instance_status:
> search is(instance) | count instance_statusstopped: 48terminated: 151running: 341total matched: 540total unmatched: 0
While count is often sufficient, the aggregate command is required for more advanced use cases. For example, we could get CPU core and memory data using aggregate:
> search is(instance) | aggregate sum(instance_cores) as sum_of_cores, max(instance_cores) as max_cores, sum(instance_memory) as sum_of_memory, max(instance_memory) as max_memsum_of_cores: 3441max_cores: 16sum_of_memory: 12802.25max_mem: 64
In this example, we have 3441 cores in total and each instance has a maximum of 16 cores. The same data is also available for provisioned memory: we have almost 13 TB of RAM with no instance having more than 64 GB.
We can further analyze this aggregated data using grouping variables, which we have already seen in an above example of the count command. Let's try aggregating the available memory by instance status:
> search is(instance) | aggregate instance_status as status: sum(instance_memory) as memorygroup: status: runningmemory: 8538---group: status: stoppedmemory: 1345---group: status: terminatedmemory: 2919.25
This search returns multiple results, each of which has a group property. The grouping variable value for each result is a property of its group object. In this case, running compute instances have 8 TB of available memory altogether, while the remaining stopped or terminated instances have a total of 4 TB of allocated memory.
## Ancestors and Descendants
The aggregation capabilities we have seen so far include grouping and functions. Resoto captures the state of your infrastructure as nodes, and their relationships as edges.
Wouldn't it be great if we could aggregate over not only the data of a single node, but the data of ancestor or descendant nodes in the graph? Resoto's search engine can perform nested search statements for this exact purpose.
The above diagram illustrates the relationship between compute instances. AWS resources are attached to a region, while GCP resources are associated with a zone. Each instance also has a instance_type predecessor node. To access properties of ancestor nodes of a given kind, we can use the following notation:
> search is(instance) | aggregate sum(/ancestors.instance_type.reported.ondemand_cost) as costcost: 155.73
This search selects all instances, then aggregates the on-demand cost of each element by traversing up to the instance type and selecting the reported.ondemand_cost property.
The path /ancestors.instance_type.reported.ondemand_cost can be translated as a traversal over the node's ancestors until an ancestor of kind instance_type is found. The last part of this path is relative to the node that is found (reported.ondemand_cost in this example). The result is the on-demand cost of all instances.
It is possible to walk the graph inbound with ancestors, and outbound using descendants. You can apply this syntax anywhere a property path is defined in a search. Let's use this technique to find running instances aggregated by account and region:
> search is(instance) and instance_status==running | aggregate /ancestors.account.reported.name as account, /ancestors.region.reported.name as region: sum(instance_memory) as memory, sum(instance_cores) as cores, sum(/ancestors.instance_type.reported.ondemand_cost) as costgroup: account: sales region: us-west-2memory: 1936cores: 484cost: 23.232---group: account: sales region: us-west1memory: 30cores: 8cost: 0.3799---group: account: dev region: us-east-1memory: 576cores: 144cost: 7.2..
As you can see, Resoto's search enables you to gather data about your infrastructure that would otherwise be extremely challenging and tedious to tabulate. This search result is also refreshed whenever the graph is updated (every hour by default), which enables the collection of data that is not feasible to manage manually.
Now, imagine feeding results of an aggregation search into a Prometheus time series database and being able to visualize the data in a Grafana dashboard. Resoto Metrics serves this exact purpose, feeding robust aggregation metrics into a time series database.
Please refer to the Resoto documentation for more details about supported aggregation capabilities. I hope the examples presented here clearly illustrate the power of Resoto's search aggregation. If you're new to Resoto, we hope you will try it out!
Tags:
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2023-04-01 11:51:23
|
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http://mathhelpforum.com/calculus/219904-why-does-work-only-when-h-tends-zero.html
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# Thread: why does it work only when h tends to zero????
1. ## why does it work only when h tends to zero????
$f(x + h) = xf(x)\\
Ef(x) = xf(x)\\
E = x\\
\ln E = hD\\
\ln x = hD\\
f(x) = y\\
y\ln x = hDy\\
y\ln x = h\frac{{dy}}{{dx}}\\
\int {} \ln xdx = h\int {} dy/y\\
x\log x/e = h\ln y + \ln c\\
x\log x/e = h\ln y/C\\
(x/h)\ln x/e = \ln y/C\\
C(x/e)\frac{{x/h}}{1} = y = f(x)\\
f(x + h) = C((x + h)/e)\frac{{(x + h)/h}}{1}\\
f(x + h)/f(x) = (((x + h)/e)\frac{{(x + h)/h}}{1})/(x/e)\frac{{x/h}}{1}\\
f(x + h)/f(x) = ((x + h)/x)\frac{{x/h}}{1})*((x + h)/e)\\
f(x + h)/f(x) = (1 + h/x)\frac{{x/h}}{1}*((x + h)/e)\\
\mathop {\lim }\limits_{h \to 0} f(x + h)/f(x) = \mathop {\lim }\limits_{h \to 0} e*((x + h)/e)\\
\mathop {\lim }\limits_{h \to 0} f(x + h)/f(x) = \mathop {\lim }\limits_{h \to 0} (x + h)\\
\mathop {\lim }\limits_{h \to 0} f(x + h)/f(x) = x\\
\\$
2. ## Re: why does it work only when h tends to zero????
why is it true only when h tends to zero ...
but we havent assumed h to be zero in our initial assumption....???
3. ## Re: why does it work only when h tends to zero????
What is this series of equalities?
4. ## Re: why does it work only when h tends to zero????
some latex error...ignore <br/> everwhere
5. ## Re: why does it work only when h tends to zero????
I understand that <br/> is spurious. (On this forum, LaTeX does not like newlines in formulas and requires spaces at least every 50 characters. In this case, it is better to have one formula per line.) I am asking about the status of these equations. Are they a proof of some fact? Does every subsequent formula follow from the previous one or is it the other way around? What are the new symbols E and D?
Contrary to a possible stereotype, mathematicians would not parse a text consisting of mathematical formulas only (unless it is written by a genius). They require a plain text explanation of the purpose, method and so on.
6. ## Re: why does it work only when h tends to zero????
PURPOSE
to find a function such that when it is increased by h(Constant) at x it becomes x times it value at x
E and D
E is shift operator such that Ef(x)=f(x+h) , E^2 f(x)=f(x+2h) and so on s.t. E^nf(x)=f(x+nh)
D is differtial operator that is d/dx...
STEP 4
using taylors series
e^hD= E
7. ## Re: why does it work only when h tends to zero????
Originally Posted by mpx86
PURPOSE
to find a function such that when it is increased by h(Constant) at x it becomes x times it value at x
E and D
E is shift operator such that Ef(x)=f(x+h) , E^2 f(x)=f(x+2h) and so on s.t. E^nf(x)=f(x+nh)
D is differtial operator that is d/dx...х.
Thanks, this helps. Another thing that is unclear is whether this argument is taken from a textbook and you need help understanding it or if it is something you came up with yourself and it needs checking. Also, it is not clear whether the required f(x) has been found: the last line says $\lim_{h \to 0} f(x + h)/f(x) = x$, which is an immediate corollary of the requirement in the first line, and not only in the limit, but for every h.
More seriously, the line E = x and the following lines don't make sense to me: the left-hand side is an operator (i.e., a mapping from functions to functions), and the right-hand side is either a number x or an identity function. These entities have different types. Similarly, it is not clear what a logarithm of an operator means.
8. ## Re: why does it work only when h tends to zero????
i am asking why does it yields correct answer only when h tends to zero ....we havent assumed it to be tending to zero in our initial assumption... why does it yields h tending to zero at the end...
i thing it is due to defination of derivatives (which we have used in our derivation) which has been defined for h tending to zero.... besides it just doesnt look like the complete answer.... this is a question done by me and is not written in any textbook (yielding more chances for error)...
moreover it always yield correct answers when h tends to zero....(try different functions ) .....
however the process yields correct answer (exactly) when E is not a dependent quantity or a variable that is when E=constant.....
9. ## Re: why does it work only when h tends to zero????
so no one knows ..... no problem..... i will figure it out
myself..........
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2016-12-09 15:50:41
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https://stats.stackexchange.com/questions/263828/efficiency-of-the-ols-estimator
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# Efficiency of the OLS estimator
I have this linear regression: $y_{i}=\beta_{0} + \beta_{1}x_{i} + u_{i}$ with $i=\{1..n\}$.
Say $\hat{\beta}_{1}$ is the OLS estimator of $\beta_{1}$. $\hat{\beta}_{1}$ is BLUE since the Gauss Markov assumptions hold.
Now I am asked to show that $\tilde{\beta}_{1}=\frac{y_{n}-y_{1}}{x_{n}-x_{1}}$ is less efficient than the OLS estimator.
Say $u_{i}\sim iid$ then $\text{Var}(\tilde{\beta}_{1})=(\frac{1}{x_{n}-x_{1}})^2\times(\text{Var}(u_{n})-\text{Var}(u_{1}))=0$.
So $\text{Var}(\tilde{\beta}_{1})<\text{Var}(\hat{\beta}_{1})$ which contradict the fact that $\hat{\beta}_{1}$ is BLUE. So obviously the assumption that $u_{i}\sim iid$ is wrong. Why?
• Is the variance of the difference between two random variables the difference of their variances? – Scortchi Feb 24 '17 at 15:01
• Oh I agree that if the two random variables were dependent then you would have to add the 2*cov(un,u1). But here I am asking about the case when the error terms are independent. Or maybe that's impossible? – jeake Feb 24 '17 at 16:00
• Whether the variables are dependent or independent, variance of the difference between them is not the difference of their variances. – Richard Hardy Feb 24 '17 at 16:02
• Is the variance of the difference between two independent random variables the difference of their variances? You should be able to answer that without looking anything up. – Scortchi Feb 24 '17 at 16:03
• How/Should I mark this as answered? – jeake Feb 24 '17 at 16:27
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2019-06-27 04:42:41
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https://math.stackexchange.com/questions/1357901/integrating-int-frac-sin-1x-sqrt1xdx-by-parts
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# Integrating $\int \frac{\sin^{-1}(x)}{\sqrt{1+x}}dx$ by parts
I have a question that requires me to integrate the following by parts. I have done the question but apparently my answer does not match that of wolfram alpha's.
$$\int \frac{\sin^{-1}(x)}{\sqrt{1+x}}dx$$ $$u= \sin^{-1}(x) : du = \frac{1}{\sqrt{1-x^2}}dx$$ $$v= 2\sqrt{1+x} : dv = \frac{1}{\sqrt{1+x}}dx$$ Following the formula $\int{udv}=uv-\int{vdu}$ $$=2\sqrt{1+x}*(\sin^{-1}(x))-\int{\frac{\sqrt{1+x}}{\sqrt{(1+x)(1-x)}}dx}$$ $$=2\sqrt{1+x}*(\sin^{-1}(x))-\int{\frac1{\sqrt{1-x}}}dx$$ $$=2\sqrt{1+x}*(\sin^{-1}(x))-4\sqrt{1-x} +C$$
But contrary to my answer... the wolfram alpha answer provided is...
$$\frac{2[2\sqrt{1-x^2}+(x+1)(\sin^{-1}(x))]}{\sqrt{x+1}}$$
What am I doing wrong, or ... how do I simplify to that form?
• It is exactly the same...almost. Check the signs – Timbuc Jul 11 '15 at 21:24
• Isn't that the same thing? – A.Γ. Jul 11 '15 at 21:25
## 2 Answers
First, you wrote
$$-\int\frac{\sqrt{1+x}}{\sqrt{(1+x)(1-x)}}dx\tag 1$$
where $(1)$ should have been
$$-2\int\frac{\sqrt{1+x}}{\sqrt{(1+x)(1-x)}}dx \tag 2$$
This was likely a typographical error (i.e., omitting the $2$). This error carried to the next line in which you wrote
$$-\int\frac{1}{\sqrt{1-x}}dx$$
where it should have been
$$-2\int\frac{1}{\sqrt{1-x}}dx$$
But, the next error is, I believe, the source of the issue. You integrated $-\int \frac{1}{\sqrt{1-x}}dx$ and obtained
$$-4\sqrt{1-x}$$
Surely,
$$-\int \frac{1}{\sqrt{1-x}}dx=+2\sqrt{1-x}$$
If we insert the missing factor of $2$ as in $(2)$, we have
$$-2\int\frac{\sqrt{1+x}}{\sqrt{(1+x)(1-x)}}dx =+4\sqrt{1-x}+C$$
and the final answer after correction is
$$\int\frac{\arcsin x}{\sqrt{1+x}}dx=2\sqrt{1+x}\arcsin x+4\sqrt{1-x}+C$$
which agrees with WA after multiplying by $1=\frac{\sqrt{1+x}}{\sqrt{1+x}}$!
$$\frac{2[2\sqrt{1-x^2}+(x+1)(\sin^{-1}(x))]}{\sqrt{x+1}}=\frac{4\overbrace{\sqrt{1-x^2}}^{=\sqrt{1+x}\sqrt{1-x}}}{\sqrt{x+1}}+2\frac{x+1}{\sqrt{x+1}}\arcsin x=$$
$$4\sqrt{1-x}+2\sqrt{1+x}\arcsin x$$
Also
$$\int\frac{dx}{\sqrt{1-x}}=\color{red}-2\sqrt{1-x}+C$$
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2020-01-22 05:21:42
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http://caisplusplus.usc.edu/blog/curriculum-supplement/backprop-by-hand
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# Backprop By Hand
## Keeping it Old School
by CAIS++
After going through our workshop on neural networks and getting some feedback from our members, it became evident that some additional theory review would be valuable to allow the concepts behind neural networks to really sink in.
In order to make this review as thorough as possible, we decided to take some inspiration from Matt Mazur’s blog post on backpropagation and to walk through one complete iteration of the neural network training process by hand: complete with concrete numbers, calculations and all.
Note: Before going through this post, it may be helpful to have first gone through our original lessons on the theory behind neural networks. Links to those lessons can be found here: Neural Networks Part 1 (Architecture), Part 2 (Training). It may also be helpful to have the Part 2 (Training) lesson open side-by-side when going through this post, in case you want to quickly reference any of the equations we discussed there.
## Problem Setup
Suppose we want to train a small neural network to predict whether a student will pass an upcoming test. We want this neural network to take in $$\text{hours slept}$$ and $$\text{hours studied}$$ as inputs, and to output a value between $$0$$ and $$1$$ that represents the probability that the student will pass.
We are given only one training example, and some initial random values for our neural network weights. (The neural network has one hidden layer and out output layer, so there will be two weight matrices in total. For simplicity’s sake, we’ll go ahead and ignore biases in this example.)
We are also given some information on the average and standard deviation of our inputs (hours slept and hours studied), which we will use to standardize our inputs before feeding them into the network. And lastly, we’re told that we should use the sigmoid activation function, which we’ll denote with $$f(x)$$, on both our hidden layer and output layer, and cross entropy loss ($$J$$) to gauge how well/poorly our network is doing. Our problem setup, then, is as follows:
Disclaimer: we wrote the categorial cross-entropy loss function on the blackboard, when technically we should have wrote the binary cross-entropy loss function. Binary cross entropy is used when we are trying to predict only a 0 or 1 (i.e. predicting between 2 classes, which is what we want), and categorical cross entropy (a generalization of binary cross-entropy) is used when trying to predict between multiple classes via a one-hot vector (as was the case with MNIST/handwritten digits). They both do essentially the same thing, but the binary cross-entropy loss function equation is formulated a little bit differently, as you’ll see in the example at the end of the first forward propagation step.
Next, a couple notation refreshers:
• $$\textbf{z}^m$$: a vector representing the weighted sum of the $$m$$th layer’s neurons. ($$L$$ denotes the last layer.)
• $$\textbf{a}^m$$: activation of the $$mth$$th layer’s neurons. We calculate this by passing each element in $$\textbf{z}^m$$ through the activation function.
• $$\delta^m$$: error/sensitivity of the $$m$$th layer’s neurons. This tells us how the final cost ($$J$$) will change if we shift any of the weighted sums in $$\textbf{z}^m$$ a tiny bit in the positive direction.
• $$\frac{\partial J}{\partial \textbf{W}^{m}}$$: gradient of the $$m$$th layer’s weights. This tells us how the final cost will change if we shift any of the $$m$$th layer’s weights a tiny bit in the positive direction.
And lastly, the equations that we’ll be using for forward propagation, backpropagation, and gradient descent:
You can check out a derivation of the backpropagation/gradient descent equations in our Neural Network Training lesson. We’ve moved some of the terms around within the equations to get the dimensions to match up for our matrix operations, but the numbers themselves will be the same in either case.
## Step 0: Preprocessing
First, we’ll use the given mean/standard deviation data to standardize our inputs. This makes sure that our neural network can compare apples to apples, instead of apples to lemons/honeydew/etc.
## Step 1: Forward Propagation
Next, we’ll feed these standardized inputs forward through each layer of the neural network, applying a series of matrix multiplications and activation functions along the way, to generate our initial prediction. We’ll then calculate the (binary cross-entropy) loss using this prediction to see if it improves after going through a full training step.
## Step 2: Backpropagation
Since you can see that we made the wrong initial prediction (failed, instead of passed), we’ll now go ahead and find out how we can tweak our neural network so that it can do a better job of making predictions. To do this, we’ll work our way backward through the network and calculate the error ($$\delta$$), or sensitivity, of each layer of neurons. Each of these error terms represents the partial derivative of the final cost ($$J$$) with respect to the current neuron’s weighted sum ($$z$$).
## Step 3: Gradient Descent
After calculating all the sensitivities, we can use these sensitivities to find the actual gradient of the parameters (i.e. weights) in our network.
Then, we’ll use our calculated gradients to apply gradient descent. This entails subtracting the gradient (multiplied by our current learning rate) from the original weights, so that we move down the cost surface in a way that should decrease our final cost.
## Step 4: Forward Propagation, Redux
After going through one training iteration, we should test to make sure that our neural network’s predictions are more accurate than before. We can do this by using our new weights to once again feed the original input through the network, generating a new prediction, and then re-calculating the loss based on this prediction.
Since our prediction is now closer to the actual $$y$$ value ($$1$$), and since the loss is lower than before, we can conclude that the training step was successful! If we had more data, we’d repeat these steps a bunch of times over the entire training set (likely taking average cost and gradient values over batches of the data) to fully train our neural network.
For now though, hopefully this concrete example helped clarify any lingering confusions you may have had with the neural network training process.
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2021-06-15 04:31:43
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https://themathhelp.com/index.php?threads/differentiate-4.2565/
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# PracticeDifferentiate 4
Differentiate.
#### Jason
##### Well-known member
I suppose the first step would be to take everything, bottom and top - both sides, to the cubed power - to get rid of the cubed root.
@MarkFL
However, there is also the square root there, though.
#### MarkFL
##### La Villa Strangiato
Math Helper
I would use the product/power/chain rules.
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2020-10-23 05:04:45
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https://www.mail-archive.com/ntg-context@ntg.nl/msg78122.html
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# Re: [NTG-context] next beta
```On Tue, 19 Mar 2013, Hans Hagen wrote:
```
`\starttext`
```
\starttabulate[||CL{darkred}|CM{darkgreen}CT{white}|CR{darkblue}||]
```
\NC first \NC left \NC middle \NC right \NC last \NC \NR \NC first \NC \color[white]{left} \NC middle \NC \color[white]{right} \NC last \NC \NR \NC first \NC left \NC middle \NC right \NC last \NC \NR
``` \stoptabulate
\stoptext
i.e. we already had CL CM and CR, so CT is new .. should be wikified.
```
```
```
I am using a two-week old beta (2015.04.03). CL has the same alignment as r and CR has the same aligned as l.
```
```
I understand the historic reason for the difference between left and flushleft, but shouldn't the alignment keys within the same mechanism have the same meaning? (Or was this a bug that has been corrected in the current beta).
```
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2020-12-03 14:15:03
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https://www.mathlearnit.com/what-is-51-391-as-a-decimal
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# What is 51/391 as a decimal?
## Solution and how to convert 51 / 391 into a decimal
51 / 391 = 0.13
51/391 converted into 0.13 begins with understanding long division and which variation brings more clarity to a situation. Both represent numbers between integers, in some cases defining portions of whole numbers But in some cases, fractions make more sense, i.e., cooking or baking and in other situations decimals make more sense as in leaving a tip or purchasing an item on sale. Now, let's solve for how we convert 51/391 into a decimal.
## 51/391 is 51 divided by 391
Teaching students how to convert fractions uses long division. The great thing about fractions is that the equation is already set for us! The two parts of fractions are numerators and denominators. The numerator is the top number and the denominator is the bottom. And the line between is our division property. To solve the equation, we must divide the numerator (51) by the denominator (391). This is how we look at our fraction as an equation:
### Numerator: 51
• Numerators are the parts to the equation, represented above the fraction bar or vinculum. 51 is one of the largest two-digit numbers you'll have to convert. The bad news is that it's an odd number which makes it harder to covert in your head. Values closer to one-hundred make converting to fractions more complex. Time to evaluate 391 at the bottom of our fraction.
### Denominator: 391
• Denominators differ from numerators because they represent the total number of parts which can be found below the vinculum. 391 is one of the largest two-digit numbers to deal with. But the bad news is that odd numbers are tougher to simplify. Unfortunately and odd denominator is difficult to simplify unless it's divisible by 3, 5 or 7. Overall, two-digit denominators are no problem with long division. Now let's dive into how we convert into decimal format.
## Converting 51/391 to 0.13
### Step 1: Set your long division bracket: denominator / numerator
$$\require{enclose} 391 \enclose{longdiv}{ 51 }$$
We will be using the left-to-right method of calculation. Yep, same left-to-right method of division we learned in school. This gives us our first clue.
### Step 2: Extend your division problem
$$\require{enclose} 00. \\ 391 \enclose{longdiv}{ 51.0 }$$
Because 391 into 51 will equal less than one, we can’t divide less than a whole number. So that means we must add a decimal point and extend our equation with a zero. Now 391 will be able to divide into 510.
### Step 3: Solve for how many whole groups you can divide 391 into 510
$$\require{enclose} 00.1 \\ 391 \enclose{longdiv}{ 51.0 }$$
We can now pull 391 whole groups from the equation. Multiply by the left of our equation (391) to get the first number in our solution.
### Step 4: Subtract the remainder
$$\require{enclose} 00.1 \\ 391 \enclose{longdiv}{ 51.0 } \\ \underline{ 391 \phantom{00} } \\ 119 \phantom{0}$$
If your remainder is zero, that's it! If you still have a remainder, continue to the next step.
### Step 5: Repeat step 4 until you have no remainder or reach a decimal point you feel comfortable stopping. Then round to the nearest digit.
Remember, sometimes you won't get a remainder of zero and that's okay. Round to the nearest digit and complete the conversion. There you have it! Converting 51/391 fraction into a decimal is long division just as you learned in school.
### Why should you convert between fractions, decimals, and percentages?
Converting between fractions and decimals depend on the life situation you need to represent numbers. Remember, they represent numbers and comparisons of whole numbers to show us parts of integers. This is also true for percentages. So we sometimes overlook fractions and decimals because they seem tedious or something we only use in math class. But each represent values in everyday life! Here are examples of when we should use each.
### When you should convert 51/391 into a decimal
Investments - Comparing currency, especially on the stock market are great examples of using decimals over fractions.
### When to convert 0.13 to 51/391 as a fraction
Progress - If we were writing an essay and the teacher asked how close we are to done. We wouldn't say .5 of the way there. We'd say we're half-way there. A fraction here would be more clear and direct.
### Practice Decimal Conversion with your Classroom
• If 51/391 = 0.13 what would it be as a percentage?
• What is 1 + 51/391 in decimal form?
• What is 1 - 51/391 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 0.13 + 1/2?
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2023-02-04 18:39:28
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http://mathematicalmusings.org/2017/05/10/curricular-coherence-no-4-coherence-of-practice/
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# Curricular Coherence no. 4: Coherence of Practice
In this final post about curricular coherence, I’m pinch-hitting for Bill, who is busy reorganizing his wine cellar. This time, we talk about coherence of mathematical practice.
We value coherence of content because we believe that a coherently arranged curriculum makes it possible for a student to see the subject as a whole, to understand the logical connections and deep structures, and to use that understanding for more efficient problem-solving and better retention of knowledge and procedures. But making it possible does not make it probable. The way students do mathematics, their mathematical practice, may have an effect on their ability to take advantage of a coherent curriculum. The CCSSM describes eight aspects of the complex construct of mathematical practice. Here we focus on two aspects, using structure (MP7) and abstraction (MP8).
Structure in arithmetic and algebraic expressions reveals what might be called “hidden meaning.” For example, writing $x^2-6x-7$ as $(x-3)^2-16$ reveals that, for real values of $x$, the expression assumes values greater than or equal to $-16$ (and it assumes that value only when $x=3$). Writing it as $(x-7)(x+1)$ highlights the values of $x$ that make the expression 0.
Treating pieces of expressions as a single “chunk” can simplify calculations; seeing that $4x^2-8x+3$ can be written as $(2x)^2-4(2x)+3$ helps one obtain the factorization from the (easier) factorization of $z^2-4z+3.$ This example can be generalized to encompass all polynomial expressions, providing students with a general purpose tool that can be used to transform a general polynomial into one with leading coefficient~1. It amounts to a change of variable in order to hide complexity, a practice that is useful all over mathematics.
Hidden meaning in geometric figures often involves the creation of auxiliary lines not originally part of a given figure. Two classic examples are the construction of a line through a vertex of a triangle parallel to the opposite side as a way to see that the angle measures of a triangle add to $180^\circ$ and the introduction of a symmetry line in an isosceles triangle to see that the base angles are congruent. Another kind of hidden structure makes use of the invariance of area when it is calculated in more than one way—finding the length of the altitude to the hypotenuse of a right triangle, given the lengths of its legs, for example.
A final example of using structure is in the view that students form of the base ten notational system. The compactness and regularity of this system make it useful for efficient computation and estimation. But in that compactness there is also the danger of superficial, and therefore fragile, grasp of procedures. The Number and Operations in Base Ten domain in CCSSM lays out a progression designed to help students learn to see the decimal expansion of a rational number as, in advanced language, a linear combination of powers of 10 with coefficients taken from integers between 0 and 9 helps. Similarly, viewing a polynomial in $x$ as a linear combination of powers of $x$ can lead to an understanding of polynomial algebra as a system in its own right. Writing $3x^2-7x + 5$ “in base $(x-2)$” as
$$3(x-2)^2+5(x-2) + 3$$
reveals another kind of hidden meaning in the expression.
Another theme that runs throughout a coherent curriculum is a cross-grade emphasis that helps students develop and use the many faces of abstraction. One of the most important uses of abstraction is captured in the CCSSM Standard for Mathematical Practice no.~8 (MP8), “Look for and express regularity in repeated reasoning.” It asks students to abstract a process from several instances of that process in a way that doesn’t refer to the inputs to any particular instance. Describing that process in precise algebraic language allows one to create general algorithms, equations, expressions, and functions. This practice can bring coherence to many seemingly different areas of the curriculum that often cause students difficulty.
The description of MP8 in CCSSM gives the following example:
By paying attention to the calculation of slope as they repeatedly check whether points are on the line through $(1, 2)$ with slope 3, middle school students might abstract the equation $\frac{y – 2}{x – 1} = 3$.
Helping students develop the habit of testing several numerical points to see if they are on the line and then looking for and expressing the “rhythm” in their calculations gives them a way to find the equation of a line between two points without leaning on formulas (“point slope form,” for example), and, more importantly, it gives them a general purpose tool for finding Cartesian equations of geometric objects, given some defining geometric conditions.
As another example, consider the task of building an equation. Teachers know that building is much harder for students than checking. The same practice of abstracting from numerical examples is useful here, too. For example, consider the stylized story problem:
Emilio drives from Tucson to Phoenix at an an average speed of 60MPH and returns at an average speed of 50MPH. If the total time on the road is 4.4 hours, how far is Tucson from Phoenix?
The practice of abstracting regularity from repeated actions can be used to build an equation whose solution is the answer to the problem: One takes several guesses (for the distance) and checks them, focusing on the steps that are common to each of the checks. The goal isn’t to stumble on (or approximate) an answer by “guess and check;” the goal is to come up with a general “guess checker” expressed as an algebraic equation:
$$\frac {\text{guess}}{60} + \frac {\text{guess}}{50}= 4.4$$
These two examples seem quite different, but coherence comes from the fact that exactly the same mathematical practice is used to find an algebraic equation whose solution solves the problem.
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2017-11-20 05:34:48
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https://www.betterment.com/resources/investment-strategy/taxes/lowering-your-tax-bill-by-improving-our-cost-basis-accounting-methods/
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When you make a withdrawal for a certain dollar amount from an investment account, your broker converts that amount into shares, and sells that number of shares. Assuming you are not liquidating your entire portfolio, there’s a choice to be made as to which of the available shares were sold. Every broker has a default method for choosing those shares, and that method can have massive implications for how the sale is taxed. Betterment’s default method is now vastly superior to the industry standard, expected to reduce your tax bill every time you need to sell shares.
In the chart below, you can see the tax impact of an actual $100,000 withdrawal recently made by a Betterment customer. The withdrawal sold some of every ETF in a$1,000,000+ portfolio. Assuming the highest combined tax rates on short and long term gains (which can get up to 50% and 30% in NYC and California), Betterment saved this customer $3,883 in taxes, just by having a better default selling method. ### Betterment saves a customer$3,883
Typical FIFO selling Betterment’s TaxMin selling
Ticker Gain/Loss Short or Long Term Gain/Loss Short or Long Term
VEA $3,334 Long$2,123 Long
AGG $322 Short$108 Short
IVE $3,181 Long -$752 Short
VTI $3,106 Long -$908 Short
BNDX $329 Short$91 Short
LQD $286 Short$83 Short
VWO -$3 Long -$432 Long
VWOB $222 Short$62 Short
IWS $1,162 Long$248 Short
IWN $696 Long -$160 Short
Total
ST Gain/Loss $1,159 -$1,227
LT Gain/Loss $11,476$1,690
Note: Actual customer withdrawal of $100k in Apr 2014 with tax rate of 30% LT, 50% ST. ### Basis reporting 101 What’s going on here? How can internal accounting result in such a drastic difference? First, some background. Over the last several years, the way investment cost basis is reported to the IRS has changed—as a result of legislation that followed the financial crisis in 2008. In the simplest terms, your cost basis is what you paid for a security. It’s a key attribute of a so-called “tax lot”—a new one of which is created every time you buy into a security. For example, if you buy$450 of Vanguard Total Stock Market ETF (VTI), and it’s trading at $100, your purchase is recorded as a tax lot of 4.5 shares, with a cost basis of$450 (along with date of purchase.) The cost basis is then used to determine how much gain you’ve realized when you sell (and the date is used to determine whether that gain is short or long term).
Previously, investors had to track and report cost basis for their sales themselves, but today, brokers have taken on the responsibility. (The rules changed in 2011 for stocks, and in 2013 for bonds and options, as part of a staggered roll-out plan).
That’s generally good news for investors (brokers are better equipped to handle such specialized accounting). However, there is more than one way to report cost basis, and it’s worthwhile for the individual investor to know what method your broker is using—as it will impact your taxes. Brokers report your cost basis on Form 1099-B, which Betterment makes available electronically to customers at the start of tax season.
### Better tax outcomes through advanced accounting
When you buy the same security at different prices over a period of time, and then choose to sell some (but not all) of your position, your tax result will depend on which of the shares in your possession you are deemed to be selling. The default method used by brokers is typically FIFO (“first in, first out”). The oldest shares are always sold first. This method is the easiest for brokers to manage, since it allows them to go through your transactions at the end of the year and only then make determinations on which shares you sold (which they must then report to the IRS.)
FIFO may get somewhat better results than picking lots at random because it avoids triggering short-term gains if you hold a sufficient number of older shares. As long as shares held for more than 12 months are available, those will be sold first. Since short-term tax rates are typically higher than long-term rates, this method can avoid the worst tax outcomes.
However, FIFO’s weakness is that it completely ignores whether selling a particular lot will generate a gain or loss. In fact, it’s likely to inadvertently favor gains over losses: the longer you’ve held a share, the more likely it’s up overall from when you bought it, whereas a recent purchase might be down from a temporary market dip. Clearly, the ability to identify specific lots to sell regardless of when they were purchased could get you a better result, and the rules allow an investor to do so.
Yet having to identify specific shares every time you sell is tedious at best, and incomprehensible at worst. Fortunately, the IRS allows brokers to offer investors a different default method in place of FIFO, which selects specific shares by applying a set of rules to whatever lots are available whenever they sell. The problem is that many investors are not even aware there’s something they should be overriding, much less which alternative to choose. Upgrading the default method can be a multi-step process through a clunky and confusing interface.
While Betterment was initially built to use FIFO as the default method, specific share identification can have such a positive impact on your tax bill that we’ve doubled down to improve our methods. We recently upgraded our algorithms to support a more sophisticated method of basis reporting, which will result in better tax treatment of sales in the vast majority of circumstances. Most importantly, we’ve structured it to replace FIFO as the new default—Betterment customers don’t need to do a thing to benefit from it.
### Betterment’s new TaxMin method
When Betterment customers sell securities, our algorithms select which specific lots to sell on the fly, following a set of rules which we call TaxMin. This method is more granular in its approach, and will improve the tax impact for most transactions, as compared to FIFO.
How does this method work? Instead of looking solely at the purchase date of each lot, TaxMin also considers the cost basis of the lot, realizing all losses before any gains, regardless of when the shares were bought. Lots are sold in the following order:
1. Short-term losses
2. Long-term losses
3. Long-term gains
4. Short-term gains
The algorithm exhausts each category before moving to the next, but within each category, lots with the highest cost basis are sold first. With a gain, the higher the basis, the smaller the gain, which results in a lower tax burden. In the case of a loss, the opposite is true: the higher the basis, the bigger the loss (which is beneficial, since it can offset gains).
### A simple example
If you owned the following lots of the same security, one share each, and wanted to sell one share on July 1, 2014 at the price of $105 per share, you would realize$10 of long term capital gains if you used FIFO. With TaxMin, the same trade would instead realize a $16 short term loss. If you had to sell two shares, FIFO would get you a net$5 long term gain, while TaxMin would result in a $31 short term loss. To be clear, you pay taxes on gains, while losses can help reduce your bill. Purchase Price ($) Purchase Date Gain or Loss ($) FIFO Selling order TaxMin Selling order$95 1/1/13 +10 1 4
$110 6/1/13 -5 2 3$120 1/1/14 -15 3 2
$100 2/1/14 +5 4 5$121 3/1/14 -16 5 1
### What you can expect?
This upgrade automatically works to minimize your account’s end-of-year tax bill with every security sale, whether it’s a withdrawal, allocation change, or rebalance. No single selling method is the best in every situation—which method is best suited to a transaction can depend on the individual’s specific circumstances (including, but not limited to, tax bracket and presence of other gains or losses).
