text:
# Add a text in Latex in front of a result

%display latex var('A, x, y, l, alpha, beta, R, p_x, p_y'); U= Ax^(alpha)y^(beta); show(U)

this print U. But I would like to see "U(x) = ..." in a larger font that the standard one which is too small printed on a large device. More generaly , I would like to print some sentences before to disply a result

edit retag close merge delete

Sort by » oldest newest most voted

That's two (very different) questions in one.

1) To concatenate various $\LaTeX$ (math) elements, the LatexExp function is well suited. In your case,

LatexExpr("U(x)="+latex(U))

yelds:

$$U(x)= A x^{\alpha} y^{\beta}$$.

2) "I would like to print some sentences before to display a result".

Your best bet is to write your text in $\LaTeX$, using Sagetex macros to insert relevant Sage snippets and their results.

This needs some learning ; I'd recommend reading "The not so short introduction to $\LaTeX2\epsilon$" tor deciding if $\LaTeX$ is for you. If you intend to spend more than a few weeks in your life using mathematics or writing structured texts (i. e. witth explicit outlines, cross-references and/or citations, etc..), it is probably worth it.

An alternative solution is to use Sage's Jupyter notebook. This will allow you to intersspede math or graphics "cells" between tet cells, that can receive some Markdown formatting. Markdown is much lighter than $\LaTeX$, therefore faster to learn, and might be sufficient for quick n' dirty tasks. But its possibilities are much more limited.

more

I use BakomaTeX since 20 years and before other Latex systems. My question was only for a notebook presentation

( 2019-09-19 22:22:53 +0200 )edit

I use BakomaTeX since 20 years and before other Latex systems. My question was only for a notebook presentation

Since you already know $\LaTeX$, you might try to (ab)use LatexExpr to create a minipage rendering what you want. But I have trouble seeing the point...

( 2019-09-20 10:02:25 +0200 )edit

You may use something like this:

var('A, x, y, alpha, beta')
U = A*x^(alpha)*y^(beta)
text = fr"""

This is a title

This is some text explaining several
interesting things. HTML can be used
to format these lines.

Now we write an inline mathematical expression
$U(x,y)={latex(U)}$, as well as a displayed one:
$$\frac{{\partial^2 U}}{{\partial x \partial y}}(x,y)= {latex(diff(U,x,y))}$$

"""
show(html(text))

The result is similar to:

### This is a title

This is some text explaining several interesting things. HTML can be used to format these lines.

Now we write an inline mathematical expression $U(x,y)=A x^{\alpha} y^{\beta}$ as well as a displayed one: $$\frac{{\partial^2 U}}{{\partial x \partial y}}(x,y)=A \alpha \beta x^{\alpha - 1} y^{\beta - 1}$$

more


text:
# B Help with understanding the Doppler effect

#### frostysh

Summary
Why it is so 'absolute' and why the case of source of waves is different from the observers at concept level?
My answer on this question for now is that producing a waves in the medium is an event which is basically must be invariant in the any of frame of references. For an example: a brick is freely falling, then the brick suddenly splinted into two pieces — no matter from which frame will we observe this situation, the brick will not glue off together because of that. That is means an event such as destroying of bricks is absolute to the any frame of