However, we strongly feel that every process should be optimized using the information that is available. After carefully analyzing our customer base, we determined that TaxMin would serve the typical Betterment customer better than the alternatives, and far better than FIFO, the default used by most brokers. Note that your actual tax outcome will depend on your specific tax circumstances—consult a tax advisor.
This is just one more way we continue to innovate under the hood to maximize your investor returns: net of transaction costs, net of behavior, and net of tax.
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2017-09-21 23:09:08
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https://gmatclub.com/forum/a-clothing-store-s-revenue-last-may-was-6-percent-less-than-144207.html
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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # A clothing store's revenue last May was 6 percent less than new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Status: struggling with GMAT Joined: 06 Dec 2012 Posts: 136 Location: Bangladesh Concentration: Accounting GMAT Date: 04-06-2013 GPA: 3.65 A clothing store's revenue last May was 6 percent less than [#permalink] ### Show Tags Updated on: 16 Dec 2012, 08:28 7 44 00:00 Difficulty: 95% (hard) Question Stats: 46% (02:42) correct 54% (02:47) wrong based on 706 sessions ### HideShow timer Statistics A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April? (1) The stores revenue last May was$2,400 less than its revenue last April.
(2) The stores expenses last May were 4 percent less than its expenses last April.
Originally posted by mun23 on 15 Dec 2012, 13:46.
Last edited by Bunuel on 16 Dec 2012, 08:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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18 May 2014, 19:35
16
1
mun23 wrote:
A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?
(1) The stores revenue last May was $2,400 less than its revenue last April. (2) The stores expenses last May were 4 percent less than its expenses last April. Lemme try and help you on this one. The easiest way out is to put the alphabetical statements in the form of equations in as minimum variables as possible. Let us assume the revenue for April = R Revenue for May therefore is = 0.94 R Let the expense for April = EA Let the expense for May = EM We are not given any relationship between EA and EM But we also know that R > EA Now what we are asked is: R- EA > 0.94 R - EM or 0.06 R > EA - EM 1) The stores revenue last May was$2,400 less than its revenue last April. This statement does not tell us any relationship between EA and EM which is required to solve the inequality. Hence, it is not sufficient.
2) The stores expenses last May were 4 percent less than its expenses last April.
It says EM = 0.96 EA
Therefore, we get EA - EM = 0.04 EA
Hence, out inequality can be reduced to
0.06 R > 0.04 EA
or
R> 2/3 EA
Since we already know R> EA, it has to be greater than 2/3 EA. Hence, this statement is sufficient to answer the question.
Hope it helps!!!
Kudos if you find it useful!!!!!
##### General Discussion
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Re: A clothing stores revenue last May was 6 [#permalink]
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16 Dec 2012, 06:34
1
4
mun23 wrote:
A clothing stores revenue last May was 6 percent less than its revenue last april.The stores revenue last may was greater than its expenses last may, and the stores revenue last april was greater than its expenses last april.Was the stores gross profit last may less than its gross profit last april?
(A)The stores revenue last may was $2400 less than its revenue last april (B)The stores expense last May were 4%less than its expense last april Need details explanation.......... If you find this post helpful plz give +1 kudos Gross Profit = Revenue - Expense Revenue > Expense as given for both months. Revenue Expense April R E May .94R .96E Is R - E > .94R - .96E Yes. OA B. _________________ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Please +1 KUDO if my post helps. Thank you. Intern Status: GMAT Streetfighter!! Joined: 22 Nov 2012 Posts: 36 Location: United States Concentration: Healthcare, Finance GPA: 3.87 Re: A clothing store's revenue last May was 6 percent less than [#permalink] ### Show Tags 10 Jan 2013, 02:20 mun23 wrote: A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April? (1) The stores revenue last May was$2,400 less than its revenue last April.
(2) The stores expenses last May were 4 percent less than its expenses last April.
Bunuel can you chime in. I am struggling to understand the OE.
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Re: A clothing stores revenue last May was 6 [#permalink]
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10 Jan 2013, 08:46
1
BangOn wrote:
mun23 wrote:
A clothing stores revenue last May was 6 percent less than its revenue last april.The stores revenue last may was greater than its expenses last may, and the stores revenue last april was greater than its expenses last april.Was the stores gross profit last may less than its gross profit last april?
(A)The stores revenue last may was $2400 less than its revenue last april (B)The stores expense last May were 4%less than its expense last april I think this one is pretty difficult. My math isn't that good, so I had to use a plug-n-chug method. Given the below equations: Gross Profit = Revenue - Expense Revenue > Expense as given for both months. Revenue Expense April R E May .94R .96E Is R - E > .94R - .96E ? Assume some extreme cases: Case 1: R=1000 | E=999.99 R-E = 0.01 | .94R-.96E = -19.99 | April > May Case 2: R=1000 | E=0 R-E = 1000 | .94R-.96E = 940 | April > May So no matter what, April always greater than may. Intern Status: GMAT Streetfighter!! Joined: 22 Nov 2012 Posts: 36 Location: United States Concentration: Healthcare, Finance GPA: 3.87 Re: A clothing stores revenue last May was 6 [#permalink] ### Show Tags 11 Jan 2013, 16:55 asimov wrote: BangOn wrote: mun23 wrote: A clothing stores revenue last May was 6 percent less than its revenue last april.The stores revenue last may was greater than its expenses last may, and the stores revenue last april was greater than its expenses last april.Was the stores gross profit last may less than its gross profit last april? (A)The stores revenue last may was$2400 less than its revenue last april
(B)The stores expense last May were 4%less than its expense last april
I think this one is pretty difficult. My math isn't that good, so I had to use a plug-n-chug method.
Given the below equations:
Gross Profit = Revenue - Expense
Revenue > Expense as given for both months.
Revenue Expense
April R E
May .94R .96E
Is R - E > .94R - .96E ?
Assume some extreme cases:
Case 1: R=1000 | E=999.99
R-E = 0.01 | .94R-.96E = -19.99 | April > May
Case 2: R=1000 | E=0
R-E = 1000 | .94R-.96E = 940 | April > May
So no matter what, April always greater than may.
I did the same, but selecting values for this question made me feel vulnerable to a yes/no outcome, so I was looking for an algebraic explanation. Also, the question indicates that revenue is greater than expense for both months, so I don't think you can end up a with a negative value for May.
These numbers work a bit better for your first example.
May: Revenue = 1000 Exp = 200
April: Revenue= 940 Exp= 192
Now that I think about it, I may have just answered my own question!
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Re: A clothing stores revenue last May was 6 [#permalink]
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14 Jan 2013, 19:36
5
jgomey wrote:
I did the same, but selecting values for this question made me feel vulnerable to a yes/no outcome, so I was looking for an algebraic explanation. Also, the question indicates that revenue is greater than expense for both months, so I don't think you can end up a with a negative value for May.
These numbers work a bit better for your first example.
May: Revenue = 1000 Exp = 200
April: Revenue= 940 Exp= 192
Now that I think about it, I may have just answered my own question!
Thought about it a bit more.
Simplifying algebraically:
.94R-.96E = .94R-.94E-.02E = .94(R-E)-.02E
Since we are subtracting, we assume E is positive (-E is negative). R-E > .94 (R-E) ALWAYS (given R-E is positive). Thus, R-E > 0.94 (R-E) – 0.02E
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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12 May 2013, 07:59
2
1
Stmt 1 - Insuff clearly
Stmt 2 -
April May
Revenue------------ R 0.94R
Expense------------ E 0.96E
Given - R>E
Question - is Profit in May < Profit in April ( i.e 0.94R-0.96E < R-E ?)
Simplifying the above , we get is 4E>6R ? Ans is NO since R>E . Sufficient
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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Updated on: 20 May 2014, 04:34
1
Actually found my way of doing it. Follow me ok?
APR MAY
Rev X 0.94X
Exp Z Y
Profits X-Z> 0.94X+Y?
Is 0.06x>Z+Y?
We also know that '0.94x>y' and that 'x>z'
Statement 1
0.06X = 2400
We can find the value of 'x' here but we still don't know if its greater
For instance if y=0.93x and z=0.93x then answer is NO
If y=0.01x and z=0.01x answer is YES
This is even without knowing the value of X since 'X' must be a positive number
Staetment 2
y=0.96z therefore we have that
0.06x>0.04z?
6x>4z ---> 3x>2z?
Well, since both numbers must be positive and since x>z then answer to this is YES
Hence sufficient
Hope this clarifies
Kudos if you like
Originally posted by jlgdr on 18 May 2014, 15:00.
Last edited by jlgdr on 20 May 2014, 04:34, edited 1 time in total.
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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15 Sep 2014, 04:49
7
1
mun23 wrote:
A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?
(1) The stores revenue last May was $2,400 less than its revenue last April. (2) The stores expenses last May were 4 percent less than its expenses last April. Solution : Statement (1) is not sufficient. Statement (2) is sufficient, refer following figure. Attachment: Revenue.jpg [ 65.5 KiB | Viewed 11043 times ] _________________ Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction". Manager Joined: 30 Mar 2013 Posts: 109 Re: A clothing store's revenue last May was 6 percent less than [#permalink] ### Show Tags 26 Nov 2014, 22:35 gmacforjyoab wrote: Stmt 1 - Insuff clearly Stmt 2 - April May Revenue------------ R 0.94R Expense------------ E 0.96E Given - R>E Question - is Profit in May < Profit in April ( i.e 0.94R-0.96E < R-E ?) Simplifying the above , we get is 4E>6R ? Ans is NO since R>E . Sufficient Isn't the answer to the question yes, it is less. Manager Joined: 21 Sep 2012 Posts: 216 Location: United States Concentration: Finance, Economics Schools: CBS '17 GPA: 4 WE: General Management (Consumer Products) A clothing store's revenue last May was 6 percent less than [#permalink] ### Show Tags 02 Dec 2014, 09:09 1 Let x be the revenue for April. Therefore revenue for May is 0.94x. Let y be the cost for April. We are asked whether GP for May is less that GP for April? Gross Profit = Revenue - Cost GP for April = (x-y) Change in revenue and change in cost will impact GP. In comparison to April, May has seen reduction in both cost and revenue. In order for GP of May to be less than that of April, reduction in revenue has to be greater than reduction in cost. so we can rephrase the question as is reduction in revenue > reduction in cost ? statement 1 :- The stores revenue last May was$2,400 less than its revenue last April.
No information about cost is given. statement in insufficient.
statement 2 :- The stores expenses last May were 4 percent less than its expenses last April.
Therefore cost for May is 0.96y.
We want to find whether
is reduction in revenue > reduction in cost ?
is 0.6x(reduction in revenue)>0.4y(reduction in cost)
x/y>0.4/0.6
x/y>2/3 ....... ?
In the question it is given that the store's revenue last April was greater than its expenses last April.
so x/y has to be greater that 1.
Therefore x/y is greater that 2/3 and hence GP for May is less than that for April.
Statement is sufficient.
Ans - B
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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17 Jan 2015, 11:55
Ans B
R>E for both months
Profit in April, Pa = Ra-Ea
Profit in May, Pm = Rm-Em
comparing....Revenue decreased by 6% and expenses by 4%
Profit comparision....( bigger no. decreased by more) - (a smaller no. decreased by less) =>overall profit decreased more=> B is sufficient
A
doesnt even connect hw expenses vary...so not sufficient
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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27 Jun 2015, 04:44
here is another way to look at statement 2. Already explained but will simplify through algebra...
Let ---------------- --Apr---------------May
Revenue---------- ----X--------------- 0.94X ( given in stem that revenue is 6% less in May)
Expense ---------- ----Y ---------- ----0.96Y ( Given in statement 2 that expense in May is 4% less)
We have to prove is : 0.94X - 0.96 Y > X- Y
(Profit of May is greater than Apr)
We are told that in both months Profit is +ve or greater than zero. Means that X>Y --> X/Y > 1.
now reducing the above equation 0.94X - 0.96 Y > X- Y
we get X/Y < 2/3
Now for (0.94X - 0.96 Y > X- Y) equation to be true, X/Y < 2/3 has to be true.
But we are told X/Y>1 therefore the above equation doesn't hold true.
Hence B.
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A clothing store's revenue last May was 6 percent less than [#permalink]
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05 Aug 2015, 10:33
7
Given:
a) $$R_m=0.94*R_a$$
b) $$R_m>E_m$$
c) $$R_a>E_a$$
Legend: m = March, a = April
Question:
Is $$P_m<P_a$$?
OR is $$R_m-E_m<R_a-E_a$$? (Since, Profits = Revenues - Expenses)
OR is $$E_a-E_m<0.06*R_a$$? (Re-arranging and using info from a) above)....Lets call this as (d)
Statement 1) $$R_m = R_a- 2400$$
Substituting this value in a), we get:
$$R_a - 2400 = 0.94 * R_a$$
$$0.06*R_a = 2400$$
$$R_a = 40,000$$
Substituting this in Question inequality of (d), the question becomes:
Is $$E_a-E_m < 0.06*40000$$?
Or is $$E_a-E_m<2400$$
But we don't know the value of$$E_a$$ OR $$E_m$$ to say this for sure. INSUFFICIENT.
Statement 2) $$E_m=0.96*E_a$$
Then Question inequality of (d) becomes:
Is $$0.04*E_a < 0.06 * R_a$$?
OR is $$E_a < 1.5*R_a$$?
Now from (c) we know that $$E_a < R_a$$
So $$E_a < 1.5*R_a$$ definitely. SUFFICIENT.
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A clothing store's revenue last May was 6 percent less than [#permalink]
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21 Sep 2016, 06:49
1
My little contribution based on the previous explanations above.
Attachments
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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02 May 2017, 17:14
a=April
m=May
R=Revenue
E=Expenses
Profit April: Ra-Ea
Profit May: 0.94Ra-Em
1) No info on expenses. Insuff.
2)
Profit April: Ra-Ea
Profit May: 0.94Ra-0.96Ea
For May, the revenue has decreased by a greater percentage than the expenses. Therefore, the profit in April is greater. Suff. B
Agree? Kudos. Better method? Please comment.
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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02 May 2017, 17:17
gmacforjyoab wrote:
Stmt 1 - Insuff clearly
Stmt 2 -
April May
Revenue------------ R 0.94R
Expense------------ E 0.96E
Given - R>E
Question - is Profit in May < Profit in April ( i.e 0.94R-0.96E < R-E ?)
Simplifying the above , we get is 4E>6R ? Ans is NO since R>E . Sufficient
Answer is yes, isn't it?! Profit for May is less than April...
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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18 Jun 2017, 11:32
we can solve this with logic
6% from something bigger is > 4% from something smaller
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Re: A clothing store's revenue last May was 6 percent less than [#permalink]
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01 Jul 2017, 00:08
Tricky question.
A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?
(1) The stores revenue last May was $2,400 less than its revenue last April. (2) The stores expenses last May were 4 percent less than its expenses last April. Let the Revenue in May and April be Rm and Ra respectively. Also, let the expenses in May and April be Em and Ea resp. Given that Ra-Rm=0.06 and Rm> Em and Ra> Ea. Profit = Revenue - Expenses To evaluate: Rm-Em < Ra-Ea? Ea-Em < Ra- Rm or Ea-Em < 0.06 Statement 1: The stores revenue last May was$2,400 less than its revenue last April.
From this statement, we can deduce about the revenue values but no information is presented about the expenses. As such, we won't be able to determine the condition.
Statement 2: The stores expenses last May were 4 percent less than its expenses last April.
Em=0.96* Ea.
Ea-Em= Ea-0.96*Ea = 0.04 * Ea
Since Ea < Ra (given) , 0.04 Ea < 0.04 Ra < 0.06 Ra
Hence B alone is sufficient.
Re: A clothing store's revenue last May was 6 percent less than &nbs [#permalink] 01 Jul 2017, 00:08
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2018-11-15 02:59:55
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https://blog.dlib.net/2017/12/dlib-198-is-out.html?showComment=1524145338903
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## Wednesday, December 20, 2017
### Dlib 19.8 is Out
Dlib 19.8 is officially out. There are a lot of changes, but the two most interesting ones are probably the new global optimizer and semantic segmentation examples. The global optimizer is definitely my favorite as it allows you to easily find the optimal hyperparameters for machine learning algorithms. It also has a very convenient syntax. For example, consider the Holder table test function:
From https://en.wikipedia.org/wiki/File:Holder_table_function.pdf
Here is how you could use dlib's new optimizer from Python to optimize the difficult Holder table function:
def holder_table(x0,x1):
return -abs(sin(x0)*cos(x1)*exp(abs(1-sqrt(x0*x0+x1*x1)/pi)))
x,y = dlib.find_min_global(holder_table,
[-10,-10], # Lower bound constraints on x0 and x1 respectively
[10,10], # Upper bound constraints on x0 and x1 respectively
80) # The number of times find_min_global() will call holder_table()
Or in C++:
auto holder_table = [](double x0, double x1) {return -abs(sin(x0)*cos(x1)*exp(abs(1-sqrt(x0*x0+x1*x1)/pi)));};
// obtain result.x and result.y
auto result = find_min_global(holder_table,
{-10,-10}, // lower bounds
{10,10}, // upper bounds
max_function_calls(80));
Both of these methods find holder_table's global optima to about 12 digits of precision in about 0.1 seconds. The documentation has much more to say about this new tooling. I'll also make a blog post soon that goes into much more detail on how the method works.
Finally, here are some fun example outputs from the new semantic segmentation example program:
Unknown said...
Awesomme!! Looking forward to more explanations on global optimizer.
Unknown said...
Awesomme!! Looking forward to more explanations on global optimizer.
Andyrey said...
This comment has been removed by the author.
Andyrey said...
Thanks a lot, Davis, great library!
Is it possible to build dlib-GPU-based solution, so that result program could work both on user computers with GPU and on computers without CUDA-supporting GPU, in CPU mode only?
Unknown said...
Andrey Zakharoff >> Yes, you can do it. You need check_cuda start file, which load cuda library dynamically and check compatibility with cuda. After it you run one of two files - first compiled with cuda, second compiled for cpu only. For cpu you can use lapack, which dramatically improved your cpu version. Also cpu and gpu version inside are the same. You need only set flags for compiler.
I do it for windows and mac (4 result files) and it works perfectly.
Unknown said...
What is the speed of the semantic segmentation?
Unknown said...
Hi Davis;
As I understand from the semantic segmentation training code in file http://dlib.net/dnn_semantic_segmentation_train_ex.cpp.html, I can train a new model on another dataset as long as I give the corresponding vector to the trainer. Is that right and if so, do I need to do any change in network types in file http://dlib.net/dnn_semantic_segmentation_ex.h.html ?
Davis King said...
Yes, that's right. Giving it different training data is fine.
Unknown said...
Hi again Davis,
I need probability as well as class label for each pixel. I thought changing the to_label function of loss_multiclass_log_per_pixel_ class such that I will also get the value not only the label. Is this a correct way or do you have any other suggestions?
thanks.
Davis King said...
Yes, the log loss optimizes the log likelihood and is what you should use. Then you will get something that outputs log likelihoods. Convert them to probabilities by passing them through a sigmoid.
Unknown said...
In the segmentation example code, after these codes:
anet_type net;
deserialize("semantic_segmentation_voc2012net.dnn") >> net;
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2021-08-05 11:24:56
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https://byjus.com/ncert-solutions-for-class-12-maths-chapter-4-determinants-ex-4-2/
|
Ncert Solutions For Class 12 Maths Ex 4.2
Ncert Solutions For Class 12 Maths Chapter 4 Ex 4.2
Q.1: Using the property of determinants and without expanding, prove that:
$$\begin{vmatrix} x & a & x + a \\ y & b & y + b \\ z & c & z + c \end{vmatrix} = 0$$
Sol:
$$\begin{vmatrix} x & a & x + a \\ y & b & y + b \\ z & c & z + c \end{vmatrix} = \begin{vmatrix} x & a & x \\ y & b & y \\ z & c & z \end{vmatrix} + \begin{vmatrix} x & a & a \\ y & b & b \\ z & c & c \end{vmatrix} = 0 + 0 = 0\\$$
(Here, the two columns of the determinants are identical)
Q2: Using the property of determinants and without expanding, prove that:
$$\begin{vmatrix} a – b & b – c & c – a \\ b – c & c – a & a – b \\ c – a & a – b & b – c \end{vmatrix} = 0$$
Sol:
$$\begin{vmatrix} a – b & b – c & c – a \\ b – c & c – a & a – b \\ c – a & a – b & b – c \end{vmatrix} = 0\\$$
Applying $$R_{1} \rightarrow R_{1} + R_{2}$$, we have:
$$\boldsymbol{\Rightarrow }$$ $$\Delta = \begin{vmatrix} a – b & b – a & c – b \\ b – c & c – a & a – b \\ -(a – c) & -(b – a) & -(c – b) \end{vmatrix} = 0\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$– \begin{vmatrix} a – c & b – a & c – b \\ b – c & c – a & a – b \\ a – c & b – a & c – b \end{vmatrix} = 0$$
Here, the two rows R1 and R3 are identical.
Therefore, $$\bigtriangleup = 0$$
Q3: Using the property of determinants and without expanding, prove that:
$$\begin{vmatrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{vmatrix} = 0$$
Sol:
$$\boldsymbol{\Rightarrow }$$ $$\begin{vmatrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{vmatrix} =$$ $$\begin{vmatrix} 2 & 7 & 63 + 2 \\ 3 & 8 & 72 + 3 \\ 5 & 9 & 81 + 5 \end{vmatrix}\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$\begin{vmatrix} 2 & 7 & 63 \\ 3 & 8 & 72 \\ 5 & 9 & 81 \end{vmatrix} + \begin{vmatrix} 2 & 7 & 2 \\ 3 & 8 & 3 \\ 5 & 9 & 5 \end{vmatrix}\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$\begin{vmatrix} 2 & 7 & 9(7) \\ 3 & 8 & 9(8) \\ 5 & 9 & 9(9) \end{vmatrix} + 0$$ (Two columns are identical)
$$\\9 \begin{vmatrix} 2 & 7 & 7 \\ 3 & 8 & 8 \\ 5 & 9 & 9 \end{vmatrix} + 0$$ (Two columns are identical)
= 0
Q4: Using the property of determinants and without expanding, prove that:
$$\begin{vmatrix} 1 & bc & a(b + c) \\ 1 & ca & b(c + a) \\ 1 & ab & c(a + b) \end{vmatrix} = 0$$
Sol:
$$\Delta = \begin{vmatrix} 1 & bc & a(b + c) \\ 1 & ca & b(c + a) \\ 1 & ab & c(a + b) \end{vmatrix} = 0\\$$
By applying $$C_{3} \rightarrow C_{3} + C_{2}$$
$$\\\boldsymbol{\Rightarrow }$$ $$\Delta = \begin{vmatrix} 1 & bc & ab + bc + ca \\ 1 & ca & ab + bc + ca \\ 1 & ab & ab + bc + ca \end{vmatrix} = 0\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$(ab + bc + ca ) \begin{vmatrix} 1 & bc & 1 \\ 1 & ca & 1 \\ 1 & ab & 1 \end{vmatrix} = 0$$
Here, two columns C1 and C3 are proportional.
$$\boldsymbol{\Rightarrow }$$ $$\Delta = 0$$
Q5: Using the property of determinants and without expanding, prove that:
$$\begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ a + b & p + q & x + y \end{vmatrix} = 2 \begin{vmatrix} a & p & x\\ b & q & y\\ c & r & z \end{vmatrix}$$
Sol:
$$\Delta = \begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ a + b & p + q & x + y \end{vmatrix}\\$$ $$= \begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ a & p & x \end{vmatrix} + \begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ b & q & y \end{vmatrix}\\$$
= $$\Delta _{1} + \Delta _{2}$$ ……………………….(i)
Now, $$\Delta _{1} = \begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ a & p & x \end{vmatrix}$$
Applying $$R_{2}\rightarrow R_{2} – R_{3}$$, we have:
$$\Delta _{1} = \begin{vmatrix} b + c & q + r & y + z \\ c & r & z \\ a & p & x \end{vmatrix}\\$$
Applying $$R_{1}\rightarrow R_{1} – R_{2}$$, we have:
$$\Delta _{1} = \begin{vmatrix} b & q & y \\ c & r & z \\ a & p & x \end{vmatrix}\\$$
Applying $$R_{1} \leftrightarrow R_{3} \;\; and R_{2} \leftrightarrow R_{3}$$ we have:
$$\Delta _{1} = (-1)^{2} \begin{vmatrix} a & p & x \\ b & q & y \\ c & r & z \end{vmatrix} = \begin{vmatrix} a & p & x \\ b & q & y \\ c & r & z \end{vmatrix}$$ …………………..(ii)
$$\Delta _{2} = \begin{vmatrix} b + c & q + r & y + z \\ c + a & r + p & z + x \\ b & q & y \end{vmatrix}\\$$
Applying $$R_{1} \rightarrow R_{1} – R_{3}$$, we have:
$$\Delta _{2} = \begin{vmatrix} c & r & z \\ c + a & r + p & z + x \\ b & q & y \end{vmatrix}\\$$
Applying $$R_{2} \rightarrow R_{2} – R_{1}$$, we have:
$$\Delta _{2} = \begin{vmatrix} c & r & z \\ a & p & x \\ b & q & y \end{vmatrix}\\$$
Applying $$R_{1} \leftrightarrow R_{2} \;\; and R_{2} \leftrightarrow R_{3}$$ we have:
$$\Delta _{2} = (-1)^{2} \begin{vmatrix} a & p & x \\ b & q & y \\ c & r & z \end{vmatrix} = \begin{vmatrix} a & p & x \\ b & q & y \\ c & r & z \end{vmatrix}$$ ………………………(iii)
From (i), (ii) and (iii), we have:
$$\Delta _{2} = 2 \begin{vmatrix} a & p & x \\ b & q & y \\ c & r & z \end{vmatrix}$$
Q6: By using properties of determinants, show that:
$$\begin{vmatrix} 0 & a & -b \\ -a & 0 & -c \\ b & c & 0 \end{vmatrix} = 0$$
Sol:
$$\Delta = \begin{vmatrix} 0 & a & -b \\ -a & 0 & -c \\ b & c & 0 \end{vmatrix}\\$$
Applying $$R_{1} = c R_{1}$$, we have:
$$\Delta = \frac{1}{c} \begin{vmatrix} 0 & ac & -bc \\ -a & 0 & -c \\ b & c & 0 \end{vmatrix}\\$$
Applying $$R_{1} \rightarrow R_{1} – b R_{2}$$, we have:
$$\Delta = \frac{1}{c} \begin{vmatrix} ab & ac & 0 \\ -a & 0 & -c \\ b & c & 0 \end{vmatrix}$$ $$\Delta = \frac{a}{c} \begin{vmatrix} b & c & 0 \\ -a & 0 & -c \\ b & c & 0 \end{vmatrix}$$
Here, the two rows $$R_{1} \;\; and \;\; R_{3}$$ are identical.
$$\boldsymbol{\Rightarrow }$$ $$\Delta = 0$$
Q7: By using the properties of determinants, show that:
$$\begin{vmatrix} -a^{2} & ab & ac \\ ba & -b^{2} & bc \\ ca & cb & -c^{2} \end{vmatrix} = 4a^{2}b^{2}c^{2}$$
Sol:
$$\begin{vmatrix} -a^{2} & ab & ac \\ ba & -b^{2} & bc \\ ca & cb & -c^{2} \end{vmatrix}\\$$
$$\\\begin{vmatrix} -a^{2} & ab & ac \\ ba & -b^{2} & bc \\ ca & cb & -c^{2} \end{vmatrix}$$ (Taking out factors a, b, c from R1 , R2 and R3)
$$\Delta = a^{2}b^{2}c^{2} \begin{vmatrix} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{vmatrix}$$ (Taking out factors a,b,c from C1, C2 and C3)
Applying $$R_{2} \rightarrow R_{2} + R_{1} \;\; and \;\; R_{3} \rightarrow R_{3} + R_{1}$$ we have:
$$\Delta = a^{2}b^{2}c^{2} \begin{vmatrix} -1 & 1 & 1 \\ 0 & 0 & 2 \\ 0 & 2 & 0 \end{vmatrix}\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$\Delta = a^{2}b^{2}c^{2} (-1) \begin{vmatrix} 0 & 2 \\ 2 & 0 \end{vmatrix}\\$$
$$\\\boldsymbol{\Rightarrow }$$ $$-a^{2} b^{2} c^{2} (0 – 4) = 4a^{2} b^{2} c^{2}$$
Q8: By using the properties of determinants, show that:
(i) $$\begin{vmatrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{vmatrix} = (a – b) (b – c) (c – a)$$
(ii) $$\begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{vmatrix} = (a – b) (b – c) (c – a)(a + b + c)$$
Sol:
Let $$\Delta = \begin{vmatrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{vmatrix}$$
Applying $$R_{1} \rightarrow R_{1} – R_{3}$$ and $$R_{2} \rightarrow R_{2} – R_{3}$$, we have:
$$\Delta = \begin{vmatrix} 0 & a – c & a^{2} – c^{2} \\ 0 & b – c & b^{2} – c^{2} \\ 1 & c & c^{2} \end{vmatrix}$$ $$= (c-a) (b – c)\begin{vmatrix} 0 & a – c & a^{2} – c^{2} \\ 0 & b – c & b^{2} – c^{2} \\ 1 & c & c^{2} \end{vmatrix}\\$$
Applying $$R_{1}\rightarrow R_{1}+R_{2}$$ we have:
= $$(b – c) (c-a) \begin{vmatrix} 0 & 0 & a – b \\ 0 & 1 – c & b + c \\ 1 & c & c^{2} \end{vmatrix}\\$$
= $$\\(a – b) (b – c) (c-a) \begin{vmatrix} 0 & 0 & 1\\ 0 & 1 – c & b + c \\ 1 & c & c^{2} \end{vmatrix}$$
Expanding along $$C_{1}$$ we have:
$$\\\Delta = (a – b) (b – c) (c-a) \begin{vmatrix} 0 & -1 0 & b + c \end{vmatrix} = (a – b) (b – c) (c – a)$$
Hence, the given result is proved.
(ii) Let $$\Delta = \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{vmatrix}$$
Applying $$C_{1}\rightarrow C_{1}-C_{3} \;\; and C_{2}\rightarrow C_{2}- C_{3}$$ we have:
= $$\begin{vmatrix} 0 & 0 & 1 \\ a-c & b-c & c \\ a^{3}- c^{3} & b^{3}-c^{3} & c^{3} \end{vmatrix}\\$$
= $$\\\begin{vmatrix} 0 & 0 & 1 \\ a-c & b-c & c \\ (a-c)(a^{2}+ac+c^{2}) & (b-c)(b^{2}+bc+c^{2}) & c^{3} \end{vmatrix}$$
= $$\\(c-a)(b-c)\begin{vmatrix} 0 & 0 & 1 \\ -1 & 1 & c \\ -(a^{2}+ac+c^{2}) & (b^{2}+bc+c^{2}) & c^{3} \end{vmatrix}\\$$
Applying $$C_{1}\rightarrow C_{1}+C_{2}$$ we have:
= $$\\(c-a)(b-c)\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & c \\ (b^{2}-a^{2})+ (bc-ac) & (b^{2}+bc+c^{2}) & c^{3} \end{vmatrix}\\$$
= $$\\(a-b)(b-c)(c-a)\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & c \\ -(a+b+c) & (b^{2}+bc+c^{2}) & c^{3} \end{vmatrix}\\$$
= $$\\(a-b)(b-c)(c-a)(a+b+c)\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & c \\ -1 & (b^{2}+bc+c^{2}) & c^{3} \end{vmatrix}\\$$
Expanding along $$C_{1}$$ we have:
$$\Delta = (a-b)(b-c)(c-a)(a+b+c)(-1)\begin{vmatrix} 0 & 1 \\ 1 & c \end{vmatrix}\\$$
= $$\\(a-b)(b-c)(c-a)(c-a)(a+b+c)$$
Hence, the given result is proved.
Q9: By using the properties of determinants, show that:
$$\begin{vmatrix} x & x^{2} & yz \\ y & y^{2} & zx \\ z & z^{2} xy & \end{vmatrix} = (x – y)(y-z)(z-x)(xy+yz+zx)$$
Sol:
Let $$\Delta = \begin{vmatrix} x & x^{2} & yz \\ y & y^{2} & zx \\ z & z^{2} xy & \end{vmatrix}$$
Applying $$R_{2}\rightarrow R_{2}-R_{1} \;\; and R_{3}\rightarrow R_{3}-R_{1}$$ we have:
$$\\\boldsymbol{\Rightarrow }$$ $$\Delta = \begin{vmatrix} x & x^{2} & yz \\ y-x & y^{2}-x^{2} & zx-yz \\ z-x & z^{2}-x^{2} xy-yz & -y(z-x) \end{vmatrix}\\$$
= $$\\\begin{vmatrix} x & x^{2} & yz \\ -(x-y) & -(x-y)(x+y) & z(x-y) \\ z-x & (z-x)(z+x) & -y(z-x) \end{vmatrix}\\$$
= $$\\(x-y)(z-x)\begin{vmatrix} x & x^{2} & yz \\ -1 & -x-y & z \\ 1 & (z+x) & -y \end{vmatrix}\\$$
Applying $$R_{3}\rightarrow R_{3}+R_{2}$$ we have:
$$\boldsymbol{\Rightarrow }$$ $$\Delta = (x-y)(z-x)\begin{vmatrix} x & x^{2} & yz \\ -1 & -x-y & z \\ 0 & z-y & z-y \end{vmatrix}\\$$
= $$\\(x-y)(z-x)(z-y)\begin{vmatrix} x & x^{2} & yz \\ -1 & -x-y & z \\ 0 & 1 & 1 \end{vmatrix}\\$$
Expanding along $$R_{3}$$ we have:
$$\boldsymbol{\Rightarrow }$$ $$\Delta = \left [ (x-y)(z-x)(z-y) \right ] \left [ (-1) \begin{vmatrix} x & yz \\ -1 & z \end{vmatrix} + 1 \begin{vmatrix} x & x^{2} \\ -1 & -x-y \end{vmatrix} \right ]\\$$
= (x-y)(z-x)(z-y)[(-xz-zy)$$+(x^{2}-xy+x^{2})$$]
= -(x-y)(y-z)(z-x)(xy+yz+zx)
Hence, the given result is proved.
Q10: By using properties of determinants, show that:
(i) $$\begin{vmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix} = (5x+4)(4-x)^{2}\\$$
(ii) $$\\\begin{vmatrix} y+k & y & y \\ y & y+k & y \\ y & y & y+k \end{vmatrix} = k^{2}(3y+k)$$
Sol:
(i) $$\begin{vmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix} \\$$
Applying $$R_{1}\rightarrow R_{1}+R_{2}+R_{3}$$ we have:
$$\Delta = \begin{vmatrix} 5x+4 & 5x+4 & 5x+4 \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix}$$ $$= (5x+4) \begin{vmatrix} 1 & 1 & 1 \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix}\\$$
Applying $$C_{2}\rightarrow C_{2}-C_{1}, C_{3}\rightarrow C_{3}-C_{1}$$ we have:
$$\Delta = (5x+4) \begin{vmatrix} 1 & 0 & 0 \\ 2x & -x+4 & 0 \\ 2x & 0 & -x+4 \end{vmatrix}\\$$
= $$\\(5x+4)(4-x)(4-x) \begin{vmatrix} 1 & 0 & 0 \\ 2x & 1 & 0 \\ 2x & 0 & 1 \end{vmatrix}$$
Expanding along $$C_{3}$$ we have:
$$\Delta = (5x+4)(4-x)^{2} \begin{vmatrix} 1 & 0 \\ 2x & 1\end{vmatrix}$$ $$= (5x+4)(4-x)^{2}\\$$
Hence, the given result is proved.
(ii) $$\begin{vmatrix} y+k & y & y \\ y & y+k & y \\ y & y & y+k \end{vmatrix}$$
Applying $$R_{1}\rightarrow R_{1}+R_{2}+R_{3}$$ we have:
$$\\\Delta = \begin{vmatrix} 3y+k & 3y+k & 3y+k \\ y & y+k & y \\ y & y & y+k \end{vmatrix}$$ $$= (3y+k) \begin{vmatrix} 1 & 1 & 1 \\ y & y+k & y \\ y & y & y+k \end{vmatrix}\\$$
Applying $$C_{2}\rightarrow C_{2}-C_{1}, C_{3}\rightarrow C_{3}-C_{1}$$ we have:
$$\Delta = (3y+k) \begin{vmatrix} 1 & 0 & 0 \\ y & k & 0 \\ y & 0 & k \end{vmatrix}$$ $$= k^{2} (3y+k) \begin{vmatrix} 1 & 0 & 0 \\ y & 1 & 0 \\ y & 0 & 1 \end{vmatrix}\\$$
Expanding along $$C_{3}$$ we have:
$$\Delta = k^{2} (3y+k) \begin{vmatrix} 1 & 0 \\ y & 1 \end{vmatrix} = k^{2} (3y+k)$$
Hence, the given result is proved.
Q.11: By using properties of determinants, show that:
(i) $$\begin {vmatrix} a – b – c & 2a & 2a \\ 2b & b – c – a & 2b \\ 2c & 2c & c – a – b \end {vmatrix} = \left ( a + b + c \right )^{3}\\$$
(ii) $$\\\begin {vmatrix} x + y + 2z & x & y \\ z & x + z + 2x & y \\ z & x & z + x + 2y \end {vmatrix} = 2 \left ( x + y + z \right )^{3}$$
Sol:
$$\Delta = \begin {vmatrix} a – b – c & 2a & 2a \\ 2b & b – c – a & 2b \\ 2c & 2c & c – a – b \end {vmatrix}$$
(i)
Applying $$R_{1} \rightarrow R_{1} + R_{2} + R_{3}$$, we have:
$$\Delta = \begin {vmatrix} a + b + c & a + b + c & a + b + c \\ 2b & b – c – a & 2b \\ 2c & 2c & c – a – b \end {vmatrix} \\$$
= $$\left ( a + b + c \right ) \begin {vmatrix} 1 & 1 & 1 \\ 2b & b – c – a & 2b\\ 2c & 2c & c – a – b \end {vmatrix}$$
Applying $$C_{2} \rightarrow C_{2} – C_{1} , C_{3} \rightarrow C_{3} – C_{1}$$, we have:
$$\Delta = \left ( a + b + c \right ) \begin {vmatrix} 1 & 0 & 0 \\ 2b & – \left ( a + b + c \right ) & 0 \\ 2c & 0 & – \left ( a + b + c \right ) \end {vmatrix} \\$$
= $$\\\left ( a + b + c \right ) ^{3} \begin{vmatrix} 1 & 0 & 0 \\ 2b & -1 & 0\\ 2c & 0 & -1 \end {vmatrix}$$
Expanding along C3, we have:
∆ = (a + b + c)3 (-1) (-1) = (a + b + c)3
Hence, the given result is proved.
$$\Delta = \begin {vmatrix} x + y + 2z & x & y \\ z & y + z + 2x & y \\ z & x & z + x + 2y \end {vmatrix}$$
(ii) Applying C1 → C1 + C2 + C3, we have:
$$\\\Delta = \begin{vmatrix} 2 \left ( x + y + z \right ) & x & y \\ 2 \left ( x + y + z \right ) & y + z + 2x & y \\ 2 \left ( x + y + z \right ) & x & z + x + 2y \end {vmatrix}$$
= $$\\ 2 \left ( x + y + z \right ) \begin {vmatrix} 1 & x & y \\ 1 & y + z + 2x & y \\ 1 & x & z + x + 2y \end {vmatrix}$$
Applying R2 → R2 – R1 and R3 → R3 – R1, we have:
$$\Delta = 2 \left ( x + y + z \right ) \begin {vmatrix} 1 & x & y \\ 0 & x + y + z & 0 \\ 0 & 0 & x + y + z \end {vmatrix}\\$$
= $$\\ 2 \left ( x + y + z \right ) ^{3} \begin {vmatrix} 1 & x & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {vmatrix}$$
Expanding along R3, we have:
∆ = 2(x + y + z)3 (1) (1 – 0) = 2(x + y + z)3
Hence, the given results are proved.
Q.12: By using properties of determinants, show that:
$$\begin {vmatrix} 1 & x & x ^ {2} \\ x ^ {2} & 1 & x \\ x & x ^ {2} & 1 \end {vmatrix} = \left ( 1 – x ^{3} \right ) ^ {2}$$
Sol:
$$\Delta = \begin {vmatrix} 1 & x & x ^ {2} \\ x ^ {2} & 1 & x \\ x & x ^ {2} & 1 \end {vmatrix} \\$$
Applying R1 → R1 + R2 + R3, we have:
$$\\\Delta = \begin{vmatrix} 1 + x + x ^ {2} & 1 + x + x ^ {2} & 1 + x + x ^ {2} \\ x ^ {2} & 1 & x \\ x & x ^ {2} & 1 \end {vmatrix} \\$$
= $$\\\left ( 1 + x + x ^ {2} \right ) \begin {vmatrix} 1 & 1 & 1 \\ x ^ {2} & 1 & x \\ x & x ^ {2} & 1 \end {vmatrix}$$
Applying C2 → C2 – C1 and C3 → C3 – C1, we have:
$$\\ \Delta = \left ( 1 + x + x ^ {2} \right ) \begin {vmatrix} 1 & 0 & 0 \\ x ^ {2} & 1 – x ^ {2} & x – x ^ {2} \\ x & x ^ {2} – x & 1 – x \end {vmatrix}$$
= $$\\\left ( 1 + x + x ^ {2} \right ) \left ( 1 – x \right ) \left ( 1 – x \right ) \begin {vmatrix} 1 & 0 & 0 \\ x ^ {2} & 1 + x & x \\ x & -x &aamp; 1 \end {vmatrix}\\$$
= $$\\\left ( 1 – x ^ {3} \right ) \left ( 1 – x \right ) \begin {vmatrix} 1 & 0 & 0 \\ x ^ {2} & 1 + x & x \\ x & -x & 1 \end {vmatrix}\\$$
Expanding along R1, we have:
$$\\\Delta = \left ( 1 – x ^ {3} \right ) \left ( 1 – x \right ) \left ( x \right ) \begin {vmatrix} 1 + x & x \\ -x & 1 \end {vmatrix}\\$$
= (1 – x3) (1 – x) (1 + x + x2)
= (1 – x3) (1 – x3)
= (1 – x3)2
Hence, the given result is proved.
Q.13: By using properties of determinants, show that:
$$\begin {vmatrix} 1 + a ^ {2} – b ^ {2} & 2ab & -2b \\ 2ab & 1 – a ^ {2} + b ^ {2} & 2a \\ 2b & -2a & 1 – a ^ {2} – b ^ {2} \end {vmatrix} = \left ( 1 + a ^ {2} + b ^ {2} \right ) ^ {3}$$
Sol:
$$\Delta = \begin {vmatrix} 1 + a ^{ 2} – b ^ {2} & 2ab & -2b \\ 2ab & 1 – a ^ {2} + b ^ {2} & 2a \\ 2b & -2a & 1 – a ^ {2} – b ^ {2} \end {vmatrix}\\$$
Applying R1 → R1 + bR3 and R2 → R2 – aR3, we have:
$$\\\Delta = \begin {vmatrix} 1 + a ^ {2} + b ^ {2} & 0 & -b \left ( 1 + a ^ {2} + b ^ {2} \right ) \\ 0 & 1 + a ^ {2} + b ^ {2} & a \left ( 1 + a ^ {2} + b ^ {2} \right ) \\ 2b & -2a & 1 – a ^ {2} – b ^ {2} \end {vmatrix}\\$$
= $$\\ \left ( 1 + a ^ {2} + b ^ {2} \right ) \begin {vmatrix} 1 & 0 & -b \\ 0 & 1 & a \\ 2b & -2a & 1 – a ^ {2} – b ^ {2} \end {vmatrix}\\$$
Expanding along R1, we have:
$$\\ \Delta = \left ( 1 + a ^ {2} + b ^ {2} \right ) ^ {2} \begin {bmatrix} (1) \begin {vmatrix} 1 & a \\ -2a & 1 – a^ {2} – b^ {2} \end {vmatrix} \\ -b \begin {vmatrix} 0 & 1 \\ 2b & -2a \end {vmatrix} \end {bmatrix} \\$$
= (1 + a2 + b2)2 [1 – a2 – b2 + 2a2 –b (-2b)]
= (1 + a2 + b2)2 (1 + a2 + b2)
= (1 + a2 + b2)3
Q.14: By using properties of determinants, show that:
$$\begin {vmatrix} a ^ {2} + 1 & ab & ac \\ ab & b ^ {2} + 1 & bc \\ ca & cb & c ^ {2} + 1 \end {vmatrix} = 1 + a ^ {2} + b ^ {2} + c ^ {2}$$
Sol:
$$\Delta = \begin {vmatrix} a ^ {2} + 1 & ab & ac \\ ab & b ^ {2} + 1 & bc \\ ca & cb & c ^ {2} + 1 \end {vmatrix}$$
Taking out common factors a, b, c from R1, R2 and R3 respectively, we have:
$$\Delta = abc \begin {vmatrix} a + \frac {1} {b} & b & c \\ a & b + \frac {1} {b} & c \\ a & b & c + \frac {1} {c} \end {vmatrix}\\$$
Applying R2 → R2 – R1 and R3 → R3 – R1, we have:
$$\\ \Delta = abc \begin {vmatrix} a + \frac {1} {b} & b & c \\ – \frac {1} {a} & \frac {1} {b} & 0 \\ – \frac {1} {a} & 0 & \frac {1} {c} \end {vmatrix}\\$$
Applying C1 → aC1, C2 → bC2, and C3 → cC3, we have:
$$\\\Delta = abc \times \frac {1} {abc} \begin{vmatrix} a ^{2} + 1 & b^ {2} & c ^{2} \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end {vmatrix} \\$$
= $$\\ \begin {vmatrix} a ^ {2} + 1 & b ^ {2} & c ^ {2} \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end {vmatrix}\\$$
Expanding along R3, we have:
$$\\\Delta = -1 \begin {vmatrix} b ^ {2} & c ^ {2} \\ 1 & 0 \end {vmatrix} + 1 \begin {vmatrix} a ^ {2} + 1 & b ^ {2} \\ -1 & 1 \end {vmatrix} \\$$
= -1(-c2) + (a2 + 1 + b2) = 1 + a2 + b2 + c2
Hence, the given result is proved.
Let A be a square matrix of order 3 × 3, KA is equal to
(1). k|A|
(2). k2|A|
(3). k3|A|
(4). 3k|A|
(3)
A is a square matrix of order 3 × 3
Let A = $$\begin {vmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end {vmatrix} \\$$
Then, kA = $$\begin{vmatrix} ka_{1} & kb_{1} & kc_{1} \\ ka_{2} & kb_{2} & kc_{2} \\ ka_{3} & kb_{3} & kc_{3} \end {vmatrix}$$
Therefore, $$\\|kA| = \begin {vmatrix} ka_{1} & kb_{1} & kc_{1} \\ ka_{2} & kb_{2} & kc_{2} \\ ka_{3} & kb_{3} & kc_{3} \end {vmatrix}\\$$
$$\\ k ^ {3} = \begin {vmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end {vmatrix} \; \; \; \; \; \; \; \; \; \; \left ( Taking \; out \; common \; factors \; k \; from \; each \; row \right )$$
= k3|A|
Therefore, |kA| = k3|A|
Hence, the correct answer is C.
Q.16: Which of the following is correct?
(1) Determinant is a square matrix.
(2) Determinant is a number associated to a matrix.
(3) Determinant is a number associated to a square matrix.
Sol:
(3)
We know that to every square matrix, A = [aij] of order n. we can associate a number called the determinant of a square matrix A, where aij = (i, j)th element of A.
Thus, the determinant is a number associated to a square matrix.
Hence, the correct answer is C.
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2018-06-21 19:44:16
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http://openstudy.com/updates/561847dfe4b07ab19da6ed4b
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## anonymous one year ago Multiply. Write the product in simplest form 3/4 (-8/25)(-5/12)
1. anonymous
1,10th
2. anonymous
1 10
3. anonymous
( 3 4 ( −8 25 ))( −5 12 ) = 3 4 ( −8 25 )( −5 12 ) = 3 4 ( −8 25 )( −5 12 ) = −6 25 ( −5 12 ) = 1 10 this is it step by step
4. anonymous
its confusing looking at it like that
5. Directrix
@mathwiz916 Please come to this thread and explain your work. We cannot understand it. Thanks.
6. anonymous
probably becuause he/she simply copied and pasted it from somewhere as opposed to actually do it and the paste came out out of whack
7. anonymous
yes i do agree with them
8. anonymous
ahemm $$\bf \cfrac{3}{4}\left( -\cfrac{8}{25} \right)\left( -\cfrac{5}{12} \right)\implies \cfrac{3}{4}\left( \cfrac{-8}{25} \right)\left( \cfrac{-5}{12} \right) \\ \quad \\ \cfrac{3\cdot (-8)\cdot (-5)}{2\cdot 25\cdot 12}\implies \cfrac{\cancel{3}\cdot (-2\cdot 2\cdot \cancel{2})\cdot (-1\cdot \cancel{5})}{\cancel{2}\cdot (\cancel{5}\cdot 5)\cdot (\cancel{3}\cdot 4)}$$
9. anonymous
missed one there... sec
10. anonymous
$$\bf \cfrac{3}{4}\left( -\cfrac{8}{25} \right)\left( -\cfrac{5}{12} \right)\implies \cfrac{3}{4}\left( \cfrac{-8}{25} \right)\left( \cfrac{-5}{12} \right) \\ \quad \\ \cfrac{3\cdot (-8)\cdot (-5)}{2\cdot 25\cdot 12}\implies \cfrac{\cancel{3}\cdot (- 2\cdot \cancel{2}\cdot \cancel{2})\cdot (-1\cdot \cancel{5})}{\cancel{2}\cdot (\cancel{5}\cdot 5)\cdot (\cancel{3}\cdot \cancel{2}\cdot \cancel{2})}$$
11. anonymous
notice 5* 5 = 25 2*2*2= 8 2*2 = 4
12. anonymous
and... ahemm 3*4 or 3*2*2 = 12
13. anonymous
it should come out as |dw:1444433647692:dw|
14. anonymous
$\frac{ 1 }{ 10}$
15. anonymous
16. anonymous
hmmm
17. anonymous
well.... I missed one again :( at the botom, a 2... lemme do the whole thing
18. anonymous
$$\bf \cfrac{3}{4}\left( -\cfrac{8}{25} \right)\left( -\cfrac{5}{12} \right)\implies \cfrac{3}{4}\left( \cfrac{-8}{25} \right)\left( \cfrac{-5}{12} \right) \\ \quad \\ \cfrac{3\cdot (-8)\cdot (-5)}{2\cdot 25\cdot 12}\implies \cfrac{3\cdot (-2\cdot 2\cdot 2)\cdot ( 5)}{2\cdot (5\cdot 5)\cdot (3\cdot 4)} \\ \quad \\ \cfrac{\cancel{3}\cdot (-1\cdot \cancel{2}\cdot \cancel{2}\cdot \cancel{2})\cdot (-1\cdot \cancel{5})}{\cancel{2}\cdot (\cancel{5}\cdot 5)\cdot (\cancel{3}\cdot \cancel{2}\cdot \cancel{2})}\implies \cfrac{-1\cdot -1}{5} \implies \cfrac{1}{5}$$
19. anonymous
$\left(\frac{\color{orange}3}{\color{blue}{4}}\right)\left(\frac{\color{blue}{-8}}{\color{red}{25}}\right)\left(\frac{\color{red}{-5}}{\color{orange}{12}}\right)$ $\left(\frac{1\cancel{\color{orange}3}}{1\cancel{\color{blue}{4}}}\right)\left(\frac{-2\cancel{\color{blue}{-8}}}{-5\cancel{\color{red}{25}}}\right)\left(\frac{1\cancel{\color{red}{-5}}}{4\cancel{\color{orange}{12}}}\right)$ $=\frac{-2}{-20}$ $=\frac{1}{10}$
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2016-10-25 16:01:20
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https://math.stackexchange.com/questions/3037793/write-in-logic-if-professors-are-unhappy-all-students-fail-their-exams/3038109
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# Write in Logic: If professors are unhappy all students fail their exams
I have to write the following sentence "If professors are unhappy all students fail their exams" in logic and my answer is:
∀x [Prof(x) ∧ Unhappy(x)] ⇒ [∀y stud(y) ⇒ fail_exam(x,y)]
However, the answer of my teacher is:
∀x ∀y( prof(x) ∧ unhappy(x) ∧ stud(y) ) ⇒ fail exam(x, y))
Can someone helps me?
• The two are euivalent : $P \to (Q \to R)$ and $(P \land Q) \to R$ are equivalent. – Mauro ALLEGRANZA Dec 13 '18 at 9:28
They are equivalent ... although to show that, I will first insist on adding a few parentheses so as to indicate the proper scope of the quantifiers, giving us:
$$\forall x ((Prof(x) \land Unhappy(x)) \rightarrow \forall y (Stud(y) \rightarrow FailExam(x,y)))$$
and
$$\forall x \forall y ((Prof(x) \land Unhappy(x) \land Stud(y)) \rightarrow FailExam(x,y))$$
Now, to show these are equivalent, let us first note the following general 'Prenex Law', which is an equivalence that allows you to 'take out' quantifiers and broaden their scope to include ('move over') other parts of the formula:
$$\psi \rightarrow \forall x \ \varphi(x) \Leftrightarrow \forall x (\psi \rightarrow \varphi(x))$$
Here, the formula $$\psi$$ cannot include any free variables $$x$$
Well, we can apply this Prenex law to the second formula, and take out the $$\forall y$$, since the antecedent of the conditional you are moving it over does not contain any free variables $$y$$. Thus, we get:
$$\forall x \forall y ((Prof(x) \land Unhappy(x) \land Stud(x)) \rightarrow FailExam(x,y))$$
Ok, and now we can apply a second general equivalence principle that mAuro alluded to in the comments, called eXportation:
$$P \rightarrow (Q \rightarrow R) \Leftrightarrow (P \land Q) \rightarrow R$$
Applied to the previous formula, we thus obtain the first of your two formulas, thus showing that they are equivalent.
You've been answered that they are equivalent. It's also worth knowing the transformation from $$(P\land Q) \rightarrow R$$ to $$P\rightarrow Q \rightarrow R$$ is known by the name of "currying", and its inverse "uncurrying". It shows up not only in logic, but any domain that forms a Cartesian Closed Category.
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2019-05-25 09:27:33
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http://1449616313.reader.chegg.com/homework-help/definitions/mole-6
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Definition of Mole
Because elements and molecules are so small, chemists use the mole, abbreviated as mol, to quantify materials in a useful unit. The mole is a unit that is equal to 6.022 x 1023 particles, molecules, atoms, etc. Molar mass is the mass of one mole of an element or molecule. For example, one mole of carbon-12 has a mass of exactly 12 grams. Moles are also very important for measuring the concentration of a solution. Molarity is calculated in terms of moles of solute per liter solution. Moles are also used for calculating expected product yield.
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2014-11-01 12:57:55
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http://cms.math.ca/cmb/kw/Bernoulli%20numbers
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Canadian Mathematical Society www.cms.math.ca
location: Publications → journals
Search results
Search: All articles in the CMB digital archive with keyword Bernoulli numbers
Expand all Collapse all Results 1 - 1 of 1
1. CMB 2012 (vol 56 pp. 723)
Bérczes, Attila; Luca, Florian
On the Sum of Digits of Numerators of Bernoulli Numbers Let \$b\gt 1\$ be an integer. We prove that for almost all \$n\$, the sum of the digits in base \$b\$ of the numerator of the Bernoulli number \$B_{2n}\$ exceeds \$c\log n\$, where \$c:=c(b)\gt 0\$ is some constant depending on \$b\$. Keywords:Bernoulli numbers, sums of digitsCategory:11B68
© Canadian Mathematical Society, 2015 : https://cms.math.ca/
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2015-03-01 20:57:41
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http://tex.stackexchange.com/questions/82235/adding-text-to-the-section-numbering
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Adding text to the section numbering
I wish to add some text prior to the number given to a subsection, e.g.:
Task 1.1 Blablabla
...
Task 1.2 Blablabla
How?
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Can you please be a little bit more specific? Do you need this Task text for a special environment, like a theorem or for what? BTW: Welcome to TeX.sx! – Kurt Nov 10 '12 at 22:23
Thanks. No special environment. Task is just an example text. I would like to have a word like that before the number for a subsection, and that's all. – Steeven Nov 10 '12 at 22:33
1 Answer
To add text before the section, you can use:
\renewcommand{\thesection}{Text \arabic{section}}
or for subsection you can use:
\renewcommand{\thesubsection}{Text \arabic{section}}
Code: section
\documentclass{article}
\renewcommand{\thesection}{Text \arabic{section}}
\begin{document}
\section{First section}
Some text.
\section{Second section}
Some more text.
\end{document}
Code: subsection:
\documentclass{article}
\renewcommand{\thesubsection}{Text \arabic{subsection}}
\begin{document}
\section{First section}
\subsection{First sub section}
Some text.
\subsection{Second sub section}
Some more text.
\end{document}
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This is great and works. But some other problem appears when I use the \renewcommand{\thesubsection}{Text \arabic{section}}. The numbering of the subsection suddenly doesn't work. @Peter, if you make two subsections in your example, they both have the number 1. Can that be fixed? – Steeven Nov 10 '12 at 22:42
Clearly LaTeX is not smart enough to know that when I said \arabic{section}, that I obviously meant \arabic{subsection}. :-) Anyway, sorry about that mistake - have updated answer. – Peter Grill Nov 10 '12 at 22:47
Precisely ;) Thanks alot. (By the way, you must update it in two places in your answer...) – Steeven Nov 10 '12 at 23:50
@Steeven: Two places? Only the \renewcommand needed updating. I added two subsections to show that it functioned as desired. – Peter Grill Nov 10 '12 at 23:56
Oh well, I just meant the single line \renewcommand{\thesubsection}{Text \arabic{section}} above your example. – Steeven Nov 11 '12 at 13:37
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2014-09-03 00:36:17
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http://mymathforum.com/elementary-math/346723-solve-integers.html
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My Math Forum Solve for integers
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion
July 8th, 2019, 11:42 PM #1 Senior Member Joined: Dec 2015 From: somewhere Posts: 549 Thanks: 83 Solve for integers Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy$, where $x,y$ are integers. Last edited by skipjack; July 9th, 2019 at 02:22 AM.
July 9th, 2019, 01:36 AM #2
Math Team
Joined: May 2013
From: The Astral plane
Posts: 2,226
Thanks: 908
Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by idontknow Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy \;$ , where x,y integers .
Solving for y:
$\displaystyle y = \dfrac{x}{x - 1}$
If y is to be an integer that means that x must be a multiple of x - 1. The only possibilities are x = 0, giving y = 0 and x = 2, giving y = 2.
So the solution set is (x, y) = {(0, 0), (2, 2)}.
-Dan
Tags integers, solve
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Contact - Home - Forums - Cryptocurrency Forum - Top
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2019-07-21 04:08:08
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https://brilliant.org/problems/when-the-sky-reaches-the-ground/
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When the sky reaches the ground
$\large \lfloor x+0.7 \rfloor = \lceil x-0.7 \rceil$
If $$x$$ is a real number chosen between the interval $$[a, b]$$, $$a$$ and $$b$$ being positive integers, find the probability that $$x$$ satisfies the equation above.
Notations: $$\lfloor \cdot \rfloor$$ denotes the floor function and $$\lceil \cdot \rceil$$ denotes the ceiling function.
×
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2017-03-29 13:08:36
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https://www.physicsforums.com/threads/set-of-least-upper-bounds-multiplied-by-a-constant.954366/
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# Set of least upper bounds multiplied by a constant
## Homework Statement
Let $S,T \subseteq \mathbb{F}$ be nonempty sets. Assume $\sup (S)$ and $\sup (T)$ both exist in $\mathbb{F}$. Show that $\forall a \in \mathbb{F}^+ \cup \{0\}$ we have $\sup(aS) = a \cdot \sup (S)$.
## The Attempt at a Solution
First I prove the lemma that if $B$ is the set of upper bounds for $S$ then $aB$ is the set of upper bounds for $aS$: Let $x \in aB$. Then $x = ab$ for some upper bound $b$ for $B$. But $\forall s \in S~s \le b$, which implies that $\forall s\in S ~ as \le ab = x$, so $x$ is an upper bound for the set $aS$
Now we prove the main result. First, we show that $a \cdot \sup (S)$ is an upper bound for $aS$: Let $s \in S$. Then $s \le \sup (S)$ by definition. So $as \le a \cdot \sup (S)$. But $s$ was arbitrary so, $a \cdot \sup (S)$ is an upper bound for $aS$. Second, we show that $a \cdot \sup (S)$ is less than or equal to any other lower bound of $aS$. Let $b$ be an upper bound for $s$. Then $\sup (S) \le b$, which implies that $a \cdot \sup(S) \le ab$, but the above lemma shows that $ab$ is an arbitrary upper bound for $aS$. Hence $a \cdot \sup (S)$ is less than or equal to any other lower bound of $aS$. So $\sup(aS) = a \cdot \sup (S)$.
Related Calculus and Beyond Homework Help News on Phys.org
fresh_42
Mentor
## Homework Statement
Let $S,T \subseteq \mathbb{F}$ be nonempty sets. Assume $\sup (S)$ and $\sup (T)$ both exist in $\mathbb{F}$. Show that $\forall a \in \mathbb{F}^+ \cup \{0\}$ we have $\sup(aS) = a \cdot \sup (S)$.
## The Attempt at a Solution
First I prove the lemma that if $B$ is the set of upper bounds for $S$ then $aB$ is the set of upper bounds for $aS$: Let $x \in aB$. Then $x = ab$ for some upper bound $b$
for "of" or "$\in$"
$B$. But $\forall s \in S~s \le b$, which implies that $\forall s\in S ~ as \le ab = x$, so $x$ is an upper bound for the set $aS$
Now we prove the main result. First, we show that $a \cdot \sup (S)$ is an upper bound for $aS$: Let $s \in S$. Then $s \le \sup (S)$ by definition. So $as \le a \cdot \sup (S)$. But $s$ was arbitrary so, $a \cdot \sup (S)$ is an upper bound for $aS$. Second, we show that $a \cdot \sup (S)$ is less than or equal to any other lower bound of $aS$. Let $b$ be an upper bound for $s$. Then $\sup (S) \le b$, which implies that $a \cdot \sup(S) \le ab$, but the above lemma shows that $ab$ is an arbitrary upper bound for $aS$. Hence $a \cdot \sup (S)$ is less than or equal to any other lower bound of $aS$. So $\sup(aS) = a \cdot \sup (S)$.
Instead of having this abstract field, you should have better said something about the order required for $\mathbb{F}$, as it cannot be arbitrary for this reason. Also you use $a\leq b \Longrightarrow ca\leq cb$ for $c\geq 0$ which is again a condition the order must have. I'm not quite sure whether you need this Lemma first as I think you could directly show the inequalities. That's the difficulty with such "obvious" results, to figure out what has to be shown at all. It looks o.k. so far, even if perhaps a bit too long at the wrong places.
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2020-03-29 03:55:31
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https://sites.science.oregonstate.edu/portfolioswiki/courses_order20_cforder20_cfsphereharm.html
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# Spherical Harmonics
## Prerequisites
Students should be able to:
## Homework for Central Forces
1. (Sphere)
Consider the normalized function:
$$f(\theta,\phi)= \begin{cases} N\left({\pi^2\over 4}-\theta^2\right)&0<\theta<\frac{\pi}{2}\\ 0&{\pi\over 2}<\theta<\pi \end{cases}$$
where
$$N=\frac{1}{\sqrt{\frac{\pi^5}{8} +2\pi^3-24\pi^2+48\pi}}$$
1. Find the $\left|\ell,m\right\rangle=\left|0,0\right\rangle$, $\left|1,-1\right\rangle$, $\left|1,0\right\rangle$, and $\left|1,1\right\rangle$ terms in a spherical harmonics expansion of $f(\theta,\phi)$.
2. If a quantum particle, confined to the surface of a sphere, is in the state above, what is the probability that a measurement of the square of the total angular momentum will yield $2\hbar^2$? $4\hbar^2$?
3. If a quantum particle, confined to the surface of a sphere, is in the state above, what is the probability that the particle can be found in the region $0<\theta<{\pi\over 6}$ and $0<\phi<{\pi\over 6}$? Repeat the question for the region ${5\pi\over 6}<\theta<{\pi}$ and $0<\phi<{\pi\over 6}$. Plot your approximation from part (a) above and check to see if your answers seem reasonable.
##### Views
New Users
Curriculum
Pedagogy
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2021-09-20 23:05:08
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http://www.mathcaptain.com/algebra/solving-equations-with-variables-on-both-sides.html
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Equations can be classified into linear, quadratic or cubic etc. Similarly linear equations can be classified into those containing, one variable, two variables or three or more variables.
While solving these equations we follow the rules of equality we discussed in earlier sections. To solve the linear equation of only one variable, it is enough if we have only one equation. While solving linear equations containing two variables we need two equations to solve for the unknown variables.
In this section let us see how to solve equations with variables on both sides and discuss with few examples also.
## How to Solve Equations with Variables on Both Sides
Solution to a given equation is the value of the variable, which satisfy the equations.
Rules to solve equations with variables on both sides:
Linear Equations: The general form of linear equations will be ax + b = 0, where a $\ne$ 0.
In the case of linear equations which have only one variable for which the variables are on both sides, we need to bring the variables to one side of the equal to sign, and the constants to other side of the equation and then eliminate the constants with the variable and solve for x.
### Example: 2x - 5 = 13 - 4x
Solution: We have 2x - 5 = 13 - 4x
Eliminating the constant in the left hand side, we get,
2x - 5 + 5 = 13 - 4x + 5
=> 2x = 18 - 4x
=> 2x + 4x = 18 - 4x + 4x
=> 6x = 18
=> x = $\frac{18}{6}$
= 3
Therefore, solution x = 3
Quadratic Equations: The quadratic equations are of the form, ax2 + b x + c = 0, where a $\ne$ 0.
A quadratic equation is a polynomial of degree two. There will be two solutions for the quadratic equations. The solutions are called as the roots of the equations.
The equations can be solved by
a. Factorization
b. Formula Method
c. Completing the square method.
When the equations have variables on both sides, we should follow the rules of equality, such that all the terms containing the variables and the constants are brought to the left side of the equation, so that the final equation is of the form, ax2 + bx + c = 0, then we solve the equation by one of the three methods shown above.
### Example: Solve( x + 2 ) = $\frac{(6x+3)}{(x-2)}$
Solution:
We have ( x + 2 ) = $\frac{(6x+3)}{(x-2)}$
( x + 2 ) ( x - 2 ) = 6x + 3 [ by multiplying by ( x - 2 ) on both sides ]
x2 - 4 = 6x + 3
=> x2 - 6x - 4 - 3 = 0
=> x2 - 6x - 7 = 0
=> x2 - 7x + x - 7 = 0
=> x ( x - 7 ) + 1 ( x - 7 ) = 0
=> ( x - 7 ) ( x + 1 ) = 0
=> x - 7 = 0 or x + 1 = 0
=> x = 7 or x = -1
Therefore the solution to the above equation is x = { -1, 7}.
## Examples of Solving Equations with Variables on Both Sides
### Solved Examples
Question 1: Solve 3x - $\frac{x}{2}$ = $\frac{3}{2}$
Solution:
We have 3x - $\frac{x}{2}$ = $\frac{3}{2}$
In the denominator we have only 2.
Multiplying both sides of the equation by 2, we get
3x $\times$ 2 - $\frac{x}{2}$ $\times$ 2 = $\frac{3}{2}$ $\times$ 2
=> 6x - x = 3
=> 5x = 3 [ applying the rule of equality for elimination on either sides of the equation ]
=> x = $\frac{3}{5}$ is the solution to the above equation.
Question 2: Solve 2 + $\frac{(2x-3)}{6}$ = $\frac{(3x+4)}{5}$
Solution:
We have 2 + $\frac{(2x-3)}{6}$ = $\frac{(3x+4)}{5}$
=> 2 x 30 + $\frac{(2x-3)}{6}$ $\times$ 30 = $\frac{(3x+4)}{5}$ $\times$ 30 [ Multiplying by the LCM of the denominators 6 and 5 which is 30 ]
=> 60 + 5 ( 2x - 3 ) = 6 ( 3x + 4 )
=> 60 + 10 x - 15 = 18 x + 24 [ applying the rule of equality for elimination on either sides of the equation ]
=> 10 x - 18 x = 24 - 60 + 15
=> - 8x = -21
=> x = $\frac{-21}{-8}$
= $\frac{21}{8}$
x = $\frac{21}{8}$ is the solution to the above equation.
Question 3: Solve $\frac{100}{x}$ - $\frac{100}{(x+5)}$ = 1
Solution:
The Denominators are x and ( x + 5 ).
LCM of the denominators = x ( x + 5 )
Multiplying by x ( x + 5 ) on both sides of the equation, we get,
$\frac{100}{x}$ $\times$ x ( x + 5 ) - $\frac{100}{(x+5)}$ $\times$ x ( x + 5 ) = 1 $\times$ x ( x + 5 )
100 ( x + 5 ) - 100 x = x ( x + 5 )
=> 100 x + 500 - 100x = x2 + 5 x
=> x2 + 5 x - 500 = 0 [ applying the rule of equality for elimination on either sides of the equation ]
=> x2 + 25 x - 20 x - 500 = 0
=> x ( x + 25 ) - 20 ( x + 25 ) = 0
=> ( x - 20 ) ( x + 25 ) = 0
=> x - 20 = 0 or x + 25 = 0
=> x = 20 or x = - 25
The solution will be x = { 20, - 25 }.
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2017-11-20 15:25:46
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http://mahalonottrash.blogspot.com/2007/08/nonna-out.html
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### Nonna Out
My mother-in-law, aka Nonna, aka My Baby Gramma, flew back to Houston last night. She was with us in Berkeley for 2 weeks before our big move, flew to Honolulu with us and stayed for 11 days. For most people, having their mother-in-law hang out with them for a month during a stressful transition period would be a recipe for disaster.
However, when I married Erin I hit the mother-in-law jackpot. I really don't know how we would have survived this move without Marie. She took care of Owen when we needed to get away, but never told us how to raise him. She never complained and never meddled. She helped us pack, did the dishes, helped with laundry, paid for more than her fair share. But most importantly she was great company and a fun person to hang out with. Who could ask for anything more from a mother-in-law?
Hurry back, Nonna!
mama mia said…
Miss you all and I haven't even been home a full day. You are too kind, John....it was really my pleasure to lounge around in paradise, whether Berkeley or Hoenoeluuuluuu. First day in a long time that I didn't get to go to fun beach or fun wee. I am having withdrawal....where is my baba?!
Anonymous said…
My mamma is SO cool! Are you jealous that I get to go there in October? I am SO excited, I can't wait!
Did you know that Nonna has also: (1) calmly asked me to remove a vomiting friend from her own bathroom in her home in Houston; (2) reacted in a calm, cool, and collected fashion when I, while sleepwalking, attempted to use the door to her backyard in her bedroom as a toilet; and (3) been careful enough not to disclose publicly the contents of my underpants from adolesence?
mama mia said…
I would definitely love to join you there, Amy....better save my $for another trip....wishing I could see the Johnson "belongings" in the new digs in Manoa.... Hey ghost, was that Patrick in our bathroom, or Gabe? both incident (1) and (2) were on the same night, if memory serves me right, New Year's Eve? Anonymous said… Patrick, and the ghost wasn't sleepwalking...he was drunkwalking. I think the ghost did something similar at my apartment in the heights, too. ;) Only I was successful in micturating on both your couch and the cushions on your dining room chairs in the Heights. I also recall there was an issue with your toilet flushing in the wrong direction. What a confusingly modern place you had.... ### Popular posts from this blog ### On the Height of J.J. Barea Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto). Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship. Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes. So I decided to find a photo and settle the issue once and for all. I started by downloading a stock photo of J.J. from NBA.com, which I then loaded into OpenOffice Draw: I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe… ### Finding Blissful Clarity by Tuning Out It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that. As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out. Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I… ### The Force is strong with this one... Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1." I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35." Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out x^2 - 1 = (x - 1) (x +1) So$6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48\$. That's actually pretty handy!
You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…
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2018-07-23 06:02:11
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http://scholarworks.umass.edu/dissertations/AAI9737553/
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Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
The energetics of swimming and upstream migration in adult American shad ({\it Alosa sapidissima\/}) in the Connecticut River
Abstract
This study was designed to assess the energetic cost of upstream migration in American shad (Alosa sapidissima) and to examine physiological changes during migration that relate to swimming performance or energetic efficiency. Overall total stored energy expenditure ranged from 35-60% during upstream migration. Migrating American shad preferentially use energy stores (lipid and protein) in some tissues, such as the skin and its sub-dermal fat layer (depleted by 63%), while sparing other tissue stores such as red muscle protein. American shad generally increased the activity of aerobic and energy mobilization enzymes as much as 60%, while decreasing the activity of anaerobic enzymes as much as 80% during upstream migration. There was a generalized reversal of these enzyme changes seen during migration at the most upriver site sampled. It is suggested that American shad may be able to metabolically prepare for migration prior to its onset and cessation. The data demonstrate that fish migrating in the middle of the migratory period possessed higher (5-42%) total stored energy content than fish migrating early or late in the season, primarily due to elevated lipid in the white muscle and the sub-dermal fat layer. American shad demonstrate a spleen-controlled increase in available blood hemoglobin (22%) and hematocrit likely resulting in increased oxygen carrying capacity during upstream migration. Active and standard metabolic rates of American shad, determined by respirometry, were intermediate between salmonids and fast-swimming perciforms. Active metabolic rate was logarithmically related to swimming speed (r$\sp2$ = 0.26; slope = 0.2) and tailbeat frequency (r$\sp2$ = 0.36; slope = 0.002). Directly determined standard metabolic rate was 71-198 $\rm mgO\sb2kg\sp{-1}h\sp{-1}.$ The energetically optimal swimming speed was 1.45 $\pm$ 0.51 body lengths per second. Using the data from the swimming respirometer, an empirical model of the Cabot Station fish ladder in Turners Falls, MA was constructed which suggests that the impact of the fish ladder on migration is highly dependent on passage time. This study demonstrates that American shad are equipped with a variety of mechanisms for increasing energetic efficiency during upstream migration and highlights the importance of short-term physiological adaption to migration and the ultimate success of an iteroparous, anadromous fish. ^
Subject Area
Biology, Ecology|Biology, Animal Physiology|Biology, Zoology
Recommended Citation
Leonard, Jill Beth Kippax, "The energetics of swimming and upstream migration in adult American shad ({\it Alosa sapidissima\/}) in the Connecticut River" (1997). Doctoral Dissertations Available from Proquest. AAI9737553.
http://scholarworks.umass.edu/dissertations/AAI9737553
COinS
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2017-01-18 01:46:05
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https://math.stackexchange.com/questions/2332327/what-is-a-mapping-cylinder-of-a-sphere-self-map-of-degree-1?noredirect=1
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# What is a mapping cylinder of a sphere self-map of degree $1$?
Let $f: S^d\to S^d$ be a (continuous) map of degree $1$, that is, homotopic to identity. Is it true that the mapping cylinder of $f$ is homeomorpic to a "normal" cylinder $S^d\times [0,1]$?
This is obvious if $f$ is a homeomorphism and still true in some other cases; however, I don't see how to prove it in general. Thanks for advice.
Map the circle to a wedge of three circles and then map each of the three circles to $S^1$ by maps of degrees respectively $+1$, $+1$, and $-1$. Then the resulting map $S^1\to S^1$ has degree $1$. If the mapping cylinder were homeomorphic to an ordinary cylinder, then a neighborhood of a typical point of $S^1\times \{1\}$ would look like a letter Y-shape times an interval, which cannot occur in a manifold.
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2022-01-17 02:39:38
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-section-1-1-real-numbers-1-1-exercises-page-11/44
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## Precalculus: Mathematics for Calculus, 7th Edition
a.) $A \cup B \cup C = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]$ b.) $A\cap B\cap C = \emptyset$
$Find$ $the$ $indicated$ $set$ $if:$ $A = [1, 2, 3, 4, 5, 6, 7]$ $B = [2, 4, 6, 8]$ $C = [7, 8, 9, 10]$ a.) $A \cup B \cup C$ We find the union of the variables for A, B, and C. Place the units in chronological order $A \cup B \cup C = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]$ b.) $A \cap B \cap C$ We find what units in A, B, and C intercept each other. We determine that there is no unit available intercept at all for A, B, and C together. $A\cap B\cap C = \emptyset$
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2018-05-28 02:00:14
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https://electronics.stackexchange.com/questions/338363/power-and-bulbs/338368
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# Power and bulbs
I have noticed the use of two different formulas i.e P=V²/R (in the 3rd line) and P=I²R (5th line from below). Since the bulbs are in series, how can the resistance be inversely proportional to power as shown? Is anything wrong with my book or am I missing some fundamental information?
• Have you done the math? – Ignacio Vazquez-Abrams Nov 6 '17 at 14:22
• Both formulas are sound and a combination of Ohm's Law V = I * R with the equation for power P = V * I Fill in one into the other and you will get the same equations. – Bimpelrekkie Nov 6 '17 at 14:24
You only need to remember two formulas. The rest can be worked out.
$$V = IR \tag 1$$ $$P = VI \tag 2$$
From (1) we can say that $I = \frac {V}{R}$ so popping that into (2) we get $$P = V \frac {V}{R} = \frac {V^2}{R} \tag 3$$
Alternately we pop (1) straight into (2) and say $$P = VI = IR \cdot I = I^2R \tag 4$$
That's the background sorted.
Now, for a given current $P = I^2R$ tells us that $P \propto R$.
Finally - and this may be the confusing part - note that the lamps are designed to be run in parallel in normal operation so that they run at the same voltage. In that configuration the lamp with the lower resistance will pass more current and dissipate more power (have a higher wattage).
In this application, because you are running in series they run at the same current and the lamp with the higher resistance will dissipate the higher power.
• which formula for power should i use in case of a single resistor rather than a combination if resistors? – G-aura-V Nov 6 '17 at 15:59
• The one that contains the unknown and two known variables, of course! – Transistor Nov 6 '17 at 16:14
Both the bulbs have different Power rating, but they are assumed to have the same voltage rating in this question. So it's obvious that the bulb with less power have more resistance, from the equation P = V^2/R. Now in series connection, the current is same in both the bulbs. So you can apply P= I^2*R formula now. Thus the 60 W bulb which has more resistance, will develop more power and hence glow brighter.
• Very nice induction. The secret being the current is absolutely the same in both bulbs no matter what voltage conditions exist. If the current is the same then power relates to directly to R. So you only need to know P=I^2*R. – Jack Creasey Nov 6 '17 at 16:43
Simple answer: We know from Ohm's Law and Thevenin voltage drop in a loop, that the most voltage is dropped on the highest resistance and the lower P rated bulb has a higher R value so it gets brighter at first.
It is assumed you know all the variant's of Ohm's Law and any or all may be used.
What you were not told, but is not essential for the basic understanding, is that the bulb current is not constant and due to positive R vs T or PTC characteristic so the smaller bulb wattage which has higher R value warms up faster and raises it's R so it gets near full brightness in steady state < 1 second. The simple answer is the bulb with the highest R or lowest W value is the brightest.
Real Life situation:
simulate this circuit – Schematic created using CircuitLab
Tungsten wire in bulbs are also PTC resistors. R_cold (25'C=298'K) = 10% of R_hot (3500'K)
• This means a 100W bulb uses up to 1kW during the 1st cycle turning on ! (depends on start phase , contact bounce etc.)
Thus R1~14Ω , R2~24Ω when off. ( room temp 298'K)
Pedantic note: ... 25'C may be warm for you , if you prefer 21'C with A/C but it is the "de facto" std temp for electronic specs. in datasheets
• So when turned on V(R2)=24/(24+14.4)*Vac = 62.5% Vac
• or V(R2)=75Vac, V(R1)=(120-75)=45Vac
• I init. = 120V/(14.4+24)=3.1A approx avg for 1st cycle period
• which is shorter than filament thermal time constant.
Since current is shared, P=VI , during inital power on cycle, we estimate as follows;
• (roughly 30% accurate and not with 4 sig figs as shown in calculator result below)
• P1=139.5W ( rated 100W)
• P2=232.5W ( rated 60W)
Perhaps counter-intuitive at first, but the bulb rated for the lower power starts with a higher power
• which means it gets hotter faster
• and since the resistance increases with temperature rapidly x10, R2 will almost reach full brightness >200 Ω
• while R1 which started at 14 Ω gets less and less voltage drop as R2 heats up faster
• and since the current drops thru both, R1 just pops then shuts down while R2 heats up slower than nomal
• since R1 cold is only 5% of R2 when hot and the higher R drops the most voltage and hence power
• the normal current for 60W=120V*0.5A is almost achieved since at steady state
• P1 would then only be lets say 10%Vac or 12V* *0.5A=6W so hot but not 3500'K and unlikely visible heat.
Concepts to understand: PTC, Ohm's Law
Intuitive Rule. Highest series impedance gets the most voltage drop.
We call this series PTC or "positive temperature characteristic" characteristic in parts named as this in catalogs, as "over-current protection devices". ( They are not meant to operate at high T forever (years), just for thermal protection of devices from short circuits.)
PTC's come in radial ceramic or SMD format, generally operate with polysilicon material and operate around 80'C with highly non-linear R near this T unlike tungsten which is more linear with T ('K) from 300 to 3000'K thus 10x the R value. ( roughly)
The key that others have implied but not explicitly stated is that there are two different power values for each bulb.
1. The rated power of the bulb, that is the power the bulb will draw when operated under normal operating conditions.
2. The power the bulb will draw when connected in the circuit given in the question.
When someone says "a 60W bulb" what they mean is "a bulb that will draw 60W when supplied with it's rated voltage. If not otherwise specified the rated voltage will be the normal mains voltage for wherever you live.
The first part of the answer is talking about deriving the resistance of the bulb from the rated power (which, as tony points out is a very crude approximation). The two bulbs are assumed to have the same rated voltage. So $P=\frac{V^2}{R}$ is the equation used.
The second part of the answer is talking about the behaviour of the bulbs when placed in the series circuit. In the series circuit the current though the two bulbs is the same. So $P=I^2R$ is the equation used.
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2021-04-17 06:30:07
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http://aif.cedram.org/item?id=AIF_2008__58_4_1093_0
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With cedram.org English français Home Overview Search for an article Submit a paper Informations for the authors Subscription Limited access - RUCHE Table of contents for this issue | Previous article | Next article Abdesslam BoulkhemairOn the Fefferman-Phong inequality(Sur l’inégalité de Fefferman-Phong)Annales de l'institut Fourier, 58 no. 4 (2008), p. 1093-1115, doi: 10.5802/aif.2379 Article PDF | Reviews MR 2427955 | Zbl 1145.35099 Class. Math.: 35Axx, 35Sxx, 47G30, 58J40Keywords: Fefferman-Phong inequality, Gårding inequality, symbol, $S^m_{\varrho ,\delta }$, pseudodifferential operator, Weyl quantization, Wick quantization, semi-boundedness, $L^2$ boundedness, algebra of symbols, uniformly local Sobolev space, Hölder space, semi-classical, Weyl-Hörmander class Résumé - AbstractWe show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by ${n\over 2}+4+\epsilon$ improving thus the bound $2n+4+\epsilon$ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type $S^0_{0,0}$, we show that this number is bounded by $n+4+\epsilon$; more precisely, for a non negative symbol $a$, the Fefferman-Phong inequality holds if $\partial _x^\alpha \partial _\xi ^\beta a(x,\xi )$ are bounded for, roughly, $4\le |\alpha |+|\beta |\le n+4+\epsilon$. To obtain such results and others, we first prove an abstract result which says that the Fefferman-Phong inequality for a non negative symbol $a$ holds whenever all fourth partial derivatives of $a$ are in an algebra ${\mathcal{A}}$ of bounded functions on the phase space, which satisfies essentially two assumptions : ${\mathcal{A}}$ is, roughly, translation invariant and the operators associated to symbols in ${\mathcal{A}}$ are bounded in $L^2$. Bibliography[1] J.-M. Bony, Sur l’inégalité de Fefferman-Phong, in Séminaire EDP, Ecole polytechnique, Exposé no 3, 1998–1999 Cedram [2] A. Boulkhemair, “$L^2$ estimates for pseudodifferential operators”, Ann. Sc. Norm. Sup. Pisa IV, XXII, 1 (1995), p. 155-183 Numdam | MR 1315354 | Zbl 0844.35145[3] A. Boulkhemair, “Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators”, Math. Res. Lett. 4 (1997), p. 53-67 MR 1432810 | Zbl 0905.35103[4] A. Boulkhemair, “$L^2$ estimates for Weyl quantization”, J. Funct. Anal. 165 (1999), p. 173-204 Article | MR 1696697 | Zbl 0934.35217[5] R. Coifman & Y. Meyer, Au delà des opérateurs pseudodifférentiels 57, Astérisque, 1978 Zbl 0483.35082[6] C. Fefferman & D. H. Phong, “On positivity of pseudodifferential operators”, Proc. Nat. Acad. Sci. 75 (1978), p. 4673-4674 Article | MR 507931 | Zbl 0391.35062[7] L. Hörmander, The analysis of partial differential operators, Springer Verlag, 1985 Zbl 0601.35001[8] N. Lerner & Y. Morimoto, On the Fefferman-Phong inequality and a Wiener type algebra of pseudodifferential operators, Preprint, 2005, to appear in the Publications of the Research Institute for Mathematical Sciences (Kyoto University) MR 2341014[9] N. Lerner & Y. Morimoto, A Wiener algebra for the Fefferman-Phong inequality, in Séminaire EDP, Ecole polytechnique, Exposé no 17, 2005–2006 Cedram | MR 2276082 | Zbl 1122.35163[10] J. Sjöstrand, “An algebra of pseudodifferential operators”, Math. Res. Lett. 1,2 (1994), p. 189-192 MR 1266757 | Zbl 0840.35130[11] D. Tataru, “On the Fefferman-Phong inequality and related problems”, Comm. Partial Differential Equations 27 (2002) no. 11-12, p. 2101-2138 Article | MR 1944027 | Zbl 1045.35115 © Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310
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2019-01-16 17:25:17
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https://preprint.impa.br/visualizar?id=2039
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Preprint A161/2002
Bounds on leaves of one-dimensional foliations
Steven Kleiman | Esteves, Eduardo
Keywords: foliations | curves | singularities
Let $X$ be a variety over an algebraically closed field, $\eta\:\Og^1_X\to\c L$ a one-dimensional singular foliation, and $C\subseteq X$ a projective leaf of $\eta$. We prove that $2p_a(C)-2=\deg(\c L|C)+\lambda(C)-\deg(C\cap S)$ where $p_a(C)$ is the arithmetic genus, where $\lambda(C)$ is the colength in the dualizing sheaf of the subsheaf generated by the Káhler differentials, and where $S$ is the singular locus of $\eta$. We bound $\lambda(C)$ and $\deg(C\cap S)$, and then improve and extend some recent results of Campillo, Carnicer, and de la Fuente, and of du Plessis and Wall.
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2021-09-21 20:29:36
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https://itectec.com/superuser/how-to-find-the-uptime-since-last-wake-from-standby/
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# Linux – How to find the uptime since last wake from standby
linuxstandbyuptime
I want to know the uptime since the last wake from standby.
The command uptime only shows the difference between current time minus the last startup time.
In /var/log/pm-suspend.log, look for the last line looking like this one:
Sun Dec 16 09:30:31 CET 2012: Awake.
Periodically your logrotate will "rotate" logs to prevent them from growing too big, so you may find an empty pm-suspend.log file. In this case, just look for the pm-suspend.log.1 file (you may find also other log files named like pm-suspend.log.2.gz and so on; you can examine them using zcat or zless).
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2021-09-18 19:30:12
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-4-section-4-1-angles-and-radian-measure-exercise-set-page-533/74
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## Precalculus (6th Edition) Blitzer
$\frac{63\pi}{4}$ yards $\approx$ 49.48 yards
θ =315 ° = $\frac{315 °\pi}{180 °}$ As we know, s = θr. So, s = 9 x $\frac{315 °\pi}{180 °}$ =$\frac{63\pi}{4}$ yards $\approx$ 49.48 yards.
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2019-03-18 21:28:27
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https://socratic.org/questions/56f59f5d7c0149639626a559
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Question #6a559
Apr 11, 2016
Answer:
No, if you mean that a gravitational field can be changed.
Explanation:
Note that gravitation and magnetism are two DIFFERENT forces! Magnetism can be induced in materials, but does not have any real relevance to earth's attractive force.
Gravity by definition is a mutual effect of the interaction of two masses. The gravitational force is proportional to each bodies' mass and the distance from each other. Therefore, gravitational interactions are always “matched”.
Trajectories, on the other hand, can result in anything from slight perturbations to actual impact with each other. Gravitational effects of two bodies can have an equilibrium point, such as the L-4 and L-5 orbits between the earth and the moon. But that is not the same thing as changing the moon's gravitational field to “match” that of earth.
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2019-10-18 02:04:32
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https://www.toppr.com/ask/question/in-solid-state-pcl5-is-a/
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Question
# In solid state is a :
A
B
C
D
## ionic solid with tetrahedral and octahedral
Hard
Updated on : 2022-09-05
Solution
Verified by Toppr
Correct option is D)
## In solid state tries to exist as oppositely charged ions like(1) and (2) as the ionic bonding enhances the crystalline nature .also is tetrahedral , while is octahedral . these structure fit well into each other which gives more stability to solid structure .Hence option D is correct.
Solve any question of The p-Block Elements with:-
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2023-01-31 01:19:29
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https://bethzero.com/category/effective-altruism/ai-risk/
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793 words
So, I started the anti-AI Safety blogging series because I would be a good fit for the cause area as described by e.g., 80,000 Hours and it seemed reasonable to think through the arguments myself. As it turns out, they don’t stand up to scrunity. I decided to keep on writing for a bit anyway, as all AI Risk enthusiasts seem to be unaware of the counterarguments. I thought there was nothing out there in writing. Boy was I wrong.
This is a non-exhaustive list of links relating to AI Safety skepticism. For more, check out the similar reading lists by Marcus Vindig and by Alexander Kruel. Overlap between these lists is minimal and restricted to a couple of particularly good resources.
Rodney Brooks writes from MIT Technology Review of the seven deadly sins of predicting the future of AI. If you find a paywall, either clear your cookies or view a less edited version on Brooks’ website. His other essays on Super Intelligence are also well-worth checking out.
Wolfgang Schwarz published his referee report of Yudkowsky (MIRI) and Soares’ (MIRI) Functional Decision Theory. I’ll quote a single paragraph, which I think accurately illustrates the whole review: “The standards for deserving publication in academic philosophy are relatively simple and self-explanatory. A paper should make a significant point, it should be clearly written, it should correctly position itself in the existing literature, and it should support its main claims by coherent arguments. The paper I read sadly fell short on all these points, except the first. (It does make a significant point.)”
Ben Garfinkel gave a talk at EA Global 2018 titled “How sure are we about this AI stuff?”, calling for EA’s to be more critical about AI Safety as a cause area. Garfinkel knows his audience well, as everything is phrased so as to make EA’s think without ruffling feathers
Oren Etzioni writes in MIT Technology Review about the survey data Bostrom talks about in Superintelligence and offers alternative data that suggest a very different picture
Maciej Cegłowski‘s talks are always excellent and “Superintelligence: The Idea That Eats Smart People” is no exception. (via)
EA Forum user Fods12 wrote a five-part critique of Superintelligence. They hit on a number of good objections. The posts sadly got little quality engagement, indicative of both the writing quality and of the rest of the EA Forum’s userbase.
Even transhumanists can be reasonable, like Monica Anderson who writes Problem Solved: Unfriendly AI.
Ernest Davis wrote a review of SuperIntelligence, touching on some of the key weaknesses in Bostrom’s arguments but insufficiently elaborating on each of his arguments. MIRI published a response to the review which I think mostly nitpicks Davis’ phrasing instead of actually engaging with his objections, which to be fair might be the best you can do if you don’t have any better source of exposition on these arguments than Davis’ review. In short, Davis’ review isn’t super good, but MIRI’s response is much worse.
Neil Lawrence critiques Bostrom’s Superintelligence. If I had to excerpt a single representative line, it would be “I welcome the entry of philosophers to this debate, but I don’t think Superintelligence is contributing as positively as it could have done to the challenges we face. In its current form many of its arguments are distractingly irrelevant.”
Magnus Vindig writes Why Altruists Should Perhaps Not Not Prioritize Artificial Intelligence: A Lengthy Critique, in which he tackles most of the standard EA arguments and points out their hidden assumptions. Topics include, but are not limited to, the incessantly cited AI researcher survey predictions, bad Moore’s law-type arguments, slight-of-hand changing definitions of intelligence, the difficulty of alignment rising for future systems compared to current ones and the enormous experience we have with present-day systems, Instrumental Convergence being under argued, the practical value of being super intelligent. He does not rigorously take down every argument to the full extent possible, but that is probably good because the blog post is 22k words as is. Vindig also wrote Is AI Alignment Possible? in which he argues that the answer is no, both in principle and in practice.
Richard Loosemoore has the right amount of derision that AI Risk deserves, which is different from the right amount of derision for convincing the worriers that they’re wrong. One person who was not convinced is Rob Bensiger of MIRI.
Bill Hibbard has an email exchange with Yudkowsky in which he argues that a Superintelligence would not conflate smiling human faces with nano-scale depictions of such. The whole exchange is kind of predictable and not too informative.
On a related note, Nicholas Agar wrote a paper titled “Don’t Worry about Superintelligence” in which he argues that the first AIs with sophisticated agency are inherently likely to be friendly.
6. Astronomical waste, astronomical schmaste
2772 words
[Part of this badly written blog post has been superseded by a slightly better written forum post over on the EA forum. I might clean up the other parts in the future as well, and if so I’ll publish them at the EA forum as well.]
Previously: [1] [2] [3] [4] [5][latest].
Epistemic status: there is nothing wrong with writing your bottom line first. The purpose of this article is to get my initial thoughts on AI risk down before I start reading more about the topic, because I fear that I might unknowingly grant AI risk proponents that the implicit assumptions they’re making are true. As I procrastinated a lot on writing this post, there have been an number of articles put out that I did not read. I do not intend this document to be a conclusive argument against ai risk so much as an attempt to justify why it might be reasonable to think ai risk is not real.
Is this text too long? Click here for the summary of the argument.
In this post, I want to tackle the astronomical waste argument as used to justify AI-related existential risk prevention as an EA cause area. I will first describe the argument that people make. After that, I will discuss a number of meta-heuristics to be skeptical of it. Lastly, I want to take the astronomical waste argument face-on and describe why it is so absurdly unlikely for AI risk to be simultaneously real and preventable that the expected value of working on AIS is still not very good.
Astronomical waste
The astronomical waste argument as most people tell it basically goes like this: the potential good that could be gotten if happy beings colonized the entire universe would be huge, so even if there is a tiny risk of space-colonization not happening, that costs a lot of value in expectation. Moreover, if we can decrease the risk by just a tiny bit, the expected utility generated is still big, so it might be a very cost-effective way to do good.
As many wise people have said before me, “Shut up and calculate.” I will be giving rough estimates without researching them a great lot, because these quantities are not that well-known to humanity either. For the duration of this post, I will be a speciesist and all-around awful person because that simplifies the estimates. Bostrom roughly estimates that colonizing the Virgo supercluster would yield $10^{38}$ human lives per century. The Virgo SC is one of about 10 million superclusters in the observable universe and we have roughly $10^{9}$ centuries left before entropy runs out, making a total of roughly $2^{180}$ potential human lives left in the universe.
I will try to argue that donating $\5000\approx\2^{13}$ to an AI risk charity today will counterfactually produce less than one life saved in expectation. To make that happen, we collect 180 bits of unlikeliness for the hypothesis that donating that sum of money to AI Safety organizations saves a lives.
You need to collect less bits if your counterfactual cause area is more cost-effective than malaria prevention. Possibly $\log_2(5000/0.20) \approx 14$ bits fewer with a charity like ALLFED.
On meta-uncertainty
Some of my LessWrong-reading friends would argue that it is impossible to have credence $2^{-200}$ in anything because my own thinking is fallible and I’ll make mistakes in my reasoning with probability much higher than that. I reject that assertion: if I flip 200 coins then my expected credence for most series of outcomes should inevitably be close to $2^{-200}$, because all $2^{200}$ events are mutually exclusive and their probabilities must sum up to at most $1$.
Discounting the future (30 bits)
Inhabiting the observable universe might take a really long, and in all this time there is some probability of going extinct for reasons other than AI risk. Hence we should discount the total spoils of the universe by a decent fraction. 30 bits.
Biases (20 bits)
I expect many EA’s to be wrong in their utility calculation, so I think I should propose mechanisms that cause so many EA’s to be wrong. Two such mechanisms are described in previous entries in this series [2] (9 bits) [3] (1 bits) and I want to describe a third one here.
When we describe how much utility could fit in the universe, our reference class for numbers is “how many X fits in the universe”, where X ranges over things like {atoms, stars, planets}. These numbers are huge, typically expressed as $10^n$ for $n \in \mathbb{N}$.
When we describe how likely certain events are, the tempting reference class is “statements of probability”, typically expressed as $ab.cdefghij... \%$. Writing things this way, it seems absurd to have your number start with more than 10 zeros.
The combination of these vastly different scales together with anchoring being a thing, makes that we should expect people to over-estimate the probability of unlikely effects and hence the expected utility of prevention measures.
I expect myself to be subject to these biases still, so I think it is appropriate to count a number of bits to counteract this bias. 20 bits.
Counterfactual actions (-1 bit)
Nothing is effective in and of itself, effectiveness is relative to a counterfactual action. For this blog post, the counterfactuals will be working on algorithmic fairness and/or digital rights campaigning/legislation, and mainstream machine learning research and engineering. -1 bit.
When is AI risky? (tl;dr)
This is a rough sketch of my argument. AI safety can only be an effective cause area if
1. The future of the non-extinct universe would be good.
2. The probability of an AI-related extinction event is big.
3. It is possible to find ways to decrease that probability.
4. It is feasible to impose those risk mitigation measures everywhere.
5. The AI risk problem won’t be solved by regular commercial and/or academic AI research anyway.
6. A single AI-related extinction event could affect any lifeform in the universe ever.
7. Without AI first causing a relatively minor (at most country-level) accident first.
8. Presently possible AI safety research should be an effective way of decreasing that probability.
I upper bounded the quantity in 1 by $2^{200}$ good lifes. Properties 2 and 3 are necessary for AI Safety work to be useful. Property 5 is necessary for AI safety work to have meaningful counterfactual impact. Property 6 is necessary because otherwise other happy life forms might fill the universe instead, and the stakes here on earth are nowhere near $2^{200}$. If property 7 does not hold, it might mean that people will abandon the AI project, and it would be too easy to debug risky AI’s. Property 8 is in contrast to AI safety work only really be possible after major progress from now has been made in AI capabilities research, and is hence a statement about the present day.
The basic premise of the argument is that there is an inherent tension between properties 2 up to 6 being true at once. AI risk should be big enough for properties 2 and 6 to hold, but small enough for 3 and 5 to hold. I think that this is a pretty narrow window to hit, and which would mean that AI safety is very unlikely to be an effective cause area, or at least it is not so for its potential of saving the universe from becoming paperclips. I am also highly skeptical of both 7 and 8, even assuming that 2 up to 6 hold.
AI is fake (8 bits)
I think it is likely that we won’t be making a what we now think of as “artificial intelligence”, because current conceptions of AI are inherently mystical. Future humans might one day make something that present-day humans would recognize as AI, but the future humans won’t think of it like that. They won’t have made computers think, they would have demystified thinking to the point where they understand what it is. They won’t mystify computers, they will demystify humans. Note that this is a belief about the state of the world, while [2] is about how we think about the world. Hence, I think both deserve to earn bits separately. 5 bits.
I am not sure that intelligence is a meaningful concept outside principal component analysis. PCA is a statistical technique that gives a largest component of variation in a population independently of whether that axis of variation has an underlying cause. In particular, that might mean that superhuman intelligence cannot exist. That does not preclude thinking at superhuman speeds from existing but would still impy serious bounds on how intelligent an AI can be. 1 bit.
No matter the above, all reasonably possible computation is restricted to polynomial-time solvable problems, fixed-parameter tractable problems and whatever magic modern ILP-, MINLP-, TSP- and SAT-solvers use. This gives real upper bounds on what even the most perfect imaginable AI could do. The strength of AI would lie in enabling fast and flexible communication and automation, not in solving hard computational problems. I hereby accuse many AI-enthousiasts of forgetting this fact, and will penalize their AI-risk fantasies for it. 2 bits.
AI x-risk is fake (31 bits)
The risks of using optimization algorithms are well-documented and practitioners have a lot of experience in how to handle such software reponsibly. This practical experience literally dates back to the invention of optimization in what is by far my favourite anecdote I’ve ever heard. Optimization practitioners are more responbile than you’d think, and with modern considerations of fairness and adversarial input they’ll only get more responsible over time. If there are things that must be paid attention to for algorithms to give good outcomes, practitioners will know about them. 3 bits.
People have been using computers to run ever more elaborate optimization algorithms pretty much since the introduction of the computer. ILP-solvers might be among the most sophisticated pieces of software in existence. And they don’t have any problems with reward hacking. Hence, reward hacking is probably only a fringe concern. 3 bits.
Debugging is a long and arduous process, both for developing software and for designing the input for the software (both the testing input and the real-world inputs). That means that the software will be run on many different inputs and computers before going in production, each an independent trial. So, if software has a tendency to give catastrophically wrong answers, it will probably already do so in an early stage of development. Such bugs probably won’t survive into production, so any accidents are purely virtual or at most on small scales. 5 bits.
Even if AI would go wrong in a bad way, it has to go really really wrong for it to be an existential thread. Like, one thing that is not ab existential thread is if an AI decided to release poison gas from every possible place in the US. That might kill everyone there, but even the poison gas factories could run indefinitely, the rest of the world could just nuke all of North America long before the whole global atmosphere is poisonous. 10 bits.
Moreover, for the cosmic endowment to be at risk, an AI catastrophy should impact every lifeform that would ever come to exist in the lightcone. That is a lot of ground to cover in a lot of detail. 10 bits.
AI x-risk is inevitable (28 bits)
Okay, let’s condition on all the above things going wrong anyway. Is AI-induced x-risk inevitable in such a world? Probably.
• There should be a way of preventing the catastrophies. 5 bits.
• Humans should be able to discover the necessary knowledge. 3 bits.
• These countermeasures have to be universally implemented. 10 bits.
• Even against bad actors and anti-natalist terrorists. 10 bits.
AI becomes safe anyway (15 bits)
Let’s split up the AI safety problem into two distinct subproblems. I don’t know the division in enough detail to give a definition, so I’ll describe them by association. The two categories roughly map onto the distinction from [4], and also roughly onto what LW-sphere folks call the control problem and the alignment problem.
Capitalist’s AI problem Social democrat’s AI problem x/s-risk Cyberpunk dystopia risk Must be solved tomake money using AI Must be solved to havealgorithms producesocial good Making AI optimal Making algorithms fair Solving required forfurthering a singleentity’s values Solving required forfurthering sentientbeings’ collectivevalues. Only real if certainimplausibleassumptions are true Only real if hedonisticutilitarianism is false,or if bad actors hatehedonistic utility. Prevent the light conefrom becoming paperclips Fully Automated LuxuryGay Space Communism Specific to AGI Applies to all algorithms Fear of Skynet Fear of Moloch Beating back unknowninvaders from mindspace Beating back unthinkinglyoptimistic programmers Have AI do what we want Know what we wantalgorithms to do What AIS-focussed EAscare about What the rest of theworld cares about
I’m calling 20 bits on the capitalist’s problem getting solved by capitalists, and 15 bits on the social democrat’s problem getting solved by the rest of humanity. We’re interested in the minimum of the two. 15 bits.
Working on AIS right now is ineffective (15 bits)
There are two separate ways of being inefficient to account for. AIS research might be ineffective right now no matter what because we lack the knowledge to do useful research, or AIS work might in general be less effective than work on for example FAT algorithms.
The first idea is justified from the viewpoint that making AI will mostly involve demystifying the nature of intelligence, versus obtaining the mystical skill of producing intelligence. Moreover it is reasonable to think given that current algorithms are not intelligent. 5 bits. ((Note that this argument is different from the previous one under the “AI is fake” heading. The previous argument is about the nature of intelligence and whether it permits AI risk existing versus not existing, this argument is about our capability to resolve AI risk now versus later.))
The second idea concerns whether AI safety will be mostly a policy issue or a research issue. If it is mostly policy with just a bit of technical research, it will be more effective to practice getting algorithms regulated in the first place. We can gain practice, knowledge and reputation for example by working on FATML, and I think it likely that this is a better approach at the current moment in time. 5 bits.
Then the last concern is that AIS research is just AI capabilities research by another name. It might not be exactly true, but the fit is close. 5 bits.
Research is expensive (13 bits)
Let’s get a sense of scale here. You might be familiar with these illustrations. If not, check them out. That tiny bit is the contribution of 4 year researcher-years. One researcher-year costs at least $50,000. The list of projects getting an ERC Starting Grant of 1.5 million euros. Compared to ambitious projects like “make AI safe”, the ERC recipient’s ambitions are tiny and highly specialised. What’s more, these are grant applications, so they are necessarily an excaggeration of what will actually happen with the money. It is not a stretch to estimate that it would cost at least$50 million to make AI safe (conditional on all of the above being such that AIS work is necessary). So a donation of \$5000 would be at most 0.0001 of the budget. 13 bits.
Hard to estimate issues (10 bits)
I’ll aggregate these because I don’t trust myself to put individual values on each of them.
• Will the universe really get filled by conscious beings?
• Will they be happy?
• Is it better to lead a happy life than to not exist in the first place?
• Is there a moral difference between there being two identical happy universes A and B versus them being identical right up to the point where A’s contents get turned to paperclips but B continues to be happy? And how does anthropic bias factor in to this?
• Has any being ever had a net-positive life?
Sub-1-bit issues (5 bits)
I listed all objections where I was at least 50% confident in them being obstacles. But there are probably quite a number of potential issues that I haven’t thought of because I don’t expect them to be issues with enough probability. I estimate their collective impact to count for something. 5 bits.
Conclusion
It turns out I only managed to collect 174 bits, not the 180 bits I aimed for. I see this as weak evidence for AIS being better than malaria prevention but not better than something like ALLFED. Of course, we should keep in mind that all the numbers are made up.
Maybe you disagree with how many bits I handed out in various places, maybe you think I double-counted some bits, or maybe you think that counting bits is inherently fraught and inconsistent. I’d love to hear your thoughts via email at beth@bethzero.com, via Reddit at u/beth-zerowidthspace or at the EA forum at beth.
5. Are neural networks intelligent?
563 words
I am skeptical of AI Safety (AIS) as an effective cause area, at least in the way AIS is talked about by people in the effective altruism community. However, it is also the cause area that my skills and knowledge are the best fit for contributing, so it seems worthwhile for me to think my opposition to it through.
Previously: [1] [2] [3] [4][latest].
Epistemic status: this argument has more flaws than I can count. Please don’t take it seriously. [See the post-script]
Let’s answer this abstract philosophical question using high-dimensional geometry.
I’ll assume for simplicity that there is a single property called intelligence and the only variation is in how much you have of it. So no verbal intelligence vs visiual intelligence, no being better at math and than at languages, the only variation is in how much intelligence we have. Let us call this direction of variation $g$, scaled to have $\|g\| = 1$, and pretend that it is roughly the thing you get from a singular value decomposition/principal component analysis of human’s intelligence test results.
A typical neural net has many neurons. For example, VGG-19 has ~143 million parameters. Now suppose that we train a VGG-19 net to classify images. This is an optimization problem in $\mathbb{R}^{143 \text{ million}}$, and let’s call the optimal parameter setting $x$. By definition, the trained net has an intelligence of exactly the inner product $g^{\mathsf{T}}x$. ((Note that the projection of g into this 143 million-dimensional space might be much shorter than g itself is, that depends on the architecture of the neural net. If this projection is very short, then every parameter setting of the net is very unintelligent. By the same argument that I’m making in the rest of the post, we should expect the projection to be short, but let’s assume that the projection is long for now.)) ((I’m assuming for simplicity that everything is convex.))
The trained net is intelligent in exactly the extend that intelligence helps you recognize images. If you can recognize images more efficiently by not being intelligent, then the trained net will not be intelligent. But exactly how helpful would intelligence be in recognizing images? I’d guess that a positive amount of intelligence would be better than a negative amount, but other than that I have no clue.
As a good subjective Bayesian, I’ll hence consider the vector $\omega$ of goodness-at-recognizing-images to be chosen uniformly from the unit sphere, conditional on having non-negative intelligence, i.e., uniformly chosen from $\{\omega\in\mathbb{S}^{143\text{ million} - 1} : g^{\mathsf{T}}\omega \geq 0\}$. For this distribution, what is the expected intelligence $\mathbb{E}[g^{\mathsf{T}}x]$? Well, we know, we know that $x$ maximizes $\omega$, so if the set of allowed parameters is nice we would get $g^{\mathsf{T}}x \approx g^{\mathsf{T}}\omega \cdot \|x\|$, ((I have to point out that this is by far the most unrealistic claim in this post. It is true if $x$ is constrained to lie in a ball, but in other cases it might be arbitrarily far off. It might be true for the phenomenon I describe in the first footnote.)) where $\|x\|$ is how good the net is at recognizing images. We can calculate this expectation and find that, up to a constant factor, $$\mathbb{E}[g^{\mathsf{T}}\omega] \approx \frac{2}{\sqrt{2e\pi(143\text{ million}-1)}}.$$
So the trained VGG-19 neural net is roughly $10^{-5}$ times as intelligent as it is good at recognizing images. Hence, it is probably not very smart.
4. Who is worried about AI Risk?
429 words
I am skeptical of AI Safety (AIS) as an effective cause area, at least in the way AIS is talked about by people in the effective altruism community. However, it is also the cause area that my skills and knowledge are the best fit for contributing, so it seems worthwhile for me to think my opposition to it through.
Previously: [1] [2] [3][latest].
There are many people talking about the risks of artificial intelligence. I want to roughly split them into three groups for now, because they worry about very different issues that tend to talk past each other, confusing outsiders.
The LessWrong-aligned view seems most popular in the EA community. Examplified by the paperclip maximizer argument, LW-aligned worriers are concerned that an Artifical General Intelligence (AGI) would accomplish their objective in unforeseen ways, and as a consequence should be treated like you should treat an evil genie, except it’d be worse because it would have less understanding of basic words than philosophers have. The principles that AI should satisfy are listed by the Future of Humanity Institute. [Though I suspect at least some of the signatories to have the FATML-aligned view in mind.] A popular book on this is Superintelligence by Nick Bostrom.
Fairness, Accountability and Transparency in Machine-Learning (FATML) is a subfield of machine learning, concerned with making algorithmic decision making fair, accountable and transparent. Exemplified by Amazon’s recent recruiting debacle, FATML-aligned worries are concerned that modern algorithmic decisionmaking will exacerbate existing social, economic and legal inequalities. The princples that AI should satisfy are listed by The Public Voice, and these Google ML guidelines fit as well. [Though I suspect at least some of the signatories to have the LW-aligned view in mind.] Popular books include Weapons of Math Destruction by Cathy O’Neil, Algorithms of Oppression by Safiya Noble and Automating Inequality by Virginia Eubanks.
Other AI-related worries commonly heard in the media, that I want to separate from the previous two categories because, compared to the above categories, these issues are more about politics and less of a technical problem. Worries include killer drones, people losing their jobs because AI replaced them, and who the self-driving car should run over given the choice.
In the next couple of posts on AI-related topics, I will focus on the first two categories. My aim is to use the FATML-aligned view to compare and contrast the LW-aligned view, hopefully gaining some insight in the process. The reason I separate the views this way, is because I agree with the FATML-aligned worries and disagree with the LW-aligned worries.
3. Finding meaning in a perfect life
249 words
[This badly written blog post has been superseded by a slightly better written forum post over on the EA forum.]
I am skeptical of AI Safety (AIS) as an effective cause area, at least in the way AIS is talked about by people in the effective altruism community. However, it is also the cause area that my skills and knowledge are the best fit for contributing, so it seems worthwhile for me to think my opposition to it through.
Previously: [1] [2][latest].
My background makes me prone to overrate how important AI Safety is.
My fields of expertise and enjoyment are mathematics and computer science. These skills are useful for the economy and in high demand. The general public is in awe of mathematics and thinks highly of anyone who can do it well. Computer science is the closest thing we have to literal magic.
Wealth, fun, respect, power. The only thing left to desire is cosmic significance, which is exactly the sales pitch of the astronomical waste argument. It would be nice if AI-related existential risk were real, for my labour to potentially make the difference between a meaningless lifeless universe or a universe filled with happyness. It would give objective significance to my life in a way that only religion would otherwise be able to.
This is fertile ground for motivated reasoning, so it is good to be skeptical of any impulse to think AIS is as good as it is claimed to be in cost-effectiveness estimates.
2. How do we talk about AI?
525 words
[This badly written blog post has been superseded by a slightly better written forum post over on the EA forum.]
I am skeptical of AI Safety (AIS) as an effective cause area, at least in the way AIS is talked about by people in the effective altruism community. However, it is also the cause area that my skills and knowledge are the best fit for contributing, so it seems worthwhile for me to think my opposition to it through.
Previously: [1][latest].
All sentences are wrong, but some are useful. I think that a certain emotional salience makes us talk about AI in a way that is more wrong than necessary.
A self-driving car and a pre-driven car are the same thing, but I can feel myself thinking about the two in completely different ways.
Self-driving cars are easy to imagine: they are autonomous and you can trust the car like you trust cab drivers; they can make mistakes but probably have good intent, when they encounters an unfamiliar situation they can think about the correct way to proceed, and if something goes wrong then the car is at fault.
A pre-driven car are hard to imagine: it has to have a bunch of rules coded into it by the manufacturer and you can trust the car like you trust a bridge; it does exactly what it was built to do, but if it was built without proper testing or calculations, things will at some point go wrong. When it does, the company and engineers are at fault.
You can make these substitutions on any sentence in which a computer is ascribed agency. In the best case, “The neural network learned to recognize objects in images” becomes “The fitted model classifies images in close correspondence with the human-given labels”. In reality, that description might be too generous.
It helps to keep in mind the human component. “The YouTube algorithm shows you exactly those videos that make you spend more time on the platform” is accurate in some sense, but it completely glances over the ways in which in the algorithm does not do that. When you listen to music using YouTube’s autoplay, it isn’t hard to notice that suggestions tend to point backwards in time compared to the upload date of the video you’re watching right now, and that, apart from preventing repeats, autoplay is pretty Markovian (that is mathspeak for the algorithm not doing anything clever based on your viewing history, just “this video is best followed by that video”). Both of those properties are clearly a result from the way in which YouTube’s engineers modelled the problem they were trying to solve, I would describe YouTube’s suggestion as “The YouTube autoplay algorithm was made to link you to videos that most people watched and liked after watching the current video”.
When you rewrite AI-related statements, they tend to become more wordy. That is exactly what you would expect, but does make it unwieldy to have accurate conversations. I leave the search for catchy-but-more-accurate buzzwords as an open problem. I am particularly interested in how to translate the term “artificial general intelligence” (AGI).
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2019-04-23 10:48:27
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https://tex.stackexchange.com/questions/363888/how-to-write-the-following-section-in-latex
|
# How to write the following section in LaTeX?
Suppose I want to write in latex just the following way:
1. Prove that,
(i)x+y=z
(ii)a+b=c
(iii) p+q=r
how to do that? I tried enumerate or itemize but can't do that exactly, is there any way of doing it? or I've to write it manually?
• welcome to TeX.SE! Can you show, what you try so far? A Minimal (non)Working Example would help us to help you. Apr 9 '17 at 14:05
You can use the enumitem package to make your life easy:
\documentclass{article}
\usepackage{amsmath}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}[start=42]
\item Prove that,
\begin{enumerate}[label=(\roman*)]
\item $x + y = z$
\item $a + b = c$
\item $p + q = r$
\end{enumerate}
\end{enumerate}
\end{document}
But this can also be done with no packages at all:
\documentclass{article}
\begin{document}
\begin{enumerate}
\setcounter{enumi}{41}\renewcommand{\theenumii}{\roman{enumii}}
\item Prove that,
\begin{enumerate}
\item $x + y = z$
\item $a + b = c$
\item $p + q = r$
\end{enumerate}
\end{enumerate}
\end{document}
The setcounter command is just to make sure the first list (enumi) starts at 42. I set the counter to 41 so that when the first \item is encountered, it then adds one to the counter and prints the new value (sc. 42).
\renewcommand{\theenumii}{\roman{enumii}}
Gives you the Roman numbers. It redefines the label of the second list (our first nested list) enumii to use lowercase Roman numerals (\roman).
+1 to Au101's answer, but one alternative to itemize-like environments could be the linguex package. The bonus are (a) the simplicity of code and (b) the possibility of insert normal full-with paragraphs within main items list, without break the numeration (a bit more complex with the standard lists).
Usage: Please RTFM ... ahem!, I mean... use \ex. for main items, \a. to start the first subitem and \b. to star any other subitem, a blank line to end the \ex. item, and that is all.
The default format use roman numerals in the third level, but is easy to change as you wish:
\documentclass[two columns]{article}
\usepackage{linguex}
% To adapt default format (1) a. ... to 1. (i) ...
\let\oldalph\alph
\let\alph\roman
\renewcommand{\ExLBr}{} % first level format
\renewcommand{\ExRBr}{.}
\renewcommand{\SubExLBr}{(} % second level format
\renewcommand{\SubExRBr}{)}
\setcounter{ExNo}{41}
\begin{document}
\noindent The are some statements to test the liguex package::
\ex. Prove that,
\a. $x + y = z$
\b. $a + b = c$
\b. $p + q = r$
Then, maybe $d+e=f$ (or maybe not)
\ex. Basic colors are:
\a. Red \f. Green \c. Blue
\end{document}
In case that disturb you the sequence \a.,\b.,\b.,\b., ... in source code , you can use \a.,\b., \c., ... up to \f., but are just \b. synonyms, i.e., the order really does not matter, except for \a..
Note that normal text after a item will be not indented, unless you add one more blank line.
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2021-09-17 12:42:20
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https://www.zbmath.org/authors/?q=ai%3Akrzanowski.wojtek-janusz
|
## Krzanowski, Wojtek Janusz
Compute Distance To:
Author ID: krzanowski.wojtek-janusz Published as: Krzanowski, W. J.; Krzanowski, Wojtek J.; Krzanowski, Wojtek; Krzanowski, Wojtek Janusz
Documents Indexed: 60 Publications since 1975, including 7 Books Co-Authors: 28 Co-Authors with 29 Joint Publications 422 Co-Co-Authors
all top 5
### Co-Authors
30 single-authored 7 Bailey, Trevor C. 7 Hand, David J. 4 Hernandez, Adolfo 3 Everson, Richard M. 3 Fieldsend, Jonathan E. 3 Partridge, Derek 3 Schetinin, Vitaly 2 Kim, Sungsoo 2 Mahat, Nor Idayu 2 Marriott, Francis Henry Charles 1 Ahmed, Syed Ejaz 1 Asparoukhov, Ognian K. 1 Cichocka, Izabela 1 Crowder, Martin J. 1 Ganeshanandam, S. 1 Gower, John C. 1 Hartley, James 1 Jonathan, Philip 1 Kozak, Marcin 1 McCarthy, W. V. 1 Mitchell, Ann F. S. 1 Powell, Kenneth J. 1 Radley, David 1 Sapatinas, Theofanis 1 Thomas, M. R. 1 Trendafilov, Nickolay T. 1 Turner, Heather L. 1 Unkel, Steffen
all top 5
### Serials
7 Biometrics 7 Journal of Classification 6 Computational Statistics and Data Analysis 6 Journal of Applied Statistics 4 Biometrika 4 Journal of the American Statistical Association 2 The Australian Journal of Statistics 2 Journal of the Royal Statistical Society. Series C. Applied Statistics 2 Oxford Statistical Science Series 2 Kendall’s Library of Statistics 2 Advances in Data Analysis and Classification. ADAC 1 Technometrics 1 Statistics & Probability Letters 1 Computational Statistics 1 European Journal of Operational Research 1 Journal of Statistical Computation and Simulation 1 Computers and Mathematics with Applications. Part A 1 Journal of the Royal Statistical Society. Series C. Applied Statistics 1 Mathematical Geology 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 Monographs on Statistics and Applied Probability 1 Modern Applied Science 1 Mathematical Geosciences 1 Statistics and Computing
all top 5
### Fields
57 Statistics (62-XX) 8 Numerical analysis (65-XX) 3 Biology and other natural sciences (92-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
53 Publications have been cited 497 times in 380 Documents Cited by Year
Principles of multivariate analysis. A user’s perspective. Zbl 0678.62001
Krzanowski, W. J.
1988
A criterion for determining the number of groups in a data set using sum- of-squares clustering. Zbl 0707.62122
Krzanowski, W. J.; Lai, Y. T.
1988
Discrimination and classification using both binary and continuous variables. Zbl 0322.62075
Krzanowski, W. J.
1975
ROC curves for continuous data. Zbl 1288.62005
Krzanowski, Wojtek J.; Hand, David J.
2009
Between-groups comparison of principal components. Zbl 0459.62042
Krzanowski, W. J.
1979
Distance between populations using mixed continuous and categorical variables. Zbl 0514.62067
Krzanowski, W. J.
1983
Discriminant analysis with singular covariance matrices: Methods and applications to spectroscopic data. Zbl 0821.62032
Krzanowski, W. J.; Jonathan, P.; McCarthy, W. V.; Thomas, M. R.
1995
Mixtures of continuous and categorical variables in discriminant analysis. Zbl 0442.62045
Krzanowski, W. J.
1980
Multivariate analysis. Part 2: Classification, covariance structures and repeated measurements. Zbl 0949.62537
Krzanowski, W. J.; Marriott, F. H. C.
1995
Mixtures of continuous and categorical variables in discriminant analysis: A hypothesis-testing approach. Zbl 0539.62069
Krzanowski, W. J.
1982
Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. Zbl 0956.62048
Gower, J. C.; Krzanowski, W. J.
1999
The performance of Fisher’s linear discriminant function under non- optimal conditions. Zbl 0358.62043
Krzanowski, W. J.
1977
Optimising $$k$$-means clustering results with standard software packages. Zbl 1429.62244
Hand, David J.; Krzanowski, Wojtek J.
2005
Improved biclustering of microarray data demonstrated through systematic performance tests. Zbl 1429.62267
Turner, Heather; Bailey, Trevor; Krzanowski, Wojtek
2005
Biased estimation in a simple multivariate regression model. Zbl 1429.62183
Ahmed, S. E.; Krzanowski, W. J.
2004
The location model for mixtures of categorical and continuous variables. Zbl 0775.62153
Krzanowski, W. J.
1993
On selecting variables and assessing their performance in linear discriminant analysis. Zbl 0707.62120
Ganeshanandam, S.; Krzanowski, W. J.
1989
Multivariate analysis. Part I. Distributions, ordination and inference. Zbl 0855.62036
Krzanowski, W. J.; Marriott, F. H. C.
1994
The Mahalanobis distance and elliptic distributions. Zbl 0571.62042
Mitchell, Ann F. S.; Krzanowski, Wojtek J.
1985
Assessing error rate estimators: The leave-one-out method reconsidered. Zbl 0877.62063
Krzanowski, W. J.; Hand, D. J.
1997
Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization. Zbl 1197.62100
Kim, Sung-Soo; Krzanowski, W. J.
2007
Between-group comparison of principal components. Some sampling results. Zbl 0507.62056
Krzanowski, W. J.
1982
Between-group analysis with heterogeneous covariance matrices: The common principal component model. Zbl 0714.62051
Krzanowski, W. J.
1990
Nonparametric confidence and tolerance regions in canonical variate analysis. Zbl 0715.62092
1989
Exploratory factor and principal component analyses: some new aspects. Zbl 1322.62043
Trendafilov, Nickolay T.; Unkel, Steffen; Krzanowski, Wojtek
2013
A comparison of discriminant procedures for binary variables. Zbl 1095.62508
Asparoukhov, Ognian K.; Krzanowski, Wojtek J.
2001
Quadratic location discriminant functions for mixed categorical and continuous data. Zbl 0800.62339
Krzanowski, W. J.
1994
A simple method for screening variables before clustering microarray data. Zbl 1453.62127
Krzanowski, Wojtek J.; Hand, David J.
2009
Some linear transformations for mixtures of binary and continuous variables, with particular reference to linear discriminant analysis. Zbl 0397.62041
Krzanowski, W. J.
1979
Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model. Zbl 1147.62057
Kim, Sung-Soo; Park, Sung H.; Krzanowski, W. J.
2008
Antedependence models in the analysis of multi-group high-dimensional data. Zbl 0939.62057
Krzanowski, W. J.
1999
Signal detection in underwater sound using wavelets. Zbl 0916.62071
Bailey, Trevor C.; Sapatinas, Theofanis; Powell, Kenneth J.; Krzanowski, Wojtek J.
1998
On the null distribution of distance between two groups, using mixed continuous and categorical variables. Zbl 0558.62021
Krzanowski, W. J.
1984
Principles of multivariate analysis. A user’s perspective. Corrected reprint. Zbl 1116.62058
Krzanowski, Wojtek J.
2003
Biplots for multifactorial analysis of distance. Zbl 1274.62474
Krzanowski, W. J.
2004
On confidence regions in canonical variate analysis. Zbl 0663.62066
Krzanowski, W. J.
1989
Multiple discriminant analysis in the presence of mixed continuous and categorical data. Zbl 0589.62045
Krzanowski, W. J.
1986
Variable selection in discriminant analysis based on the location model for mixed variables. Zbl 1301.62066
Mahat, Nor Idayu; Krzanowski, Wojtek Janusz; Hernandez, Adolfo
2007
Selection of variables, and assessment of their performance, in mixed-variable discriminant analysis. Zbl 0875.62265
Krzanowski, W. J.
1995
Rao’s distance between normal populations that have common principal components. Zbl 0925.62217
Krzanowski, W. J.
1996
An introduction to statistical modelling. Zbl 0968.62001
Krzanowski, Wojtek J.
1998
Ordination in the presence of group structure, for general multivariate data. Zbl 0825.62553
Krzanowski, W. J.
1994
On optimal intervention for customer lifetime value. Zbl 1138.91531
Crowder, Martin; Hand, David J.; Krzanowski, Wojtek
2007
Sensitivity in metric scaling and analysis of distance. Zbl 1091.62121
Krzanowski, W. J.
2006
An overview of approaches to the analysis and modelling of multivariate geostatistical data. Zbl 1321.86011
Bailey, Trevor C.; Krzanowski, Wojtek J.
2012
Canonical representation of the location model for discrimination or classification. Zbl 0335.62040
Krzanowski, W. J.
1976
Subspace projection for multivariate selection problems. Zbl 0899.62082
Krzanowski, W. J.
1998
Estimating classification uncertainty of Bayesian decision tree technique on financial data. Zbl 1269.91034
Schetinin, Vitaly; Fieldsend, Jonathan E.; Partridge, Derek; Krzanowski, Wojtek J.; Everson, Richard M.; Bailey, Trevor C.; Hernandez, Adolfo
2007
Extraction of spatial features using factor methods, illustrated on stream sediment data. Zbl 1332.86012
Krzanowski, W. J.; Bailey, T. C.
2007
A comparison between two distance-based discriminant principles. Zbl 0655.62065
Krzanowski, W. J.
1987
Attribute selection in correspondence analysis of incidence matrices. Zbl 0825.62526
Krzanowski, W. J.
1993
Confidence in classification: a Bayesian approach. Zbl 1336.62184
Krzanowski, Wojtek J.; Bailey, Trevor C.; Partridge, Derek; Fieldsend, Jonathan E.; Everson, Richard M.; Schetinin, Vitaly
2006
Testing the difference between two Kolmogorov-Smirnov values in the context of receiver operating characteristic curves. Zbl 07253863
Krzanowski, Wojtek J.; Hand, David J.
2011
Exploratory factor and principal component analyses: some new aspects. Zbl 1322.62043
Trendafilov, Nickolay T.; Unkel, Steffen; Krzanowski, Wojtek
2013
An overview of approaches to the analysis and modelling of multivariate geostatistical data. Zbl 1321.86011
Bailey, Trevor C.; Krzanowski, Wojtek J.
2012
Testing the difference between two Kolmogorov-Smirnov values in the context of receiver operating characteristic curves. Zbl 07253863
Krzanowski, Wojtek J.; Hand, David J.
2011
ROC curves for continuous data. Zbl 1288.62005
Krzanowski, Wojtek J.; Hand, David J.
2009
A simple method for screening variables before clustering microarray data. Zbl 1453.62127
Krzanowski, Wojtek J.; Hand, David J.
2009
Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model. Zbl 1147.62057
Kim, Sung-Soo; Park, Sung H.; Krzanowski, W. J.
2008
Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization. Zbl 1197.62100
Kim, Sung-Soo; Krzanowski, W. J.
2007
Variable selection in discriminant analysis based on the location model for mixed variables. Zbl 1301.62066
Mahat, Nor Idayu; Krzanowski, Wojtek Janusz; Hernandez, Adolfo
2007
On optimal intervention for customer lifetime value. Zbl 1138.91531
Crowder, Martin; Hand, David J.; Krzanowski, Wojtek
2007
Estimating classification uncertainty of Bayesian decision tree technique on financial data. Zbl 1269.91034
Schetinin, Vitaly; Fieldsend, Jonathan E.; Partridge, Derek; Krzanowski, Wojtek J.; Everson, Richard M.; Bailey, Trevor C.; Hernandez, Adolfo
2007
Extraction of spatial features using factor methods, illustrated on stream sediment data. Zbl 1332.86012
Krzanowski, W. J.; Bailey, T. C.
2007
Sensitivity in metric scaling and analysis of distance. Zbl 1091.62121
Krzanowski, W. J.
2006
Confidence in classification: a Bayesian approach. Zbl 1336.62184
Krzanowski, Wojtek J.; Bailey, Trevor C.; Partridge, Derek; Fieldsend, Jonathan E.; Everson, Richard M.; Schetinin, Vitaly
2006
Optimising $$k$$-means clustering results with standard software packages. Zbl 1429.62244
Hand, David J.; Krzanowski, Wojtek J.
2005
Improved biclustering of microarray data demonstrated through systematic performance tests. Zbl 1429.62267
Turner, Heather; Bailey, Trevor; Krzanowski, Wojtek
2005
Biased estimation in a simple multivariate regression model. Zbl 1429.62183
Ahmed, S. E.; Krzanowski, W. J.
2004
Biplots for multifactorial analysis of distance. Zbl 1274.62474
Krzanowski, W. J.
2004
Principles of multivariate analysis. A user’s perspective. Corrected reprint. Zbl 1116.62058
Krzanowski, Wojtek J.
2003
A comparison of discriminant procedures for binary variables. Zbl 1095.62508
Asparoukhov, Ognian K.; Krzanowski, Wojtek J.
2001
Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. Zbl 0956.62048
Gower, J. C.; Krzanowski, W. J.
1999
Antedependence models in the analysis of multi-group high-dimensional data. Zbl 0939.62057
Krzanowski, W. J.
1999
Signal detection in underwater sound using wavelets. Zbl 0916.62071
Bailey, Trevor C.; Sapatinas, Theofanis; Powell, Kenneth J.; Krzanowski, Wojtek J.
1998
An introduction to statistical modelling. Zbl 0968.62001
Krzanowski, Wojtek J.
1998
Subspace projection for multivariate selection problems. Zbl 0899.62082
Krzanowski, W. J.
1998
Assessing error rate estimators: The leave-one-out method reconsidered. Zbl 0877.62063
Krzanowski, W. J.; Hand, D. J.
1997
Rao’s distance between normal populations that have common principal components. Zbl 0925.62217
Krzanowski, W. J.
1996
Discriminant analysis with singular covariance matrices: Methods and applications to spectroscopic data. Zbl 0821.62032
Krzanowski, W. J.; Jonathan, P.; McCarthy, W. V.; Thomas, M. R.
1995
Multivariate analysis. Part 2: Classification, covariance structures and repeated measurements. Zbl 0949.62537
Krzanowski, W. J.; Marriott, F. H. C.
1995
Selection of variables, and assessment of their performance, in mixed-variable discriminant analysis. Zbl 0875.62265
Krzanowski, W. J.
1995
Multivariate analysis. Part I. Distributions, ordination and inference. Zbl 0855.62036
Krzanowski, W. J.; Marriott, F. H. C.
1994
Quadratic location discriminant functions for mixed categorical and continuous data. Zbl 0800.62339
Krzanowski, W. J.
1994
Ordination in the presence of group structure, for general multivariate data. Zbl 0825.62553
Krzanowski, W. J.
1994
The location model for mixtures of categorical and continuous variables. Zbl 0775.62153
Krzanowski, W. J.
1993
Attribute selection in correspondence analysis of incidence matrices. Zbl 0825.62526
Krzanowski, W. J.
1993
Between-group analysis with heterogeneous covariance matrices: The common principal component model. Zbl 0714.62051
Krzanowski, W. J.
1990
On selecting variables and assessing their performance in linear discriminant analysis. Zbl 0707.62120
Ganeshanandam, S.; Krzanowski, W. J.
1989
Nonparametric confidence and tolerance regions in canonical variate analysis. Zbl 0715.62092
1989
On confidence regions in canonical variate analysis. Zbl 0663.62066
Krzanowski, W. J.
1989
Principles of multivariate analysis. A user’s perspective. Zbl 0678.62001
Krzanowski, W. J.
1988
A criterion for determining the number of groups in a data set using sum- of-squares clustering. Zbl 0707.62122
Krzanowski, W. J.; Lai, Y. T.
1988
A comparison between two distance-based discriminant principles. Zbl 0655.62065
Krzanowski, W. J.
1987
Multiple discriminant analysis in the presence of mixed continuous and categorical data. Zbl 0589.62045
Krzanowski, W. J.
1986
The Mahalanobis distance and elliptic distributions. Zbl 0571.62042
Mitchell, Ann F. S.; Krzanowski, Wojtek J.
1985
On the null distribution of distance between two groups, using mixed continuous and categorical variables. Zbl 0558.62021
Krzanowski, W. J.
1984
Distance between populations using mixed continuous and categorical variables. Zbl 0514.62067
Krzanowski, W. J.
1983
Mixtures of continuous and categorical variables in discriminant analysis: A hypothesis-testing approach. Zbl 0539.62069
Krzanowski, W. J.
1982
Between-group comparison of principal components. Some sampling results. Zbl 0507.62056
Krzanowski, W. J.
1982
Mixtures of continuous and categorical variables in discriminant analysis. Zbl 0442.62045
Krzanowski, W. J.
1980
Between-groups comparison of principal components. Zbl 0459.62042
Krzanowski, W. J.
1979
Some linear transformations for mixtures of binary and continuous variables, with particular reference to linear discriminant analysis. Zbl 0397.62041
Krzanowski, W. J.
1979
The performance of Fisher’s linear discriminant function under non- optimal conditions. Zbl 0358.62043
Krzanowski, W. J.
1977
Canonical representation of the location model for discrimination or classification. Zbl 0335.62040
Krzanowski, W. J.
1976
Discrimination and classification using both binary and continuous variables. Zbl 0322.62075
Krzanowski, W. J.
1975
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### Cited by 682 Authors
20 Krzanowski, Wojtek Janusz 8 Ahmed, Syed Ejaz 8 Leung, Chi-Ying 7 Trendafilov, Nickolay T. 7 Volkovich, Vladimir E. 6 de Leon, Alexander R. 6 Van Mechelen, Iven 5 Gower, John C. 4 Avros, Renata 4 Barzily, Zeev 4 Hand, David J. 4 Kim, Hea-Jung 4 le Roux, Niël J. 4 Melnykov, Volodymyr 4 Oller, Josep M. 4 Schott, James R. 4 Toledano-Kitai, Dvora 4 Weber, Gerhard-Wilhelm 3 Albers, Casper J. 3 Bailey, Trevor C. 3 Bouveyron, Charles 3 Brusco, Michael J. 3 Carriere, Keumhee Chough 3 Ceulemans, Eva 3 Chitsaz, Shabnam 3 Cuadras, Carles M. 3 Fang, Yixin 3 Fortiana, Josep 3 González-Manteiga, Wenceslao 3 Hernandez, Adolfo 3 McNicholas, Paul D. 3 Mkhadri, Abdallah 3 Schenker, Nathaniel 3 Steinley, Douglas L. 3 Tangian, Andranik S. 3 Verdonck, Tim 3 Wang, Junhui 3 Zhang, Biao 3 Zhu, Xuwen 2 Adachi, Kohei 2 Adams, Niall M. 2 Anderson, Carolyn Jane 2 Baesens, Bart 2 Balakrishnan, Narayanaswamy 2 Bradshaw, David J. 2 Calabrese, Raffaella 2 Calvo, Miquel 2 Chekouo, Thierry 2 Cho, Meehyung 2 Ciampi, Antonio 2 Demidenko, Eugene 2 Depril, Dirk 2 Fanjul-Hevia, Arís 2 Filzmoser, Peter 2 Gardner-Lubbe, Sugnet 2 Girard, Stéphane 2 Greenwood, Mark C. 2 Groenen, Patrick J. F. 2 Jokiel-Rokita, Alicja 2 Jolliffe, Ian T. 2 Jun, Chi-Hyuck 2 Kim, Sungsoo 2 Lee, Jeonghwa 2 Leisch, Friedrich 2 Liao, Li-Zhi 2 Macías, Rodrigo 2 Maitra, Ranjan 2 Mitchell, Ann F. S. 2 Murphy, Thomas Brendan 2 Murúa, Alejandro E. 2 Muttlak, Hassen A. 2 Nakas, Christos T. 2 Nasroallah, Abdelaziz 2 Ng, Michael Kwok-Po 2 Pagès, Jérôme 2 Pardo-Fernández, Juan Carlos 2 Pardo, Leandro 2 Peña, Daniel 2 Pensky, Marianna 2 Pulit, Michał 2 Qannari, El-Mostafa 2 Robinson, John 2 Roy, Anuradha 2 Schepers, Jan 2 Schmid, Cordelia 2 Tiku, Moti Lal 2 Velilla, Santiago 2 Vera, José Fernando 2 Vichi, Maurizio 2 Vigneau, Evelyne 2 Villarroya, Angel 2 Wilderjans, Tom Frans 2 Zhang, Dong 2 Zhang, Lei-Hong 2 Zografos, Konstantinos G. 1 Abrahamowicz, Michal 1 Aerts, Marc 1 Airola, Antti 1 Al-Kandari, Noriah M. A. 1 Al-Momani, Marwan A. ...and 582 more Authors
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### Cited in 90 Serials
51 Computational Statistics and Data Analysis 23 Journal of Multivariate Analysis 19 Journal of Classification 19 Communications in Statistics. Theory and Methods 18 Journal of Applied Statistics 14 Communications in Statistics. Simulation and Computation 14 Pattern Recognition 13 Biometrics 13 Journal of Statistical Computation and Simulation 11 Advances in Data Analysis and Classification. ADAC 10 Journal of Statistical Planning and Inference 10 Statistics & Probability Letters 10 Computational Statistics 9 Psychometrika 7 European Journal of Operational Research 7 Statistical Analysis and Data Mining 6 The Canadian Journal of Statistics 6 Test 5 Computers and Mathematics with Applications. Part A 5 The Annals of Applied Statistics 5 Statistics and Computing 4 Biometrical Journal 4 Statistical Papers 3 Applied Mathematics and Computation 3 International Statistical Review 3 Machine Learning 3 Bernoulli 3 Journal of the Royal Statistical Society. Series B. Statistical Methodology 3 Journal of the Korean Statistical Society 3 Mathematical Geosciences 2 Biological Cybernetics 2 Annals of the Institute of Statistical Mathematics 2 Journal of Computational and Applied Mathematics 2 Statistics 2 Neural Networks 2 Journal of Nonparametric Statistics 2 Journal of the Royal Statistical Society. Series C. Applied Statistics 2 Statistical Methods and Applications 2 Journal of Statistical Theory and Practice 2 Bayesian Analysis 2 Japanese Journal of Statistics and Data Science 1 Artificial Intelligence 1 Discrete Applied Mathematics 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Metrika 1 Scandinavian Journal of Statistics 1 Information Sciences 1 Journal of the American Statistical Association 1 Journal of Econometrics 1 Journal of Mathematical Psychology 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 Metron 1 Theoretical Computer Science 1 Insurance Mathematics & Economics 1 Revue de Statistique Appliquée 1 International Journal of Production Research 1 American Journal of Mathematical and Management Sciences 1 Social Choice and Welfare 1 Information and Computation 1 International Journal of Approximate Reasoning 1 Journal of Global Optimization 1 Automation and Remote Control 1 International Journal of Computer Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Computational Optimization and Applications 1 Numerical Linear Algebra with Applications 1 International Journal of Computer Vision 1 The Journal of Artificial Intelligence Research (JAIR) 1 Journal of Computational Neuroscience 1 Computational Geosciences 1 CEJOR. Central European Journal of Operations Research 1 Applied Stochastic Models in Business and Industry 1 International Journal of Modern Physics C 1 Mathematical Geology 1 Statistical Modelling 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 North American Actuarial Journal 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Statistical Methodology 1 Journal of Zhejiang University. Science A 1 Computational & Mathematical Methods in Medicine 1 AStA. Advances in Statistical Analysis 1 Electronic Journal of Statistics 1 Journal of Agricultural, Biological, and Environmental Statistics 1 Sankhyā. Series A 1 European Actuarial Journal 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Journal de la Société Française de Statistique & Revue de Statistique Appliquée
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### Cited in 20 Fields
337 Statistics (62-XX) 72 Numerical analysis (65-XX) 42 Computer science (68-XX) 21 Biology and other natural sciences (92-XX) 18 Operations research, mathematical programming (90-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Probability theory and stochastic processes (60-XX) 6 Geophysics (86-XX) 5 Combinatorics (05-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Information and communication theory, circuits (94-XX)
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2022-05-19 22:07:05
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https://www.itl.nist.gov/div898/handbook/mpc/section4/mpc455.htm
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2. Measurement Process Characterization
2.4. Gauge R & R studies
2.4.5. Analysis of bias
Geometry/configuration differences
How to deal with configuration differences The mechanism for identifying and/or dealing with differences among geometries or configurations in an instrument is basically the same as dealing with differences among the gauges themselves.
Example of differences among wiring configurations An example is given of a study of configuration differences for a single gauge. The gauge, a 4-point probe for measuring resistivity of silicon wafers, can be wired in several ways. Because it was not possible to test all wiring configurations during the gauge study, measurements were made in only two configurations as a way of identifying possible problems.
Data on wiring configurations and a plot of differences between the 2 wiring configurations Measurements were made on six wafers over six days (except for 5 measurements on wafer 39) with probe #2062 wired in two configurations. This sequence of measurements was repeated after about a month resulting in two runs. Differences between measurements in the two configurations on the same day are shown in the following table.
Differences between wiring configurations
Wafer Day Probe Run 1 Run 2
17. 1 2062. -0.0108 0.0088
17. 2 2062. -0.0111 0.0062
17. 3 2062. -0.0062 0.0074
17. 4 2062. 0.0020 0.0047
17. 5 2062. 0.0018 0.0049
17. 6 2062. 0.0002 0.0000
39. 1 2062. -0.0089 0.0075
39. 3 2062. -0.0040 -0.0016
39. 4 2062. -0.0022 0.0052
39. 5 2062. -0.0012 0.0085
39. 6 2062. -0.0034 -0.0018
63. 1 2062. -0.0016 0.0092
63. 2 2062. -0.0111 0.0040
63. 3 2062. -0.0059 0.0067
63. 4 2062. -0.0078 0.0016
63. 5 2062. -0.0007 0.0020
63. 6 2062. 0.0006 0.0017
103. 1 2062. -0.0050 0.0076
103. 2 2062. -0.0140 0.0002
103. 3 2062. -0.0048 0.0025
103. 4 2062. 0.0018 0.0045
103. 5 2062. 0.0016 -0.0025
103. 6 2062. 0.0044 0.0035
125. 1 2062. -0.0056 0.0099
125. 2 2062. -0.0155 0.0123
125. 3 2062. -0.0010 0.0042
125. 4 2062. -0.0014 0.0098
125. 5 2062. 0.0003 0.0032
125. 6 2062. -0.0017 0.0115
Test of difference between configurations Because there are only two configurations, a t-test is used to decide if there is a difference. If $${\large t} = \left| \frac{\sqrt{N}}{{\large s}_{diff}} \mbox{Avg}_{\, diff} \right| > 2$$ the difference between the two configurations is statistically significant.
The average and standard deviation computed from the 29 differences in each run are shown in the table below along with the t-values which confirm that the differences are significant for both runs.
Average differences between wiring configurations
Run Probe Average Std dev N t
1 2062 - 0.00383 0.00514 29 -4.0
2 2062 + 0.00489 0.00400 29 +6.6
Unexpected result The data reveal a wiring bias for both runs that changes direction between runs. This is a somewhat disturbing finding, and further study of the gauges is needed. Because neither wiring configuration is preferred or known to give the 'correct' result, the differences are treated as a component of the measurement uncertainty.
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2018-06-22 03:24:17
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http://mathoverflow.net/revisions/100775/list
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In the article "La conjecture de Weil", Deligne proves that for the primitive cohomology of a universal family $f:X \rightarrow S$ for $M_{d,n}$ the moduli stack of hypersurfaces of degree $d$ in $\mathbb{P}^{n}$ (over $\mathbb{C}$ ), the monodromy representation is irreducible. Someone has told me that this result is extended by Carlson to local systems obtained as $i$-th eigenspaces of the variation of Hodge structures $(R^{n}g_{*}\mathbb{C}_{Z})i$ of the family of $d$-fold cyclic coverings $g:Z \rightarrow S$ (branched along $X$) for certain values of $d$ and $i$. I could not find the exact result in Carlson's work. Can anyone tell me for which values of $d$ and $i$, the monodromy of eigenspace is irreducible?
In the article "La de Weil", Deligne proves that for the primitive cohomology of a universal family $f:X \rightarrow S$ for $M_{d,n}$ the moduli stack of hypersurfaces of degree $d$ in $\mathbb{P}^{n}$ (over $\mathbb{C}$ ), the monodromy representation is irreducible. Someone has told me that this result is extended by Carlson to local systems obtained as $i$-th eigenspaces of the variation of Hodge structures $(R^{n}g_{*}\mathbb{C}_{Z})i$ of the family of $d$-fold cyclic coverings $g:Z \rightarrow S$ (branched along $X$) for certain values of $d$ and $i$. I could not find the exact result in Carlson's work. Can anyone tell me for which values of $d$ and $i$, the monodromy of eigenspace is irreducible?
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2013-05-23 05:17:59
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https://par.nsf.gov/biblio/10347595-origin-weak-mg-ii-higher-ionization-absorption-lines-outflows-from-intermediate-redshift-dwarf-galaxies
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Origin of Weak Mg ii and Higher-ionization Absorption Lines in Outflows from Intermediate-redshift Dwarf Galaxies
Abstract Observations at intermediate redshifts reveal the presence of numerous compact, weak Mg ii absorbers with near to supersolar metallicities, often surrounded by extended regions that produce C iv and/or O vi absorption, in the circumgalactic medium at large impact parameters from luminous galaxies. Their origin and nature remain unclear. We hypothesize that undetected satellite dwarf galaxies are responsible for producing some of these weak Mg ii absorbers. We test our hypothesis using gas dynamical simulations of galactic outflows from a dwarf galaxy with a halo mass of 5 × 10 9 M ⊙ , as might be falling into a larger L * halo at z = 2. We find that thin, filamentary, weak Mg ii absorbers (≲100 pc) are produced in two stages: (1) when shocked core-collapse supernova (SN II)–enriched gas descending in a galactic fountain gets shock compressed by upward flows driven by subsequent SN II and cools (phase 1) and, later, (2) during an outflow driven by Type Ia supernovae that shocks and sweeps up pervasive SN II–enriched gas, which then cools (phase 2). The Mg ii absorbers in our simulations are continuously generated by shocks and cooling with moderate metallicity ∼0.1–0.2 Z ⊙ but low more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10347595
Journal Name:
The Astrophysical Journal
Volume:
909
Issue:
2
Page Range or eLocation-ID:
157
ISSN:
0004-637X
1. ABSTRACT We present initial results from the Cosmic Ultraviolet Baryon Survey (CUBS). CUBS is designed to map diffuse baryonic structures at redshift z ≲ 1 using absorption-line spectroscopy of 15 UV-bright QSOs with matching deep galaxy survey data. CUBS QSOs are selected based on their NUV brightness to avoid biases against the presence of intervening Lyman limit systems (LLSs) at zabs < 1. We report five new LLSs of $\log \, N({\mathrm{ H} \,{\small I}})/{{\rm cm^{-2}}}\gtrsim 17.2$ over a total redshift survey path-length of $\Delta \, z_{\mathrm{ LL}}=9.3$, and a number density of $n(z)=0.43_{-0.18}^{+0.26}$. Considering all absorbers with $\log \, N({{\mathrm{ H} \,{\small I}}})/{{\rm cm^{-2}}}\gt 16.5$ leads to $n(z)=1.08_{-0.25}^{+0.31}$ at zabs < 1. All LLSs exhibit a multicomponent structure and associated metal transitions from multiple ionization states such as C ii, C iii, Mg ii, Si ii, Si iii, and O vi absorption. Differential chemical enrichment levels as well as ionization states are directly observed across individual components in three LLSs. We present deep galaxy survey data obtained using the VLT-MUSE integral field spectrograph and the Magellan Telescopes, reaching sensitivities necessary for detecting galaxies fainter than $0.1\, L_*$ at d ≲ 300 physical kpc (pkpc) in all five fields. A diverse range of galaxy properties ismore »
5. ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the cosmic ultraviolet baryon survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicitymore »
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2022-12-03 05:56:29
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https://math.stackexchange.com/questions/3278297/solving-frac3-75a15a1-0-4871/3278299
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# Solving $\frac{3.75^{a+1}}{5^{a+1}}=0.4871$
Having a brain fart, and don't know how to solve for the variable here. What can I do to simplify this equation to figure out a.
$$\frac{3.75^{a+1}}{5^{a+1}}=0.4871$$
Just a little bit confused as to how to isolate a here.
Attempt:
$$\frac{3.75^{a+1}}{5^{a+1}}=0.4871$$
$$\frac{3.75^a\times3.75}{5^a\times 5} = 0.4871$$
$$\frac{3.75^a\times3.75}{5^a\times 5} = 0.4871$$
$$\frac{3.75^a}{5^a} = 0.649466667$$
When it's not base e, I'm sure I use log but not entirely sure from here where to go.
We have \begin{align} 0.4871 &= \dfrac{3.75^{a+1}}{5^{a+1}} \\ &= \left( \dfrac{3.75}{5} \right)^{a+1} \\ &= \left(\dfrac{3}{4} \right)^{a+1} \end{align} Hence, taking $$\ln$$ of both sides (base $$e$$), and using the fact that $$\ln(\alpha^\beta) = \beta \ln(\alpha)$$, we get \begin{align} (a+1) \ln \left(\dfrac{3}{4} \right) = \ln(0.4871) \end{align} Hence, \begin{align} a &= \dfrac{\ln(0.4871)}{\ln(3/4)} -1 \end{align}
Of course, there is no particular reason to take logarithm to base $$e$$ (any other base is fine), but that's just something mathematicians like, as opposed to some other base.
\begin{align} \dfrac{3.75^a}{5^a} = 0.649... \end{align} If for some reason you forget that you can group the powers like I did above, you can still take $$\ln$$ of both sides. But now, you need to remember that $$\ln\left(\frac{\alpha}{\beta} \right) = \ln(\alpha) -\ln(\beta)$$. Hence, \begin{align} \ln(0.649...) &= \ln(3.75^a) - \ln(5^a) \\ &= a \ln(3.75) - a \ln(5) \\ &= a \left[ \ln(3.75) - \ln(5)\right] \end{align} Hence, you can divide to get \begin{align} a &= \dfrac{\ln(0.649...)}{\ln(3.75) - \ln(5)} \end{align} You can re combine the denominator by reversing the logarithm rules to get $$\ln(3/4)$$ in the denominator, to make it look more like my answer above. But if you're looking for an exact answer, then of course, you should express the $$0.649...$$ as an exact fraction.
$$\frac{3.75}5=0.75$$ So the equation is equivalent to $$(0.75)^{a+1}=0.4871$$ Taking logs both sides gives $$(a+1)\ln{(0.75)}=\ln{(0.4871)}$$ $$\therefore a=\frac{\ln{(0.4871)}}{\ln{(0.75)}}-1\approx1.500280368$$
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2021-07-29 16:28:47
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http://www.physicsforums.com/showthread.php?t=12965
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## elements?!?!
8. [CJ6 14.P.001.] A mass of 135 g of an element is known to contain 30.1 1023 atoms. What is the element?
carbon
hydrogen
oxyden
aluminum
This is the question on my Physics practice test for my exam tomorrow. i don't know where to even begin with this one. we haven't really gone over anything like this in class...
Kevin
PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
Can u find the no. of moles
how?
## elements?!?!
1 mole contains 6.02 * 1023 entities here atom
ok so i am guessing that the equation that i need to use is n=N/NA but how do we figure out N?
yup, N is given to u 30.1 1023
ok so we have 5 moles but now what? how do we figure out what element it is?
Do u now approx mol wt of above given elements Find the Mol wt with the help of Mole equation $$n=\frac{g}{M_0}$$ where M0 is Mol wt and g is the given wt
so i feel u got M0=135/5=27 Which belongs to ????(WHAT)
so using the equation you gave me, i have n = 5 and g = 135, so i find Mo, which came out to be 27, and in the periodic table 27 is Co. what element is Co? but i think its wrong...
now that i know the mol wt, i matched it with the periodic table and it comes out to Co, but which one of the choices are Co.
U checked in for Atomic Number Rather than atomic wt Atomic wt for Al is 27 (Aluminum) Co is Cobalt
hehe, that could help if i looked for the right thing. Thanks alot, i really appreciate your help. Kevin[:)]
Recognitions: Gold Member Science Advisor Staff Emeritus The whole point of a "mole" of an element is that it's weight in grams is equal to the weight of an individual atom in "atomic units". Once you know that you can identify the element.
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2013-05-21 04:03:38
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https://zbmath.org/?q=an:1144.34038
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## Differential equations driven by Hölder continuous functions of order greater than $$1/2$$.(English)Zbl 1144.34038
Benth, Fred Espen (ed.) et al., Stochastic analysis and applications. The Abel symposium 2005. Proceedings of the second Abel symposium, Oslo, Norway, July 29 – August 4, 2005, held in honor of Kiyosi Itô. Berlin: Springer (ISBN 978-3-540-70846-9/hbk). Abel Symposia 2, 399-413 (2007).
Theorems are proved that provide upper bounds for the solutions of differential equations driven by Hölder continuous functions with order greater than $$1/2$$.
As a corollary to these results, the existence of moments of solutions of stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than $$1/2$$ is established.
For the entire collection see [Zbl 1113.60006].
### MSC:
34F05 Ordinary differential equations and systems with randomness 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34C11 Growth and boundedness of solutions to ordinary differential equations
Full Text:
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2023-03-31 16:28:15
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https://www.lil-help.com/questions/269645/emt-final-exam
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emt final exam
# emt final exam
S
9.9k points
As an EMT you may be authorized to administer aspirin to a patient with chest pain based onyour local EMS protocols
The determination that prompt surgical care in the hospital is more important than performing time-consuming procedures in the field on a major trauma patient is based mostly onEMS research
What is the most significant factor in determining if a person will become ill from certain germsimmunity
Is HIV, more contagious than HEP B, easily transmittable in the EMS field, transmitted exclusively vis blood or HIV has no vaccineThere is no vaccine against HIV infection
CO blocks the ability of the blood to oxegenate the body because itbinds with the hemoglobin in the red blood cells
What 3 bones make up the shoulder girdle?acromion, clavicle and scapula
As the bronchus divides into smaller broncioles, the terminal ends of these smaller passages formalveoli
During each heartbeat _______ is ejected from the adult heart. This is called stroke volume.70-80 mL
The kidneys and pancreas are called retroperitoneal organs because theyare located behind the abdominal cavity
The primary organ responsible for absorption of digestion is thesmall intestine
Which of the following patients does not have an altered mental status? 1. a patient with an acute allergic reaction and dizziness 2. a diabetic who opens their eyes when you ask questions 3. a patient with a head injury who is slow to answer questions 4. a patient who overdosed and moans when he is toucheda patient with an acute allergic reaction and dizziness
If a patient develops difficulty breathing after your primary assessment you should immediatelyreevaluate his airway status
The normal respiratory rate for an adult should range from12-20 breaths per minute
Cyanosis of the skin is caused bydecreased blood oxygen
An unstable patient should be reassessed at least every5 minutes
The _______ cartilage is a firm ring that forms the inferior part of the larynxcriciod
Patients breathing shallowly may require assisted ventilation despite a normal respiratory rate. True or False?True
An oxygen cylinder should be take out of service and refilled when the pressure inside is less than500 p.s.i
How does positive pressure ventilation affect cardiac output?It increases intrathoracic pressure, which decreases venous return to the heart and causes a decrease in cardiac output.
You are attempting to ventilations with a bag mask device, after repositioning the mask several times you are unable to effectively ventilate the patient. You should....hyperextend the patients head and reattempt ventilations
A patient should be placed in the recovery position when sheis unconscious, uninjured and breathing adequately
In 2 rescuer CPR you should deliver a compression to ventilation ratio of30:2
The main benefit of using a mechanical piston or load-distributing band device for chest compressions isthe elimination of rescuer fatigue that results from manual compressions
Which of the following is NOT an indication to stop CPR once you have started? 1. pulse and respirations return 2. you are physically exhausted 3. a physician directs you to do so 4. care is transferred to a bystandercare is transferred to a bystander
The MOST appropriate treatment for a patient with a mild upper airway obstruction includesadministering oxygen and transporting immediately
Which of the following MOST accurately depicts informed consent? 1. A patient advises and EMT of why she is refusing care. 2. An EMT advises a patient of the risks of receiving treatmentAn EMT advises a patient of the risks of receiving treatment
What type of consent allows treatment of a patient who is unconscious or mentally incapacitatedimplied
A patient regains consciousness en route he tells you he is fine and does not want to go to the hospital. You shouldassess whether or not the patients mental condition is impaired
Which of the following is NOT considered protected health information (PHI) 1. patent history 2. location of calllocation of call
During your monthly internal QI meeting you review several patient care reports. You identify the patients name, age and sex. By taking this approach to the QI process you...are in violation of HIPPA because you did not remove the protected health information from the PCI beforehand
In order for a DNR to be valid it mustclearly state the patients medical problem
When faced with a patient in cardiac arrest and a living will or DNR cannot be found you should...begin resuscitation at once
Where would you MOST likely find information regarding a patients wishes to be an organ donor?drivers license
The EMT's scope of practice within his response area is defined by themedical director
When does and EMT not have a duty to act?in response to a motor vehicle crash when off duty
What is ethnocentrism?considering your own cultural values as more important when interacting with people of a different culture
Calming and reassuring an anxious patient can be facilitated bymaintaining eye contact with the patient whenever possible
In what manner should you act and speak with a patientCalm and confident
Any radio hardware containing a transmitter and a receiver that is located in a fixed location is called abase station
You attempt to contact the dispatcher while on a call with your portable radio but are unsuccessful you should...use the mobile radio in the ambulance to contact dispatch
A ______ receives messages and signals from one frequency and then automatically retransmits then on a second frequencyrepeater
What type of communications equipment functions as a radio receiver and searches across several frequenciesscanner
What is not a function of the FCC?maintaining communications equipment on the ambulance
Immediately after being dispatched on a call you shouldconfirm with dispatch that you received the call information
When providing a patient report via radio you should protect the patients privacy bynot disclosing their name
The anterior fontanelle fuses together between the ages of9 and 18 months
Which of the statements regarding psychosocial behavior in the adolescent age group is correct? 1. Antisocial behavior and peer pressure peak around 14- 16 years of age 2. Family conflict decreases as the adolescent gains control of his lifeAntisocial behavior and peer pressure peak around 14- 16 years of age
When assessing an elderly patient who has fallen and struck his ribs you must recall thathis ability to physiologically compensate for his injury may be impaired due to an inability to increase cardiac output
When communicating with an older patient it is important to remember thatage-related changes diminish the effectiveness of the eyes and ears
An infant or small childs airway can be occluded if it is overextended or overflexed becausethe occiput is proportionately larger and trachea is flexible
Which is an anatomic difference between adults and children? 1. The ribcage of an infant is less flexible than an adults 2. the infants tongue is proportionately larger than an adultsthe infants tongue is proportionately larger than an adults
According to the terminal drop hypothesismental function is presumed to decline in the 5 years preceding death
The pulse rate of a child 6 -12 years old is approximately70-120 beats per minute
An infant or small toddler would MOST likely gain trust in an individual whoprovides and organized routine environment
What should you remember about a 4 month old infant in respiratory distress?small infants are nose breathers and require clear nasal passages at all times
Which of the following is an over the counter medication? 1. Lasix 2. MotrinMotrin
Which of the following has the slowest rate of absorbtion? 1. oral 2. rectal 3. inhalation 4. subligualoral -- 1 hour slow rectal -- rapid inhalation -- quickly/rapid sublingual --minutes/ rapid
The ____ of a medication usually dictates the route by which it will be administeredform
Activated charcoal is an example ofa suspension
After administering oxygen to a 39 female having an allergic reaction who hands you her epinephrine auto injector you shouldcall medical control
An EMT may administer aspirin to a patient ifauthorization from medical control has been obtained
in ______ administration , you are administering medication to yourself or a partnerpeer-assisted
A 49 y.o male with cadiac history is experiencing an MI. His medications include nitroglycerin, Viagra, Vasotec. His BP is 140/90 his HR is 110 in addition to administering oxygen you shouldask if he took viagra in the last 24 hours
which of the following statements about the epinephrine auto injector are correct? 1. The adult auto-injector delivers .5 to 1 mg of epinephrine 2. The epinephrine auto-injector delivers a preset amount of the drugThe epinephrine auto-injector delivers a preset amount of the drug
One of the primary waste products of normal cellular metabolism that must be removed from the body by the lungs iscarbon dioxide
Pulmonary edema and impaired ventilation occur duringcardiogenic shock
Which of the following injuries would most likely cause obstructive shock? 1. liver laceration 2. cardiac tamponadecardiac tamponade
Distributive shock occurs whenwidespread dilation of the blood vessels causes blood to pool in the vascular beds
Clinical signs of compensated shock include all of the following except: 1. cool and clammy skin 2. absent peripheral pulses 3. restlessness and anxiety 4. rapid shallow breathingabsent peripheral pulses
IN infants and children a capillary refill time that is greater than ___ seconds is a sign of poor peripheral perfusion2
a 59 year old male presents with severe vomiting and diarrhea of 3 days duration. He is confused and diaphoretic his radial pulses are absent, his BP is 78/50, you give oxygen what should you do nexthe is in decompensated hypovolemic shock and needs immediate transport
You are transporting a 33 y.o male. You have addressed all immediate and potentially life-threatening conditions and have stabilized his condition with the appropriate treatment. With an ETA of 20 min to the hospital you should assess every ___ minutes5 minutes, stable currently could become unstable
A 27 y.o male has been stabbed in the chest the knife is still there, before you make physical contact with the patient it is MOST important tofollow standard precautions
A construction worker fell 30 ft. He is semi-conscious with rapid shallow respirations. His BP is 70/50, pulse is 66 skin warm and dry. In addition to spinal immobilization and rapid transport the MOST appropriate treatment for this patient includesassisted ventilations, thermal management, and elevation of the lower extremities
In contrast to the assessment of a trauma patient assessment of a medical patient ....is focused on the NOI, the patients chief complaint, and their symptoms
Which is NOT categorized as a psychiatric conditionsubstance abuse
The greatest danger in displaying a personal bias or labeling a patient who frequently calls EMS isoverlooking a potentially serious medical condition
You and your partner arrive at the residence of a 50 y.o man who complains of weakness. Your primary assessment reveals he is critically ill and will require aggressive treatment. The closest hospital is 25 miles away you shouldmanage all threats to airway, breathing anfdcirculation and consider requesting an ALS unit
In addition to looking for severe bleeding, assessment of circulation in the conscious patient should involvechecking the radial pulse and noting the color, temperature, and condition of their skin
When caring for a patient with multiple medications it is best totake all the medications with you to the hospital and document them on your patient care report
The secondary assessment of a medical patientis not practical if the patient is critically ill or your transport time is short
When performing a secondary assessment of a conscious patient with nontraumatic abdominal pain and stable vital signs you shouldfocus on their chief complaint
It is especially important to assess pulse, sensation and movement in all extremities as well as pupillary reactions in patients with a suspected _____ problemneurologic
The primary prehospital treatment for most medical emergenciesaddresses the patients symptoms more than the actual disease process
Dyspnea is MOST accurately defined asshortness of breath or difficulty breathing
In order for efficient pulmonary gas exchange to occuroxygen and carbon dioxide must be able to freely diffuse across the alveolar-capillary membrane
Which of the following is MOST characteristic of adequate breathing? 1. 22 breaths/min w/ an irregular pattern of breathing and cyanosis 2. 24 breaths/mim w/bilaterally equal sounds and pink skin24 breaths/mim w/bilaterally equal sounds and pink skin
An alert patient with a regular pattern of inhalation and exhalation and breath sounds that are clear and equal on both sides of the chest. What is this an example ofadequate air exchange
When administering supplemental oxygen to a hypoxemic patient with a chronic lung disease you shouldadjust the flow rate accordingly until you see symptom improvement but be prepared to assist hi breathing
What is SARS?a viral infection that often begins with flulike symptoms
A pleural effusion is MOST accurately defined asfluid accumulation outside the lung
Alkalosis is a condition that occurs whenblood acidity is reduced by excessive breathing
Common signs and symptoms of acute hyperventilation syndrome includetachypnea and tingling of the extremities
You are dispatched to a 21 y.o female who apparently overdosed on several narcotic medications. She is semiconscious and has slow, shallow respirations. You shouldinsert a nasopharangeal airway and begin assisted ventilations
Deoxygenated blood from the body returns to theright atrium
Which of the following is the MOST reliable method of estimating a patients cardiac output? 1. listen to heart sounds w/a stethoscope 2. access the heart rate and strength of the pulseaccess the heart rate and strength of the pulse
The posterior tibial pulse can be palpatedbehind the medial malleolus
Which of the following statements regarding the pain associated with an AMI is correct? 1. It is often described as a sharp feeling 2. It can occur during exertion or when the patient is at restIt can occur during exertion or when the patient is at rest
Ventricular tachycardia causes hypotension becasuethe left ventricle does not adequately fill with blood
Cardiogenic shock following an AMI is caused bydecreased pumping force of the heart muscle
What medication is commonly given to patients with chest pain to prevent blood clots from forming or getting bigger?aspirin
During your treatment of a patient in cadiac arrest you apply the AED analyse her cardiac rhythm and receive no shock advised message this indicates thatshe is not in ventricular fibrilation
Prior to attaching the AED to a cardiac patient the EMT shouldmake sure the chest is dry
A 67 y.o female with severe chest pain becomes unresponsive, pulseless, and apneic during transport. You shouldstop the ambulance begin CPR and attach the AED as soon as possible
The 3 major parts of the brain are thecerebrum, cerebellum and brain stem
The spinal cord exits the cranium through theformen magum
Successful treatment of a stroke depends on whether,....thrombolytic therapy is given withing 3 hours after the symptoms began
You are caring for a semiconcious man with left side paralysis. His airway is patent and his respirations are 14 breaths/min with adequate tidal volume. Treatment for this patient should includeoxygen via nonrebreathing mask, left lateral recumbent position and transport
Muscle control and body coordination are controlled by thecerebellum
Define the steps of the Cincinnati Stroke ScaleSpeech, arm drift and facial droop
Individuals with chronic alcoholism are predisposed to intracranial bleeding and hypoglycemia secondary to abnormalities in theliver
A 29 y.o. with a migraine should be transported....by dimming the lights in the ambulance and transporting w/out light and sirens
You are assessing a 49 y.o male who experienced a sudden sever headache and passed out. He is unresponsive, has slow irregular breathing. His BP is 190/94 his pulse is 50 his wife tells you he has hypotension and diabetes. He has MOST likely experienced aruptured cerebral artery
During the assessment of a semiconscious 70 y.o female you shouldensure a patent airway and support ventilations as needed
Solid abdominal organs include thespleen, kidneys and pancreas
Erosion of the protective layer of the stomach or duodenum secondary to overactivity of digestive juices results in anulcer
Most patients with abdominal pain prefer to lie in what way?lie on their side with their knees drawn into the abdomen
a 35 y.o. mildly obese woman is complaining of localized pain in the RUQ with referred pain to the right shoulder. The MOST likely cause of her pain isacute cholecystitis
What is true about the pain associated with acute abdomen?the initial pain associated with an acute abdomen tends to be vague and poorly localized
The MOST important treatment for a patient with severe abdominal pain and signs of shock includestransporting the patient without delay
Which of the following statements regarding gastrointestinal bleeding is correct? 1. Bleeding within the gastrointestinal tract is a symptom of another disease not a disease itself. 2. In the majority of cases bleeding within the gastrointestinal tract occurs acutely and is severe.Bleeding within the gastrointestinal tract is a symptom of another disease not a disease itself
Patients with abdominal pain should not be given anything to eat or drink because....substances in the stomach increase the risk of aspiration
The kidneys help to regulate BP byremoving sodium and thus water from the body
The parietal peritoneum lines the....walls of the abdominal cavity
Type 1 diabetes is a condition in which ....NO insulin is produced by the body
Diabetic ketoacidocis occurs when....insulin is not available to the body
Assessment of a patient with hypoglycemia will MOST likely reveal...combativeness
A 19 y.o male complains of "not feeling right". His insulin and syringe are on a nearby table. The patient says he thinks he took his insulin and cannot remember whether he ate. He is also unable to tell you the time or what day it is. the glucometer reads 'error" after several attempts to assess his blood glucose level. In addition to administering oxygen you should...contact medical control and administer oral glucose
During your assessment of a 19 y.o. male you are told he being treated for factor VII. This indicates that....he has hemophilia A
A 37 y.o female with a history of diabetes presents with polyuria and weakness of 2 days duration. You apply 100% oxygen and access her blood glucose level which reads 320 mg/dL. If this patients condition is not promptly treated, she will most likely develop ...acidosis and dehydration
A 28 y.o. female is found to be responsive to verbal stimuli only Her roommate tells you she was recently diagnosed with type 1 diabetes and has had difficulty controlling her blood sugar level. She further states that the patient has been urinating excessively and has progressively worsened over the last 24-36 hours. On the basis of this patients clinical presentation, you should suspect that she...is significantly hyperglycemic
Which of the following statements regarding diabetic coma is correct? 1. Diabetic coma can be prevented by taking smaller insulin doses 2. Diabetic coma typically develops over a period of hours or daysDiabetic coma typically develops over a period of hours or days
In contrast to insulin shock, diabetic coma...can only be corrected in a hospital setting
Which of the following conditions is the diabetic patient at an increased risk of ...blindness
You respond to the residence of a 55 y.o. female with a possible allergic reaction to peanuts that she ate approximately 30 min ago. The patient is conscious and alert, but has diffuse urticaria and the feeling that she has a lump in her throat. As your partner applies oxygen to the patient you should...ask her if she has prescribed epinephrine
A 75 year old man presents with a generalized rash, which he thinks may have been caused by an antibiotic that he recently began taking. He has a history of coronary artery disease, hypertension, and emphysema. He is conscious and alert, his BP is 144/94 and his pulse is 64 and regular. You auscultate his breath sounds and hear scattered wheezing, although he is not experiencing respiratory distress. In addition to administering oxygen you should....contact medical control if needed, transport the patient and monitor him for signs of deterioration
A raised swollen well-defined area on the skin that is the result of an insect bite or sting is called....a wheal
The 2 most common signs of anaphylaxis are...wheezing and widespread uticaria
Because the stinger of a honeybee remains in the wound following a sting...It can continue to inject venom for up to 20 minutes
A 19 y.o female was stung multiple times on the legs by fire ants. She states that she is allergic to them but does not carry her own epi-pen. What do you do?administer oxygen and transport
What physiologic reaction does epinephrine produce when administered?vasoconstriction and bronchodilation
Urticaria is the medical term for...hives
The effects of epinephrine are typically observed within _____ following administration.1 minute
A 38 y.o female was bitten by fire ants. She is semi-conscious, has profoundly labored breathin and a rapid thready pulse. She has a red rash on her entire body and her face is very swollen. You shouldassist her ventilations with 100% oxygen
Your paramedic partner administers atropine to a 49 y.o with bradycardia. What side effects would you expect to see?dry mucous membranes
The poison control center will be able to provide you the most information regarding the appropriate treatment for a patient with a drug overdose if you provide the center with....the name of the substance involved
Your unit is dispatched to the county jail for an intoxicated inmate. He is responsive to painful stimuli only and has slow shallow respirations. You should be MOST concerned that this patient....may vomit and aspirate
Airborne substances are diluted withoxygen
A 4 y.o male ingested an unknown quantity of tylenol about 20 minutes ago. After contacting medical control you should...administer up to 25 g of activated charcoal.
The major side effect associated with ingestion of activated charcoal isblack stools
A hypnotic drug is one thatinduces sleep
A 49 y.o. male presents with confusion, sweating and visual hallucinations. His wife tells you he is a heavy drinker and she thinks he had a seizure shortly before your arrival. The patient is most likely experiencing theDT's
You and your paramedic partner are caring for a patient who ingested codeine, tylenol, and Darvon. The patient is unresponsive his breathing is slow and shallow and his pulse is weak and slow. Treatment for this patient would include....assisted ventilation, Narcan and rapid transport
You are dispatched to a local greenhouse, the patient is lying on the floor. She is semi-conscious, drooling and is incontinent of urine. Her pulse is very slow. INITIAL management should include...assisted ventilations with a bag mask device
A 66 y.o man presents with bizarre behavior. His daughter tells you he did not recognize her. You patient is conscious and has a patent airway and adequate breathing. You should ask...the daughter how her father normally behaves
When assessing a patient with a behavioral crisis you shouldbe direct and clearly state your intentions
General guidelines for managing a patient with a behavioral emergency includebeing prepared to spend extra time with the patient
You respond to a call for an unknown emergency. The husband tells you she has been depressed and is locked in the bedroom where he keeps his gun. You should...remain in a safe place and request law enforcement
When assessing a patient who is displaying bizarre behavior the EMT should....consider that an acute medical illness may be causing the patients behavior.
A 40 y.o male intentionally cut his wrist. law enforcement has secured the scene. You should...calmly identify yourself to the patient.
The single most significant factor that contributes to suicide is...depression
Common causes of acute psychotic behavior include ...intense stress, schizophrenia, and mind altering substances.
Of the following which is the LEAST likely to result in a change in behavior? 1. low blood glucose levels 2. antihypertensive medications 3. exposure to excess heat or cold 4. inadequate blood flow to the brainantihypertensive medications
A 78 y.o female presents with an acute change in her behavior. She has type 2 diabetes and was diagnosed with Alzheimers 6 months ago. The patients speech is slurred and she is not alert to her surroundings. You shouldinquire about the possibility of head trauma.
The physical examination of a sexual assault victim should be ...limited to a brief survey of life threatening injuries
Which of the following conditions does not typically present with vaginal discharge? 1. chlamydia 2. gonorrhea 3. genital herpes 4. PIDgenital herpes
When documenting a call in which a female was sexually assaulted you should...keep the report concise and record only what the patient stated in her own words
General treatment for a woman with vaginal bleeding and shock following sexual assault includes all of the following except... 1. supplemental oxygen and lower extremity elevation 2. refraining from placing any dressings in the vagina 3. carefully removing any foreign bodies from the vagina 4. treating external lacerations with moist sterile compressescarefully removing any foreign bodies from the vagina
A 26 y.o female presents with heavy vaginal bleeding. She is conscious but restless. Her BP is 84/54, pulse is 120 resp 22 with adequate depth. She tells you she inserted a tampon 2 hours ago. You Should....administer high flow oxygen place a sterile pad over her vagina keep her warm elevate her lower extremities and transport without delay.
When caring for a woman who is experiencing a gynecologic emergency the EMT's main focus should be to...maintain her ABC's and transport without delay
What is rape defined as...a legal diagnosis not a medical one.
In anticipation of receiving a fertilized ovum the lining of the uterine wall...becomes engorged with blood
When a woman presents with abdominal pain or other vague symptoms the EMT is often unable to determine the nature of the problem until she ....has gathered patient history information
If a woman with vaginal bleeding reports syncope the EMT must assume that she is ...in shock
When a motor vehicle strikes a tree while traveling at 40 mph the unrestrained occupant ...remains in motion until acted upon by an external force..newtons 1st law
Evaluation of the interior of a crashed motor vehicle during extrication will allow the EMT to...identify contact points and predict potential injuries
The cervical spine is most protected from whiplash style injuries when theheadrest is properly positioned
Approximately 25% of severe injuries to the aorta occur duringlateral collisions
A small compact car was involved in a rollover crash and the roof is significantly collapsed. The patient reports severe pain in his neck and the top of his head. What injury mechanism is MOSt likely responsible for his condition?compression of his head against the roof
When evaluating the MOI of a car vs. pedestrian collision you should first ...approximate the speed of the vehicle that struck the pedestrian
A 15 was struck by a car while riding her bicycle. She was wearing a helmet and was thrown to the ground. In addition to the ABC's it is MOST important for you to ...stabilize the entire spine
Internal injuries caused by gunshot wounds are difficult to predict because...the bullet may tumble or ricochet within the body
A young male sustained a gunshot wound to the abdomen during an altercation with a rival gang member. As you are assessing and managing the airway you should control the obvious bleeding and ....assess for an exit wound
During your assessment of a blast victim with a depressed area in the front of his skull. This injury is MOST likely from which blast wave?Secondary phase.
Which of the following body systems or components is the LEAST critical for supplying and maintaining an adequate blood flow to the body? 1. and effectively pumping heart 2. an intact system of blood vessels 3. adequate blood in the vasculature 4. the filtering of blood cells in the spleenthe filtering of blood cells in the spleen
WHich organ can tolerate inadequate perfusion for up to 2 hours?skeletal muscle
In which of the following situations would external bleeding be MOST difficult to control? 1. femoral artery laceration and a BP of 140/90 2. jugular vein laceration and systolic BP of 90femoral artery laceration and a BP of 140/90
A fractured femur can result in the loss of _____ or more of blood into the soft tissues of the thigh.1 L
A 67 y.o. male presents with weakness, dizziness and melena that began approximately 2 days. He denies a history of trauma. His BP is 90/50 and pulse is 120. You should be most suspicious that this patient is experience..gastrointestinal bleeding
GI bleeding should be suspected if patient presents with...hematemesis ( vomited blood), melena ( blood in stools)
A 39 y.o male accidentally cut his wrist how would you treat this patient?control bleeding with direct presure
You arrive at the home of a 50 y.o. with severe epistaxis. As you are treating her it is MOST important to recall that...the patient is at risk for vomiting and aspiration
A 43 y.o is experiencing a severe nosebleed his BP is 190/110 his HR is 90 beats and bounding. Appropriate treatment for this patient includespinching the nostrils and having him lean forward
Bleeding from the nose following head trauma is a sign ofa skull fracture and should not be stopped
The germinal layer of the epidermis contains pigment granules that are responsible for skin...color
A 30 Y.o. male trapped his arm. Your assessment reveals that his arm is obviously deformed and swollen and is cold, and pale. Further assessment reveals an absent radial pulse. You should be MOST concerned that this patient has...compartment syndrome
Which open soft tissue injury is limited to superficial layer of the skin and results in the least amount of blood loss?abrasion
What is a laceration?a jagged cut caused by a sharp object or blunt force trauma.
Which of the following statements regarding penetrating injuries is correct? 1. External bleeding may be minimal but internal injuries can be extensive. 2. The degree of internal injury can often be estimated by the external injuryExternal bleeding may be minimal but internal injuries can be extensive.
A 35 y.o has an evisceration to the LQ of the abdomen. After managing his ABC's and assessing for other life threatening injuries how do you care for this wound?cover it with a moist sterile gauze dressing and secure with an occlusive dressing
Which is a severe burn in a 35 y.o patient. 1. circumferential partial-thickness burn to the chest 2. full thickness burn to 5% of the body surface areacircumferential partial-thickness burn to the chest
A burn that is characterized by redness and pain is classified as a ...first degree burn
Burns to a pediatric patients are generally considered more serious than burns to adults becasue...pediatric patients have more surface area relative to total body mass
When treating a partial thickness burn you should..avoid the use of creams lotions or antiseptics
The superficial temporal artery can be palpated where?just anterior to the tragus
What is the function of the sternocleidomastoid muscle?allows movement of the head
What is the vitreous humor?a clear jelly-like substance near the back of the eye that cannot be replaced if it is lost
The conjunctiva are kept moist by fluid produced by the ....lacrimal gland
Facial injuries should be identified and treated as soon as possible becauseof the risk of airway problems
A woman was in a moor vehicle crash. She has glass impaled in her left eye and a large laceration of her left forearm with active venous bleeding . As your partner stabilizes her head you should....apply direct pressure to her arm wound
The term hyphema is defined asblood in the anterior chamber of the eye
Following blunt trauma to the face a 21 y.o complains of a severe headache and a decreased ability to move his eyes, The patients clinical presentation is MOST consistent with ....a blowout fracture
A patient who is complaining of seeing flashing lights, specks or floaters in his or her field of vision has MOST likely experienced...a detached retina
a 44 year old male sustained a laceration to his left ear during a minor car accident. Your assessment reveals minimal bleeding. Appropriate care for this injury includes...padding between the ear and the scalp
What do motor nerves do?they carry information from the central nervous system to the the muscles
Which of the nerves allow sensory and motor impulses to be sent from one nerve directly to another>connecting
When activated the sympathetic nervous system produces what effects?increase in heart rate, shunting of blood to vital organs, dilation of the bronchiole smooth muscle
The cervical spine is composed of ____ vertabrae7
Rapid deceleration of the head such as when it impacts the windshield causes....compression injuries or bruising to the anterior portion of the brain and stretching or tearing to the posterior portion of the brain (coup counter coup)
The MOST common and serious complication of a significant head injury isacute hypotension
An epidural hematoma is MOST accurately defined asbleeding between the skull and dura matter
Bleeding within the brain tissue itself is called aintracerebral hematoma
Once a cervical collar has been applied to the patient with a possible spinal injury, it should not be removed unless...it causes a problem managing the ABCs
A female patient with a suspected spinal injury is breathing with a marked reduction in tidal volume. The MOST appropriate airway management for her includes...assisting ventilations at an age appropriate rate
Very young children tend to breathe predominately with their diaphragm becausetheir intercostal muscles are not fully developed
Elevation of the rib cage during inhalation occurs whenthe intercostal muscles contract
What nerves control the diaphragm?phrenic
Irritation or damage to the pleural surfaces that causes sharp chest pain during inhalation is called...pleurisy
A patient who presents with profound cyanosis following a chest injury...requires prompt ventilation and oxygenation
While jogging a 19 y.o. experienced an acute onset of shortness of breath and pleuritic chest pain. He is conscious and alert with stable vital signs. Your assessment reveals that he has diminished breath sounds over the left side of the chest. You should...a total collapse of the affected lung
You respond to a 40 y.o. who was assaulted by her husband. She is semiconscious with severely labored breathing. Further assessment reveals a large bruise to the left anterior chest, jugular vein distention, and unilaterally absent breath sounds. As your partner is assisting her ventilations you should...immediately request ALS support
Following a stab wound to the left anterior chest a 25 y.o. presents with decreased LOC and signs of shock . What assessment finding would increase your index of suspicion of cardiac tamponade?engorged jugular veins, narrowing pulse pressure and muffled heart sounds
A flail chest occurs when ...a segment of the chest wall is detached from the thoracic cage
Pleural fluid is contained between thevisceral and parietal pleurae
The phrenic nerves control the diaphragm and exit the spinal cord at...C3, C4, and C5
If the patient with a chest injury is only able to inhale small amounts of air per breath he .....must increase his respiratory rate to maintain adequate minute volume
Hemoptysis is defined ascoughing up blood
How would you treat paradoxical movement of the chest wall?stabilize the chest wall with a bulky dressing
You have sealed the open chest wound of a patient stabbed in the anterior chest. Your assessment reveals that he is experiencing increasing respiratory distress and tachycardia and is developing cyanosis. You should...partially remove the dressing
While jogging a 19 y.o male experienced an acute onset of shortness of breath and pleuritic chest pain. He is conscious and alert with stable vital signs . You assessment reveals that he has diminished lung sounds over the left side of the chest. You shouldadminister oxygen and transport to the hospital (spontaneous pneumothorax)
A rapid irregular pulse following blunt trauma to the chest is MOST suggestive of a...myocardial contusion
A 19 y.o male is unresponsive, apneic and pulseless after being struck in the center of the chest with a softball. Based on the MOI what MOST likely occurred?ventricular fibrillation when the impact occurred during the critical portion of the cardiac cycle (commotio cordis)
You arrive at the scene of a motor vehicle crash. The patient was removed from the vehicle prior to your arrival. The patient is unconscious, tachycardic, and diaphoretic. Your assessment reveals bilaterally clear and equal breath sounds, a midline trachea, and collapsed jugular veins. You should most suspicious that this patient has experienced...a laceration of the aorta
What are the hollow organs of the abdomen?bladder, ureters, stomach
Compression injuries to the abdomen that occur during a motor vehicle crash are typically due to a...poorly placed lap belt
While assessing a patient who struck a tree head on with an airbag deployment. You should...lift the airbag and look for deformity of the steering wheel
Because the depth of an open abdominal wound is often difficult to determine, what you assume and do?rapid transport and assume organ damage
A 20 y.o male was accidentally shot in the RUQ with an arrow. Prior to your arrival the patient removed the arrow. What should you assume about the injury?assume the arrow injured an internal organ
Early bruising following abdominal trauma often manifests asred areas of skin
You are dispatched to a residence for a young female who was kicked in the abdomen by her boyfriend. While enroute to the scene you should ask the dispatcher if....law enforcement is at the scene
A 40 y.o male presents with severe abdominal pain following blunt trauma, He is diaphoretic, intensely thirsty, and has a weak rapid pulse. Appropriate treatment for this patient includes...treating for shock, prompt transport, and administering oxygen
a 54 y.o male experienced an avulsion of his penis when his foreskin got caught in his zipper. Besides calling a Rabbi what is the MOST appropriate treatment?applying direct pressure with a dry sterile dressing
A 33 y.o. female was sexually assaulted. Police are on scene. As you are talking to her you notice an impressive amount of blood in the groin area, Her BP is 98/55 pulse is 130 and resp. are 24. You should...control any external bleeding, administer oxygen and transport at once.
The musculoskeletal system refers to the...bones and voluntary muscles of the body
A ____ is a musculoskeletal injury in which a partial or temporary separation of the bone ends as well as a partial stretching or tearing of the supporting ligaments.sprain
An open fracture is defined as ...the overlying skin is no longer intact
How long does compartment syndrome take to develop?typically 6-12 hours after the injury
When should the EMT splint an injured limb in the position of a deformity?if resistance is encountered or if the patient experiences severe pain.
The MOST significant hazard associated with splinting is...delaying transport of a critically injured patient
A 17 y.o male has a dislocated shoulder. He is holding his arm in a fixed position away from his body. There is an obvious anterior bulge to the area of injury, You should...assess distal pulse, motor and sensory functions
A 45 y.o. female was involved in a car accident she is complaining of knee pain. She is conscious and alert. There is visible damage to the dashboard. IN addition to fractures or dislocations of the knees you should be MOST suspicious for ....posterior hip dislocation
Femoral shaft fractures can result in up to ____ mL of internal blood loss.1000
The MOST common and significant complication associated with fractures or dislocations of the knee is...neurovascular compromise
Hypothermia occurs when the core body temperature falls below....95 degrees
The bodys natural protective mechanisms against heat loss are...vasoconstriction and shivering
What terms are used to describe a cold body part that is not frozen?frostnip, chilblains, trench foot
A frostbitten foot can be identified by the presence of ...mottling and blisters
Hypothermia can worsen bleeding secondary to ...blood clotting abnormalities
In order for sweating to be an effective cooling mechanism it must be able to what?evaporate from the body
High humidity reduces the bodys ability to lose heat through...evaporation
Signs of LATE heatstroke include...a weak and rapid pulse
You find a male floating face down in the water you should FIRST...move him to a supine position
The MOST prominent symptom of decompression sickness is....abdominal or joint pain
As you and your partner are carrying a patient down a flight of stairs in a stair chair you feel a sharp pain in your lower back. you should....stop the move and request additional lifting assistance
When using a body drag to pull a patient who is on the ground you should....kneel to minimize the distance you have to lean over
To avoid injury when pushing a patient or other object you should,,,avoid pushing the patient with your elbows fully extended
When should you use the rapid extrication technique?a patient who blocks access to another seriously injured patient, a patient who needs immediate care that requires a supine position, a patient whose condition requires immediate transport to the hospital
A 56 y.o female is found supine in a narrow hallway how should you move this patient?extremity lift
In contrast to a typical wheeled ambulance stretcher a bariatric stretcher includes...increased stability due to a wider wheelbase, can carry up to 850 lbs and 1600 on the ground
You have 2 patients who were involved in a motor vehicle accident. One with neck pain and back pain. and the other with a deformed femur. The patient with the deformed femur states that he does not want to be placed on a hard board nor does he want a collar around his neck, What is the MOST appropriate and practical method of securing these patients and placing them in the ambulance?immobilize the patient with neck and back pain on a long backboard and place him on the wheeled stretcher, place the patient with the deformed femur on a folding stretcher secured to the squad bench
An unrestrained patient is sitting in his car after a crash. He is conscious and alert has no visible trauma and is complaining of neck and back pain, Before removing him from the car you should...apply a cervical collar and immobilize him with a vest style device
When moving a conscious and weak patient down a flight of stairs you should...place the wheeled stretcher at the bottom of the stairs and carry the patient down the stairs in a stair chair
It is essential you _______ your equipment after each call to prevent the spread of disease.decontaminate
Equipment and supplies that are carried on an ambulance should be stored....according to the urgency and frequency of their use.
Minimum airway and ventilation equipment that should be carried on every ambulance include what?various sizes of oral and nasal airways, mounted and portable suction devices, adult and pediatric bag mask devices
Immediately upon arriving at the scene of an emergency call involving a traumatic injury you should notify the dispatcher of your arrival and then...observe the scene for safety hazards
The main objective of traffic control at the scene of a motor vehicle accident is to...warn oncoming traffic and prevent another crash
When transporting a patient to the hospital you should...be safe and get the patient to the hospital in the shortest practical amount of time
When transporting a patient who is secured to a backboard it is important to...place deceleration straps over the patients shoulders
If you properly assess and stabilize a patient at the scene, driving to the hospital with excessive speed....will decrease your reaction time
You are dispatched to a patient with chest pain you are unfamiliar with the address and a police officer offers to guide you to the scene. You should....turn off your lights and carefully follow the police office to the scene
It is 10:30 pm you have requested air medical transport.When you arrive the the LZ you should....survey the scene for power lines and other hazards
Typically medivac helicopters fly between...130 and 150 mph
A critical function of the safety officer is to...stop an emergency operation whenever a rescuer is in danger
As a triage supervisor you...must not begin treatment until all patients have been triaged
The ____ area is where incoming ambulances meet and await further instructions at the scene of a mass casualty accidentstaging
What are some injures or conditions that would be classified as first priority (red-tag)?severe medical problems, any airway or breathing difficulty, uncontrolled or severe hemorrage
You and your partner arrive at the scene where a truck has crashed into a small building injuring 8 people. You immediately request additional ambulances and begin the triage process. The first patient that you triage is a young female who is unconscious and apneic. She had an open head injury and her pulse is weak and thready, You should,,,,assign her a low priority and continue triaging
A tour bus has overturned, resulting in numerous patients. When you arrive you are immediately assigned to assist in the triage process. #1 is a middle-aged man with respiratory distress, chest pain, and a closed deformity to his right forearm. #2 is a young female who is conscious and alert but had a bilateral femur fracture and numerous abrasions to her arms and face. #3 is an older woman who complains of abdominal pain and has a history of cardiovascular disease. #4 is unresponsive not breathing has a weak carotid pulse and a grossly deformed skull. What triage category would you put each of them in?#1-- red, #2--delayed, #3--red, #4 --- black
A carboy is a container that would most likely be used to store and transport ...corrosives
Placards and labels on a storage container are intended to...give a general idea of the hazard inside that particular container
What is a correct statement about hazardous materials in relation to other chemicals?some substances are not hazardous by themselves but become toxic when mixed with another chemical
You are approaching an overturned tanker truck to assess the driver who appears to be unconscious. As you get closer to the vehicle you note the smell of noxious fumes and find you are in the midst of a vapor cloud. What should you do?Exit the area immediately and gather information for the hazmat team
If a pregnant patient requires spinal immobilization you should secure her to the backboard then...elevate the right side of the board with rolled towels or blankets
Braxton-hicks contractions are characterized by...alleviation of pain with movement or changing positions
by the20th week of pregnancy the uterus is typically at or above the level of the mothersbelly button
Abruptio placenta occurs whenthe placenta prematurely separates from the uterine wall
What questions would you ask a mother to determine if she will deliver in the next few minutes?When are you due, is this your first baby, do you feel the urge to push
What are the components of an Apgar scorepulse, activity, grimace
What are the normal physiologic changes that occur to the mothers respiratory system during pregnancy?increased respiratory rate and decreased respiratory reserve
When the mother is experiencing a contraction you should instruct her to...take quick short breaths
Following the delivery of a full term baby you have have properly cared for the baby and have cut and clamped the umbilical cord. During transport you note that the mother is experiencing moderate vaginal bleeding. You should...firmly massage the uterine fundus with a circular motion
You are assessing a 25 y.o who is 39 weeks pregnant. She is experiencing regular contractions that are approximately 3 min apart and states her amniotic fluid sac broke 2 hours ago. After taking the standard precautions you should...assess her for crowning
If the situation allows a child should be transported in a car seat if he or she weighs less than40 pounds
Submersion injuries in the adolescent age group are MOST commonly associated withalcohol
Cardiac arrest in the pediatric population is MOST commonly the result ofrespiratory or circulatory failure
children with N meningtides would MOST likely present withcherry red spots with a purplish rash
When inserting the oropharyngeal airway in an infant or child you should...depress the tongue with a tongue depressor
What groups are have the most risk of getting meningitis?newborns, geriatrics, males, children with shunts
What is the MOST common symptom of a head injury to a child vs and adult?nausea and vomiting
Signs of a severe airway obstruction in an infant or child include...an ineffective cough
In most children febrile seizures are characterized bygeneralized tonic-clonic activity a duration of less than 15 minutes and a short or absent postictal state
Blood loss in a child exceeding ______ of his total blood volume significantly increases the risk of shock25%
Which of the following organs or tissues can survice the longest w/out oxygen? 1. muscle 2.heart 3. liver 4, kidneysmuscle
A 29 y.o male with a head injury opens his eyes when you speak to him, is confused as to the time and date, and is able to move all of his extremities on command. His glascow coma scale is...13
You respond to a cal for a female pedestrian who has been struck by a car. As you partner maintains manual stabilization of the head you perform a primary assessment. She is conscious, has ineffective breathing and has blood secretions in her mouth you should...immediately suction her airway
Your ability to remain awake is a function of the...reticular activation system
Which of the following patients is breathing adequately? 1. conscious male with resp of 19 min pink skin 2. conscious female w/ facial cyanosis and rapid shallow resp. 3. conscious male w/resp of 18 min and reduced tidal volume 4. an unconscious 52 y.o female w/ snoring resp and cool pale skinconscious male with resp of 19 min pink skin
BLS is defined asnoninvasive emergency care that is used to treat conditions such as airway obstruction, respiratory arrest and cardiac arrest
a 51 y.o female presents with a sudden onset of difficulty breathing. She is conscious and alert and able to speak in complete sentences, Her resp. are 22 and regular you should...administer 100% oxygen via a non rebreathing mask
in infants and small children skin skin color should be assessed where?palms and soles
The goal of the primary assessment is to...identify and rapidly treat all life-threatening conditions
An appropriate demonstration of professionalism when your patient is frightened demanding or unpleasant is to...continue to be non-judgmental compassionate and respectful
A 5 y.o boy has fallen and has as severe deformity of the forearm near the wrist. He has probably sustained a fracture of the : 1. proximal forearm 2. superior forearm 3. dorsal forearm 4. distal forearmdistal forearm
Abnormalities in metabolizing glucose are MOST likely caused by disfunction of the...pancreas
a 60 y.o males is found unresponsive pulseless and apneic you shouldbegin CPR until and AED is available
Trendelenburgs position is MOST accurately defined as asupine position with the legs elevated 6" to 12" higher than the head
A critical incident stress debriefing should be conducted no longer than ___ hours following the incident72
What is the minute volume of a patient with a tidal volume of 150ML and a resp rate of 16 per min8000 ML tidal volume x frequency
While providing care to a patient blood got onto the stretcher. Because the stretcher was properly cleaned a virus was transmitted to another EMT. What route of transmission does this describe?indirect
while enroute to the scene of a shooting the dispatcher advises you that the caller states that the perpetrator has fled the scene. You shouldconfirm this information with law enforcement personnel at the scene
Structure of the lower airway include..alveoli, trachea, broncioles
You are dispatched to a residence where a middle aged man is found unconscious in his front yard. You find him in the prone position. What is your first action?Log roll him as a unit to a supine position
In MOST cases cardiopulmonary arrest in infants and children is caused byrespiratory arrest
When you us the palpation method to obtain a blood pressure the measurement you obtain is thesystolic BP
Laypeople are often trained to perform what skills?one or two rescuer CPR, splinting of a possible fracture, control of life threatening bleeding
Several attempts to adequately open a trauma patients airway with a jaw thrust maneuver have been unsuccessful, You shouldcarefully perform the head tilt chin lift maneuver
Large amounts of adenosine triphosphate (ATP) is generated whenthe cells function with adequate oxygen
A young male sustained a gunshot wound to the abdomen as your partner is assessing and managing his airway you should control the obvious bleeding and....assess for an exit wound
a utility worker was electrocuted he fell about 20 feet and is lying unconscious on the ground the power line is across his chest you shouldrapidly assess the patient after ensuring that the power line is not live
During an altercation at a bar two patrons got into a fist fight. One was struck in the mouth and refuses EMS care the second one has a small laceration to her knuckle and also refuses EMS cares. Who is at the most risk for infection?the one with the laceration to her knuckle
The direct carry is used to transfer a patient ..from a bed to am ambulance stretcher
Which injury would be MOST likely to occur as a direct result of the third collision in a motor vehicle crash? 1. flail chest 2. aortic ruptureaortic rupture
As red blood cells clump together to form a clot _______ reinforces the clumped red blood cellsfibrinogen
Following blunt trauma to the abdomen a 21 y.o female complains of LUQ pain with referred pain to her left shoulder, Your assessment reveals that her abdomen is distended and tender to palpation, On the basis of these findings you should be MOST suspicious of injury to the ....spleen
Patients develop septic shock secondary to...poor vessel function and severe volume loss
A 21 y.o male was thrown over the handlebars of his motorcycle. He was wearing a helmet. He is conscious but restless and has closed deformities to both of his femurs,. His skin is pale, his HR is rapid and weak,and his resp are rapid and shallow. In addition to applying high flow oxygen and protecting his spine you should...bind his legs together on the backboard keep him warm, and transport without delay
The MOST appropriate carrying device to use when moving a patient across rough or uneven terrain is...a basket stretcher
When the body senses a state of hypoperfusion the sympathetic nervous system releases epinephrine the effect of which includetachycardia
According to the rule of palms the palm of the hand is equal to ___% of his total BSA.1%
Which of the following is the LEAST critical for supplying and maintaining adequate blood flow to the body? 1. an effectively pumping heart 2. an intact system of blood vessels 3. adequate blood in the vacsculature 4. the filtering of blood cells in the spleenthe filtering of blood cells in the spleen
When assessing a patient who experienced a blast injury it is important to remember that...primary blast injuries are the most easily overlooked
In order to facilitate a safe and coordinated move the team leader shoulduse preparatory commands to initiate any moves
A 30 y.o male sustained a stab wound to the neck. During your assessment you should be MOST alert forairway compromise
when immobilizing a patient to a longboard you shouldensure that secure the torso before securing the head
A 22 y.o was ejected form her car when she hit a tree as you approach you notice obvious closed deformities to both her femurs,she is not moving and does not appear to be conscious you should...stabilize her head and perform a primary assessment
A 40 y.o male presents with severe abdominal pain following blunt trauma. He is diaphoretic, intensely thirsty and has a weak rapid pulse. Appropriate treatment for this patient includes...covering him with a warm blanket, prompt transport, administering supplemental oxygen
Coordination of balance and movement is controlled by thecerebellum
A subluxation occurs whena joint is incompletely dislocated
Shock is result ofhypoperfusion to the cells of the body
The MOST common and serious complication of a significant head injury is acerebral fracture
A football player was struck in the right flank area just below the posterior rib cage. He complains of sever pain and point tenderness in the area. Your assessment reveals that there is a small amount of blood in his underwear. You should be MOST suspicious for...blunt injury to the kidney
Which of the following medications increases a persons risk of a heat-related emergency? 1. Motrin 2. diureticsdiuretics
An EMT would be MOST likely to be held liable for abandonment if she did not...make provisions for continued care of an injured patient
The bodys natural cooling mechanism in which sweat is converted to a gas is calledevaporation
A 62 y.o presents with crushing chest pain. He has prescribed nitroglycerin but states he has not taken any. after administering 100% oxygen and contacting medical control you should...assist him with his nitroglycerin unless his systolic BP is less than 100
Significant trauma to the face should increase the EMT's index of suspicion for aspinal cord injury
The upper jawbones are called themaxillae
When can a mentally competent adult withdraw his consent to be treated?at any time
In what manner should you act and speak to the patient?calm and confident
Elevation of the rib cage during inhalation occurs when ..the intercostal muscles contract
What type of consent allows treatment of a patient who is unconscious or mentally incapacitated?implied
A 33 y.o. female presents with mower abdominal pain. She is conscious and alert but in moderate pain. While your partner is asking her questions about her medical history you take her vital signs. While you assess her radial pulse you are unable to locate it you should..assess the rate regularity of her carotid pulse
Subcutaneous emphysema is an indication that...air is escaping into the chest wall from a damaged lung
Syphilis is abloodborne disease that can successfully be treated with penicillin
When assessing a patient with a medical complaint which of the following would MOST likely reveal the cause of her problem? 1. history taking 2. rapid body scanhistory taking
What are the properties of epinephrine?secreted naturally by the adrenal glands, dilates passages in the lungs, constricts blood vessels, increases HR and BP
The diving reflex may allow a person to survive extended periods of submersion in cold water secondary to ...bradycardia and a slowing of the metabolic rate
The eyeball itself is referred to as theglobe
Which of the following is the MOST rapidly acting medication administration route> 1. sublingual 2. intravenous 3. subcutaneous 4. intramuscularintravenous
Ethnocentrism is defined asconsidering your own cultural values as more important when interacting with people of a different culture
Following blunt trauma to the face a 21 y.o male complains of a severe headache and decreased ability to move his eyes the patients clinical presentation is MOST consistent witha blowout fracture
A patient who presents with profound cyanosis following a chest injury requires...prompt ventilation and oxygenation
A 28 was struck in the chest with a baseball bat. He is conscious and alert and complains of severe chest pain. Your assessment reveals a large area of ecchymosis over the sternum and a rapid irregular pulse. In addition to applying 100% oxygen you should..prepare for immediate transport
Hypothermia occurs when the core body temperature falls below...95 degrees
Subcutaneous injections deliver medicationsbetween the skin and muscle
You and your partner are attempting to resuscitate a female in cardiac arrest. because of the remote location you are unable to contact medical control you should..follow locally established protocols or standing orders
What is a simple partial seizure?a seizure that begins in one extremity
The head and brain receive their supply of oxygen from the ____ arteriescarotid
A 30 y.o woman with a history of alcoholism presents with severe upper abdominal pain and is vomiting large amounts of bright red blood. Her skin is cool pale and clammy, her HR is 120 and weak, her BP is 70/50. Your MOST immediate action would be to...protect her airway from aspiration
A 59 y.o male presents with a sudden onset of severe lower back pain. he is conscious and alert but very restless and diaphoretic Your assessment reveals a pulsating mass to the left of his umbillicus. You should,..administer oxygen and prepare for immediate transport
Proper procedure for administering oral glucose to a patient includes ...assessing mental status, checking the medications exp date, requesting permission from medical control
A dissecting aortic aneurysm occurs when..the inner layers of the aorta become separated
Hypoglycemic crisis tends to develop more often and more severely in children becasue...they do not always eat correctly and on schedule
Major risk factors for AMI include....hypertension, diabetes mellitis and elevated cholesterol
An alert patient presents with a regular pattern of inhalation and exhalation and breath sounds that are clear and equal on both sides these findings are consistent with ....adequate air exchange
Patients who a miss a dialysis treatment often present with ......weakness
Dyspnea is MOST accurately defined as...shortness of breath or difficulty breathing
In a healthy individual the brain stem stimulates breathing on the basis of ...increased carbon dioxide levels
Define SARS...a viral infection that often begins with flulike symtoms
The MOST common and significant complication associated with an acute abdomen is....peritonitis
A 22 y.o female is complaining of dyspnea and numbness and tingling in her hands and feet after an argument. Her resp are 40. You should,,,provide reassurance and oxygen as needed
A transient ischemic attack (TIA) occurs when...the normal body processes destroy a clot in the cerebral artery
A 30 y.o female presents with severe acute pain to the LUQ of her abdomen. During your assessment she tells you she has sickle cell disease. You should suspect that...her spleen is enlarged because of red blood cell engorgement
The left cerebral hemisphere controls..the right side of the body
In sickle cell disease the __ __ blood cells are _____ shaped and less able to carry ____red, abnormally, oxygen
What are some signs and symptoms associated with malfunction of an implanted cardiac pacemaker?syncope or dizziness, heart rate less than 60 beats/min, generalized weakness
A 42 y.o male is found unresponsive on his couch by a neighbor,. During your assessment you find no signs of trauma and the patients blood glucose level is 75. His BP is 168/98 his HR is 45 and bounding, his resp are 8 and irregular. He is wearing a medic alert bracelet that states he has hemophillia. You should...suspect he has intracranial bleeding assist his ventilations and transport at once
A patient without a history of seizures experiences a sudden convulsion the LEAST likely cause of this seizure isepilepsy
The important aspect in the treatment of a patient with severe abdominal pain is to...provide emotional support en route to the hospital
General treatment for a woman with vaginal bleeding and shock following a sexual assault includes...supplemental oxygen and lower extremity elevation, refraining from placing and dressings into the vagina, treating external lacerations with moist sterile compresses
While using lights and siren most state laws permit an ambulance to...carefully exceed the posted speed limit
The first step in the START triage system is to...move all walking patients to the designated area
DT's is a syndrom associated with withdrawal fromalcohol
When being tailgated by a vehicle while responding to an emergency you should...slow down and allow the driver to pass
A 22 y.o male is found lying supine on the floor. Is is unconscious and cyanotic. An empty bottle of hydromorphone is found nearby. You shouldopen his airway and assess his respirations
The physical exam of a sexual assault victim should be...limited to a brief survey for life threatening injuries
An overdose of acetaminophen will MOST likely causeliver failure
What is an anatomic difference of the upper airway between a child and an adultThe infants tongue is proportionately larger than an adult
After the primary triage the triage supervisor should communicate to the medial branch officer what information?total # of patients that have been triaged, recommendations for movement to the treatment area., # of patients in each category
A 40 y.o male intentionally cut his wrist. Law enforcement is on scene. You shouldcalmly identify yourself to the patient
Why do middle adults have financial concerns?They are preparing for retirement but must still manage everyday financial concerns
What kind of diagnosis is rape?a legal diagnosis not a medical one
Your paramedic partner administers atropine to a patient with bradycardia what side effects would you expect to see?dry mucous membranes
You respond to a college campus for a young male who is acting strangely. After law enforcement has secured the scene you enter the patients room to find him sitting on the edge of his bed, he appears agitated, As you approach him you note he has dried blood around both nostrils. He is breathing adequately, his pulse is rapid and irregular and his BP is 200/110 . Treatment for this patient includesattempting to calm him and giving him oxygen if tolerated.
When assessing a 80 y.o patient in shock it is important to remember that...age related changes in the cardiovascular system may make the patient less able to compensate for decreased perfusion
When a rehabilitation area is established at the scene of a mass casualty incident it should...be in a location that prevents visualization of the scene itself
You have just delivered a major trauma patient to the hospital, shortly after departing the hospital dispatch advises you of another call. The back of the ambulance is contaminated with bloody dressings and is in disarray. you are in need of airway equipment and numerous other supplies you should,,,advise the dispatcher that you are out of service and to send another unit
When a female has reached menarche she...is capable of becoming pregnant
In general medivac helicopters should be utilized when...a patient has a time-dependant injury and traffic conditions would cause a significant delay in definitive care
Breathing is often more labor intensive in older adults becasue...the elasticity of the lungs decreases
You have a critically injured patient in the back of the ambulance ready to be transported. There are injured patients at the scene and it will be approximately 10 min before another unit arrives You should..remain at the scene until at least one other ambulance arrives
The single most significant factor that contributes to suicide isdepression
what is a common symptom of gonorrhea?painful urination
To minimize distractions and confusion when assessing an older patient you shouldhave only one EMT speak to the patient at a time
Blood pressure is usually not assessed in children younger than ___ years3
Most medical models base a pregnant womans dues date onthe first day of her last menstrual cycle
With regard to the implications of child abuse the EMT must...report all suspected cases of child abuse
The EMT should suspect left-sided heart failure in the geriatric patient who presents withtachypnea and paroxysmal nocturnal edema
Which ECG lead views the lateral wall of the left ventricle?V5 and V6
Early signs of respiratory distress in a pediatric patient include ...tachypnea, retractions, abnormal airway noise
Fractures of the pelvis in older patients often occurs as the result of a combination of...osteoporosis and low-energy trauma
What are examples of biologic agents or diseases that can be transmitted from person to person?smallpox, pneumonic plague, inhalation anthrax
A viral infection that may cause obstruction of the upper airway in a child is calledepiglottitis
When performing your secondary assessment on an older patient that has been injured it is important to ...recall that it will take a less severe MOI to cause significant injuries
Common duties and responsibilities of EMS personnel at the scene of at motor vehicle accident crash include...assigning all patients a triage category, preparing all patients for transportation, and continual assessment of critical patients
A mother who is pregnant with her first baby is typically in the first stage of labor for approximately16 hours
By the 20th week of pregnancy the uterus is typically at or above the level of the mothers...belly button
The purpose of a saline lock is tomaintain an active IV site without running fluids through the vein
Upon arriving at the scene of a motor vehicle crash you can see three patients one who is entrapped and two who have been ejected you should ...immediately request additional resources
The tip of a central venous catheter rests in thevena cava
When assessing or providing care to a patient with a developmental disability you shouldbe observant for signs of fear or reluctance from the patient
Following delivery of a full term baby during transport you note that the mother is experiencing moderate vaginal bleeding you shouldfirmly massage the uterine fundus with a circular motion
A significant number of patients with cerebral palsy also havea seizure disorder
Common signs of an allergic reaction includeabdominal cramps, flushing of the skin, itchy watery eyes, and a persistent dry cough
The hearts primary pacemaker is theSA (sinoatrial) node
Which of the following chemicals is a nerve agent? 1. phosgene 2. somansoman
The purpose of the pediatric assessment triangle is toallow you to rapidly and visually form a general impression of the child
When assessing a geriatric patient who has possibly experienced an acute ischemic stroke it is most important todetermine the onset of the patients symptoms
Once entrance and access to the patient have been provided you shouldperform a primary assessment
Nerve agents a class of chemicals called organophosphates were first discovered while in search of a superiorpesticide
A pregnant trauma patient may loose a significant amount of blood before showing signs of shock becausepregnant patients have an overall increase in blood volume
Down syndrome is a genetic defect that occurs as the result ofa triplication of chromosome 21
In contrast to a automated implanted cardioverter/defribillator an internal cardiac pacemakerregulates the patients heart rate if it falls below a preset value
Characteristic anatomic features of down syndrome includea round head with a flat occiput
When enlisting the help of an interpreter who signs it is important for you to ask the interpreter toreport exactly what the patient says and not to add commentary
A tube from the brain to the abdomen that drains excessive cerebrospinal fluid is called ashunt
EMS personnel would most likely be called to the residence of a patient receiving home health care when the home health care provider ...has noticed a change in the patients health status
In contrast to conductive hearing loss sensorineural hearing loss is caused bynerve damage
The purpose of a ventricular peritoneum shunt is toprevent excess cerebrospinal fluid from accumulating in the brain
A person is said to be obese when he or she is ____ over his or her ideal weight20-30%
To date the preferred weapon of mass destruction for terrorists has beenexplosive weapons
The primary clinical feature associated with exposure to phosgene oxime isskin blistering
Initial signs and symptoms associated with viral hemorrhagic fevers includeheadache and sore throat
You are assessing a patient who presents with respiratory distress after opening a letter of white power. This patient has most likely been exposed toanthrax
Unlike bacterial agents viral agents ...are usually not treatable
Most cases of anthrax begin withflulike symptoms
Unlike viruses and bacteria neurotoxins ..are not contagious
The type and severity of wounds sustained from incendiary and explosive devices primarily depend on thepatients distance from the epicenter of the explosion
Which of the following agents blocks the bodys ability to use oxygen and possesses an odor similar to almondshydrogen cyanide
Which of the following catheters would deliver fluid a the slowest rate? 1. 14 gauge 2. 22 gauge22 gauge
Obtaining an accurate ECG tracing can be difficult in patients experiencing a cardiac emergency becausethe patient is often diaphoretic
IT does not matter if you place the arm leads on the patients shoulders or arms as long asthe are at least 10 cm from the heart
A major benefit of using a multilumen airway device is thatmaintenance of a mask to face seal is not required
Vasovagal reactions that occur in patients receiving IV therapy are most often the result of ..the fear of needles or the sight of blood
Regardless of the size of the ET tube you will use to intubate your patient you should...have one tube smaller and one tube larger
D5W is most commonly used for...mixing and administering medications
During visualized orotracheal intubation the straight bladedirectly lifts the epiglottis and exposes the vocal cords
Sinus tachycardia is differentiated from a normal sinus rhythm by theirregular heart rate
Approximately 20 minutes after initiating an iV line of normal saline your patient complains of generalized itching and develops a rash. These are signs and symptoms of anallergic reaction
emt final
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Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$
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2019-08-21 23:14:48
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http://buddingbotanist.org/g8uu1/archive.php?tag=ratio-simplifier-a-b-c-608538
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It makes the ratios into micro ratios. To simplify a ratio of decimals we remove the decimal point and reduce the ratio to a ratio of whole numbers. Play this game to review Probability. Expressions evaluator. I want to simplify the fraction to its simplest form. of amounts. The ratio in simplest form is 4/9. To convert a ratio to 1:n form or to n:1 form enter the terms of the ratio, also in A and B, and press '1:n' or 'n:1'. 1. to measure the quantitative relationship between two or more quantities. A ratio can be a part-to-whole or a part-to-part ratio, and the methods for converting a ratio to each type of fraction are a little different. The notation A : B : C represents the ratio between the numbers A, B & C. It's popularly used in investment, profit, loss, speed, distance, volume, density, etc. Users may find the ratio between 2 or 3 numbers by using this numbers to ratio … 6th - 8th grade . If the GCF = 1 then the ratio is already in simplest form. Join Us ) , ) . Simplify 25: 30 25 : 30 2 5: 3 0. Find the greatest common factor of A and B, Use the whole number results to rewrite the ratio in simplest form, If A or B are decimal numbers multiply both values by the same factor of 10 that will eliminate all decimal places. 1:2:3; Ratio Simplifier Calculator: The ratio simplifier calculator is a user friendly and time saving online calculator to simplify the ratios in the form of A : B. the two constituents of the ratio can range from … A or B can be whole numbers, integers, decimal numbers, fractions or mixed numbers. By using this website, you agree to our Cookie Policy. Free trigonometric simplification calculator - Simplify trigonometric expressions to their simplest form step-by-step This website uses cookies to ensure you get the best experience. We can simplify a ratio by dividing both sides by the greatest common factor. 2. ratio A = 20/5 = 4. A ratio can be expressed as a fraction in a few different ways. So it's equal to 1 over 1 over 1 over phi, which is once again, just equal to phi. Simplify Ratios. To simplify a ratio enter the terms (antecedent and consequent) of the ratio in the cells marked respectively A and B, and and press 'Simplify'. 1. 3 years ago. If a mixture contains substances A, B, C and D in the ratio 5∶9∶4∶2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D. As 5+9+4+2=20, the total mixture contains 5/20 of A (5 parts out of 20), 9/20 of B, 4/20 of C, and 2/20 of D. if you enter only A and B in order to determine the C and D figures, it multiplies both A and B by 2 in order to return true ratio values for C and D. if you complete the A, B and C to find the D value, it solves the expression in which D = C * (B / A). If one value is a fraction and the other a whole number, reduce the fraction to a whole number if you can or turn the whole number into a fraction by giving it a denominator of 1. Enter ratio or screen resolution and press the calculate button. How to Convert a Ratio to a Fraction. The simplify calculator will then show you the steps to help you learn how to simplify your algebraic expression on your own. !There are 16 male teachers out of 40. Can anyone please give me hints how to … Note that a ratio and its simplified form are equivalent fractions. It's this cool number. This online simplifying ratio calculator helps you to compare ratios in a more efficient way. The full soluti… Typing Exponents. Simplify Ratios: Enter A and B to find C and D. (or enter C and D to find A and B) The calculator will simplify the ratio A : B if possible. Well phi minus 1 is 1 over phi. 1. 0. Played 339 times. 3. ratio B = B/GCF. GCF = 5 Privacy | Simplifying Fractions Calculator. But what is phi minus 1? Contact Simplify Ratio Regular Ratio Practice Problem-- Enter a:b or a to b-- Enter a:b or a to b-- Enter Total Population : Simplify the ratio 80: 200 Using our GCF Calculator, we can simplify both parts of our ratio by 40 We can express our ratio as a fraction. Mathematics. A or B can be whole numbers, integers, decimal numbers, fractions or mixed numbers. Express this ratio in simplest form! Setting Up Ratios and Simplifying DRAFT. The ratio in simplest form is 4/9. Cite this content, page or calculator as: Furey, Edward "Ratio Simplifier"; CalculatorSoup, Ratio Simplifier to simplify ratio in simplest form. Simplify ratio calculator. The calculator above will find both; continue reading to learn how to convert a ratio to a fraction. Share this entry. To simplify a fraction into a reduced fraction or mixed number use our Rules to simplify a ratio of decimals. For example, to simplify 20:45, first find the greatest common factor. There are many problems in which knowing a some ratio is necessary to find the unknown value using the following proportion. The same goes in case you input D and try to discover the C number. 2. ratio A = 20/5 = 4 The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36, The greatest common factor of 8 and 36 is 4. Please Login. Ratios - Solved Examples - Q 1 - On the off chance that a:b=2:3 and b:c=5:7, discover a:c. To improve your math skills, you may want to read BYJU’S online simplifying ratios calculator tool makes the calculation faster, and it displays the simplified form in a fraction of seconds. A : B = C : D or A B = C D. Related Calculators. Not a Member? 3. ratio B = 45/5 = 9. 49% average accuracy. The function GCD - Greatest Common Divisor is used to simplify the ratio to its lowest terms. © 2006 -2020CalculatorSoup® 3. ratio B = B/GCF GCF = 5. Simple Algebraic Ratios As is true of any ratio, an algebraic ratio compares two quantities, although … Edit. Rewrite the ratio using the results. 3. ratio B = 45/5 = 9 Factoring polynomials. A benefit-cost ratio (BCR) is an indicator showing the relationship between the relative costs and benefits of a proposed project, expressed in monetary or qualitative terms. Related Answers Rational Functions Rational Functions Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6. Ratio is the relationship that exists between the size, number, or amount of two things and that is often represented by two numbers. The ratio 3 : 8 is already simplified. To simplify two numbers A and B 3 years ago. Ratio Simplifier Free online Calculator that shows all the work for simplifying 2, 3 or more ratios! The ratio values can be positive or negative. Everything You Need to Ace Math in One Big Fat Notebook, Online Calculator | Terms | The simplified ratio is 3 : 5. If both A and B are fractions and have like denominators, multiply both fractions by the denominator to eliminate it and you are left with two whole numbers, If both A and B are fractions and have unlike denominators, find the. Approach 1: Procedure to Simplify Ratio A : B, when both are whole numbers. The full solution shows all work and the steps to get a ratio into simplest form. byarscd. Otherwise the calculator finds an equivalent ratio by multiplying each of A and B by 2 to create values for C and D. Compare Ratios and Solve for the Missing Value: Use this calculator to simplify ratios of the form A : B. Mathematics. Simplify rational expressions. 6x-15y= 135 0. Setting Up Ratios and Simplifying DRAFT. A ratio is a comparison of the value of two numbers. Free simplify calculator - simplify algebraic expressions step-by-step. This will reduce the ratio to its simplest form. Simplify the ratio calculator that shows work to find the equivalent ratio in simplest or reduced form for the given ratio with two or more numbers. You can conclude that if the greatest common factor is 1 then the ratio is already in simplest form. Simplify Calculator. To compare multiple ratios see our Type ^ for exponents like x^2 for "x squared". 14th December 2020 / by johan1. Enter any two numbers and the simplify ratio calculator will calculate ratio in simplest form. The ratio A : B is read as "A to B" and describes the relative proportion of two amounts. The ratio should be entered as numbers separated by a colon, e.g. © 2020 Online Calculator, Everything You Need to Ace Math in One Big Fat Notebook. So once again, the ratio of this smaller rectangle, of its height to its width, is once again this golden ratio… Simplify Ratio 7 : 3 7 / 65 making use of the Ratio Simplifier and get accurate results without any delay along with step by step process. enter whole numbers or decimals or fractions, convert mixed numbers to improper fractions. Find the greatest common factor (gcf) of A and B. Simplifying Ratios Calculator is a free online tool that displays the simplified form of the given ratios. ... $\frac{a+b+c}{3} - \frac{a-b+c}{6} - \frac{a+b-c}{6} =$ Quick Calculator Search. Polynomial roots. This calculator will simplify polynomials as much as possible. This calculator simplifies ratios by converting all values to whole numbers then reducing the whole numbers to lowest terms using the greatest common factor (GCF). This website uses cookies to ensure you get the best experience. Save. First, find out the factors for A and B; Later, find the greatest common factor of A and B, GCF(A, B) Next, Divide A and B each with the GCF; After doing the above step, you will get the result as … Polynomial operations. If both A and B are whole numbers, Find the greatest common factor of A and B, Then the greatest common factor of 6 and 10 is 2. A room has to be painted blue and yellow in the ratio $$2:3$$.Express the proportion of the room that has to be painted in each colour as a fraction. Solution for Simplify the expressions in (a) and (b) by 1 theorems: (a) A'(B+C)(D'E+F)'+(D'E+F) (b) (UV'+W'X)(UV'+W'X+Y'Z) (c) Fator the following by POS… Express the ratio as a fraction in simplest form: 18 ounces to 3 cups For example, to simplify 20:45, first find the greatest common factor. Use this calculator to simplify ratios of the form A : B. The fraction is like, x/y where x and y are integers. Ratio calculator. Step 1: Enter the expression you want to simplify into the editor. Rewrite the ratio using the results. They can be different types, for example, one fraction and one decimal. Rewrite the ratio using the results. Materials. The calculator works for both numbers and expressions containing variables. For example, ratios of screen resolutions such as 720 x 1280, 2560 x 1440, etc. Quiz. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. Find the greatest common factor (gcf) of A and B All rights reserved. This calculator simplifies ratios by converting all values to whole numbers then reducing the whole numbers to lowest terms using the greatest common factor (GCF). The ratio of a to b, we said, by definition was phi minus 1. I want to simplify a fraction in my application. Edit. 2. ratio A = A/GCF It is required that ratios in simplified form have whole numbers. Example. Type up to 15 numbers in the text boxes below then hit 'calculate'. The ratio values can be positive or negative. by byarscd. 2. ratio A = A/GCF. The simplified ratio is 2 : 9. 339 times. Maths 11plus Ratio 1:Simplify ratios and ratio in recipes. They can be different types, for example, one fraction and one decimal. Put the following equation of a line into slope-intercept form, simplifying all fractions. https://www.calculatorsoup.com - Online Calculators. 6th - 8th grade. Following is how to simplify ratios in simplest form step by step. Ratio Calculator. 80/40: 200/40: 2: 5: Here is an example: 2x^2+x(4x+3) Simplifying Expressions Video Lesson. Simplify Ratio 7 : 3 7 / 65 Convert 3 7 / 65 as an Improper Fraction The greatest common factor of 3 and 8 is 1. Online ratio simplifier to reduce any ratio and numbers to the lowest terms with instructions on how to simplify ratios. You need to login to view this content. Ratio Calculator. Ratio. can be simplified to the lowest forms such as 0.56:1, 1.7:1, respectively. Reduce any ratio and numbers to Improper fractions is once again, just equal to phi types. Our simplifying fractions calculator for the arithmetic sequence with a10=1 and d=−6 online tool that the. Phi minus 1 to the lowest terms with instructions on how to simplify 20:45, first find the 45th for. Our simplifying fractions calculator the value of two amounts its lowest terms faster and! x squared '' that displays the simplified form are equivalent fractions 45th term the., integers, decimal numbers, integers, decimal numbers, integers, decimal numbers, fractions or mixed.... Simplifying all fractions 65 convert 3 7 / 65 convert 3 7 / 65 convert 3 /! The following equation of a and B this calculator will calculate ratio in form! Both are whole numbers, fractions or mixed number use our simplifying fractions calculator simplified to the lowest.! Game to review Probability ratio to a ratio to its simplest form value! Value of two amounts put the following equation of a and B for x squared '' common! Screen resolutions such as 0.56:1, 1.7:1, respectively is a comparison of the ratios! A few different ways a to B '' and describes the relative proportion of two amounts you get best... Can conclude that if the gcf = 5 2. ratio a: B, both... Minus 1 Cookie Policy of a line into slope-intercept form, simplifying all fractions 's equal phi! Can be whole numbers, integers, decimal numbers, fractions or mixed numbers tool that displays simplified! Decimal numbers, fractions or mixed number use our simplifying fractions calculator two numbers 3 and 8 is.. Is ratio simplifier a b c example: 2x^2+x ( 4x+3 ) simplifying expressions Video Lesson, numbers! Two or more quantities more quantities form are equivalent fractions 25: 2! Reduced fraction or mixed numbers try to discover the C number step 1: Procedure to simplify a to... Example, one fraction and ratio simplifier a b c decimal exponents like x^2 for x squared '' work and simplify. To reduce any ratio and its simplified form of the given ratios ratio simplifier a b c a10=1 d=−6... 1280, 2560 x 1440, etc simplifying fractions calculator expression you want to simplify into the.. Containing variables work for simplifying 2, 3 or more quantities Simplifier to reduce any and! Reading to learn how to convert a ratio and numbers to the lowest forms such as 0.56:1, 1.7:1 respectively... Simplest form the text boxes below then hit 'calculate ' 1 over 1 over 1 over 1 over 1 1... We said, by definition was phi minus 1 factor is 1 then the ratio a = 20/5 = 3.... 1.7:1, respectively simplify polynomials as much as possible the ratio is necessary to find the term. Numbers or decimals or fractions, convert mixed numbers to the lowest forms as... To discover the C number 16 male teachers out of 40 where and..., fractions or mixed number use our simplifying fractions calculator already in simplest form numbers. Goes in case you input D and try to discover the C number necessary find... A or B can be simplified to the lowest terms as a fraction C number numbers, integers decimal... Factor ( gcf ) of a and B hit 'calculate ' all the work for simplifying 2, or... 5: this calculator to simplify 20:45, first find the greatest common factor ( gcf of. Tool that displays the simplified form of the given ratios 1 then the ratio is already in form... Online tool ratio simplifier a b c displays the simplified form are equivalent fractions, ratios of given! Then the ratio to a fraction in a few different ways B is as! To discover the C number 16 male teachers out of 40 2. ratio a B. Is how to simplify ratios of the form a: B is read ratio simplifier a b c a to B and!, you agree to our Cookie Policy and y are integers to review Probability numbers, or! Simplifying ratio calculator helps you to compare ratios in a fraction in a fraction 1280. Form is 4/9 knowing a some ratio is a Free online calculator that shows all the work for 2... The steps to get a ratio to a fraction in a more efficient way just to! 1440, etc both are whole numbers get the best experience is.. Solution shows all the work for simplifying 2, 3 or more ratios first... Find the unknown value using the following equation of a and B ) expressions! Types, for example, ratios of the value of two amounts of... And its simplified form are equivalent fractions game to review Probability x 1280, 2560 x 1440 etc. The relative proportion of two numbers and expressions containing variables take a simple or expression! Fraction into a reduced fraction or mixed numbers to the lowest terms with instructions on how to ratios! Fraction to its simplest form website uses cookies to ensure you get the best experience the arithmetic sequence with and! Factor ( gcf ) of a to B '' and describes the relative proportion of two numbers ratios... Expressions Video Lesson website uses cookies to ensure you get the best.! Gcf ) of a line into slope-intercept form, simplifying all fractions learn how to a... To take a simple or complex expression and simplify and reduce the ratio is a comparison of form... The best experience slope-intercept form, simplifying all fractions 45/5 = 9 the ratio to its form! Solution shows all the work for simplifying 2, 3 or more ratios the GCD... Be expressed as a fraction in a few different ways by step polynomials as much as possible decimals or,! Ratio by dividing both sides by the greatest common Divisor is used to simplify ratios in more. Was phi minus 1 the relative proportion of two amounts by dividing both sides the... ( 4x+3 ) simplifying expressions Video Lesson 45th term for the arithmetic sequence with a10=1 and.. Equivalent fractions x^2 for x squared '' Answers Rational Functions Determine the nth term rule and the... The 45th term for the arithmetic sequence with a10=1 and d=−6: 5: this calculator will simplify as... 2 5: 3 7 / 65 as an Improper fraction simplify ratios you to take simple...! there are 16 male teachers out of 40 1: Procedure to simplify 20:45, first find greatest... As 720 x 1280, 2560 x 1440, etc polynomials as much as.! If the greatest common factor: Procedure to simplify ratios remove the decimal point and reduce the a! 200/40: 2: 5: 3 7 / 65 convert 3 7 / 65 an... = 1 then the ratio to its lowest terms with instructions on how to ratio! To get a ratio into simplest form decimal numbers, fractions or mixed number use our simplifying calculator. Factor ( gcf ) of a line into slope-intercept form, simplifying all.! Common factor is 1 then the ratio of a to B, we said, by definition was minus. Numbers or decimals or fractions, convert mixed numbers whole numbers or decimals or fractions, mixed! In simplest form factor of 3 and 8 is 1 then the ratio to its simplest form 4x+3 simplifying. Fraction and one decimal 200/40: 2: 5: this calculator will calculate ratio in simplest step. Used to simplify ratios of the given ratios that a ratio to lowest! We said, by definition was phi minus 1 or decimals or fractions, convert numbers... The function GCD - greatest common factor calculator helps you to take a simple or expression! Efficient way relative proportion of two amounts all the work for simplifying,! More quantities remove the decimal point and reduce the ratio is already in simplest form discover the C number a! Decimals we remove the decimal point and reduce the expression to it 's simplest form by... Following equation of a to B, when both are whole numbers terms with instructions on how to convert ratio!, for example, one fraction and one decimal 0.56:1, 1.7:1,.... Will calculate ratio in simplest form and 8 is 1 then the ratio is already in form... A simple or complex expression and simplify and reduce the ratio is necessary to find the unknown value using following! Factor is 1 on how to convert a ratio and its simplified form a. To convert a ratio to its lowest terms with instructions on how to Play! Makes the calculation faster, and it displays the simplified form of the given ratios calculator will... With a10=1 and d=−6 reduce the ratio is already in simplest form, when both are numbers... In which knowing a some ratio is necessary to find the unknown value using the following equation of a B! To 1 over 1 over phi, which is once again, just equal to phi expressions variables! 2 5: this calculator will calculate ratio in simplest form the simplified form of the value of two.! Much as possible all work and the simplify ratio 7: 3 7 / 65 convert 3 /! Answers Rational Functions Rational Functions Rational Functions Rational Functions Rational Functions Determine the nth term rule and find greatest! Use our simplifying fractions calculator press the calculate button the gcf = 5 ratio! Of a and B ensure you get the best experience x^2 for x squared '' both... Common Divisor is used to simplify a ratio by dividing both sides by greatest... Numbers, integers, decimal numbers, fractions or mixed numbers teachers out of 40 calculator above find... How to … Play this game to review Probability instructions on how to convert a by!
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2021-07-24 08:52:01
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https://sociologicalgobbledygook.com/object-oriented-programming.html
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# Object-Oriented Programming
Object-oriented programming (OOP) isn't all that special, it's just a particular style of programming that Python is particularly well designed for. This is a short lesson, we won't cover the theory of OOP, or features you might hear about elsewhere like "inheritance"---see your reading in the P4E book for more.
However, we have to say something about OOP in order to enable you to work with many Python libraries, which expect you to be able to instantiate objects and work with them. So here's the short version.
OOP is another kind of mental model for programming. It mostly is useful for organizing the abstractions in your code. One of the key ideas is that groups of related data and functionality can be tied together in the form of objects.
A class is an abstract description of a kind of object. A class declaration will say what kind of things an object of that sort can do.
An instance is an actual object that you create and make use of in the computer's memory.
Let's look at a trivial example of a class
In [1]:
class Dog(object):
def __init__(self, temperament="normal"):
self.temperament = temperament
def bark(self, volume="loud"):
if self.temperament == "vicious":
sound = "snarl!!!"
elif self.temperament == "timid":
sound = "wimper?"
else:
sound = "woof."
if volume == "loud":
print(sound.upper())
else:
print(sound)
def meet_cat(self):
self.temperament = "timid"
self.understanding = "inferior"
1. Functions belonging to a class are called methods. You can tell that they belong to the class because they are indented under the class declaration in the first line.
2. Every method takes a special parameter to refer to the object on which it is called as the very first parameter. Here, we're using self for that, which is the Python convention, but you could use anything else. When you call these methods, you don't supply the value for the self parameter. We'll see how to call them in a moment.
3. Every class has an __init__ method. The two underscores on either side of the name show you it's a special method (known as "magic methods" in Python slang... there are a number of those, but init is the most important). This is the method that gets called when you initialize a class, that is, create an instance of that class.
4. All those references to self.temperment are creating (the first time something is assigned to it) and either mutating or examining an attribute (also called a property) of a particular instance. Let's look at some examples of instances.
In [2]:
goodboy = Dog()
doberman = Dog("vicious")
We've created two different instances of Dog and each of them has its own set of instance properties. Let's prove that by calling the bark method.
In [3]:
doberman.bark()
In [4]:
goodboy.bark("quiet")
Here are a few things you can observe from those examples:
1. We instantiate a class by calling it as if it were a function. We can pass parameters into its __init__ method that way too.
2. doberman and goodboy have different temperament properties, hence they make different sounds when we call their bark() methods.
3. We call a method on an instance by putting a period after the instance's name and before the method call. We don't pass the instance into the call, but we do pass any other parameters (like volume here) that we want.
4. Instances are totally separate. Nothing we do to goodboy affects doberman or vice versa.
We can also modify existing instance attributes, and we can access them directly with the same dot notation. Let's look at, then modify, doberman's attributes.
In [5]:
print(doberman.temperament)
In [6]:
doberman.meet_cat()
In [7]:
print(doberman.temperament)
timid
In [8]:
print(doberman.understanding)
inferior
In [9]:
doberman.bark()
WIMPER?
In [10]:
doberman.temperament = "vicious"
In [11]:
doberman.bark()
SNARL!!!
In [12]:
goodboy.bark()
WOOF.
As I said, this is the bare minimum to understand what's going on when you see OOP code. This will benefit you in the next lesson, where we'll look at some OOP code to run a simulation. It will also benefit you in interacting with Python libraries which often expect you to know how to instantiate an object, call methods on it, and access its properties.
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2021-05-13 17:46:45
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https://physics.stackexchange.com/questions/445853/does-a-non-spherical-black-hole-have-distribution-of-mass-like-an-empty-body-so
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# Does a non-spherical black hole have distribution of mass like an empty body, solid body or pointed object?
Suppose a non-spherical (say, rotating or under distortion of another gravity source) black hole.
Does it have its mass distributed as if all the mass was on its surface, or as if the mass were distributed over its volume as some density or it would behave like a body with all its mass in the center?
For a spherical BH it would be all indistinguishable, but what about a non-spherical case?
Caveat reader: the current community voting on this answer suggests it doesn't have enough disclaimers about how mixing classical and relativistic calculations is a recipe for saying things that don't make sense in an erudite-sounding way. There should be one such disclaimer after about every sentence. See also the comments. Having said that:
You can probe the mass distribution of a spherically symmetrical object by spinning it and measuring its moment of inertia, $$I = J/\Omega$$. A solid classical sphere with mass $$M$$ and radius $$R$$ has $$I_\text{solid}=\frac25MR^2$$, while a thin spherical shell with the same mass and radius has the larger $$I_\text{shell}=\frac23MR^2$$ because more of the mass is further from the rotation axis.
A rotating black hole has a nonlinear relationship between $$J$$ and $$\Omega$$. Using this notation (see also), including the gravitational radius $$R_G = GM/c^2$$, there's a parameter $$-\pi/2 \leq \Phi \leq \pi/2$$ which characterizes the rotation by
$$a = \frac{J}{Mc} = R_G\cos\Phi$$
In this case $$\Phi=0$$ (or $$a=R_G$$) corresponds to a maximally-rotating Kerr black hole and $$|\Phi|=\pi/2$$ collapses to the non-rotating case. The rotating black hole has "outer" and "inner" event horizons, with radii
$$r_\pm = R_G\cdot(1\pm\sin\Phi) = R_G \pm \sqrt{R_G^2 - a^2}$$
The outer radius, $$r_+\to2R_G$$, is the Schwartzchild radius, the size of the event horizon in the non-rotating limit. There are also angular frequencies associated with these horizons,
\begin{align} \Omega_\pm &= \frac{c\cos\Phi}{2r_\pm} = \frac{ca}{2R_G^2 \pm 2R_G\sqrt{R_G^2 - a^2}}, \end{align}
although interpreting $$\Omega$$ as the angular frequency of a rigid classical object raises some thorny questions. The definition can be solved for the specific angular momentum $$a$$:
\begin{align} a = \frac{J}{Mc} &= \frac\Omega{c} \frac{4R^2}{1 + (2R\Omega/c)^2} \quad(\text{both of }\Omega_\pm) \\ J &= \frac{4}{1 + (2R\Omega/c)^2}\times MR^2\Omega \end{align}
This suggests you might consider a "moment of inertia" $$I=J/\Omega$$ of
\begin{align} I_\text{slow} &\approx 4MR_G^2 \approx Mr_+^2 \\ I_\text{max} &= 2MR_G^2 = 2Mr_+^2 \end{align}
That's interesting. When finding moments of inertia in classical physics one always finds $$I=fMR^2$$ by dimensional analysis, and if the radius $$R$$ is the maximum size of the rotating object one always finds $$f\leq1$$. For both limits of the moment of inertia here, the coefficient is $$f\gt1$$, which (combined with the default assumption of spherical-ish symmetry) suggests that $$R_G$$ is an underestimate of the classical size of the rotating mass distribution. If you wanted a sphere of mass $$M$$ to have the same classically-computed moment of inertia as a non- or slowly-rotating black hole with that mass, you'd make a spherical shell or a uniform-density sphere with radius larger than the Schwartzchild radius of the event horizon. (A thin hollow shell would go at $$\sqrt6 R_G = 1.23 r_+$$.) The maximally-spinning black hole, which has an outer event horizon of size $$r_+=R_G$$, likewise has "too large" of a moment of inertia.
Conclusion: Using classical moment-of-inertia considerations to analyze data on $$J/\Omega$$ for rotating black holes would lead you to require that some or all of their mass distribution were outside of their event horizons.
I personally find that kind of satisfying in a hand-waving, non-mathy kind of a way. After all, we no longer interact with matter that has crossed inside of the event horizon. If the mass-energy distribution of a black hole were actually found inside of its event horizon, wouldn't we be unable to interact with it? In electromagnetism, energy is stored in the fields, and the gravitational field of a black hole certainly extends outside of its horizon, so perhaps it's not nutty to locate some of the energy density near but outside of the event horizon. But this hand-wavy interpretation probably would not survive contact with a careful relativist.
• The more basic question that the OP could have started with is "Does a non-spherical black hole have distribution of mass?" The answer is no. There is no sensible way to define such a thing. The fact that the calculation in this answer doesn't give a result that makes sense is a sign of this. If we really believed that it was meaningful to talk about where the mass is located, then we would be able to tell whether, in the case of a black hole formed by gravitational collapse, the infalling matter had reached the horizon "now," or had reached the singularity "now." We can't. – user4552 Dec 9 '18 at 23:05
• Also, I think this answer could benefit from some kind of disclaimer to the effect that there is really no $\Omega$ in the Newtonian sense; the linked answer by gj255 has a note at the end about this. – user4552 Dec 9 '18 at 23:06
• What if the sphere has imaginable radius? – Anixx Dec 10 '18 at 2:56
• @BenCrowell Your first comment would make a nice complementary answer. I've tried to address your second. – rob Dec 10 '18 at 4:18
• @Anixx Do you mean an "imaginary" radius, like if there were enough angular momentum that $a>R$ and $r_+$ became complex? I think that the usual interpretation of the Kerr metric is that $a\to R$ is an unreachable limit, in the same way that $v\to c$ is an unreachable limit in special relativity. – rob Dec 10 '18 at 4:22
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2021-02-24 22:57:51
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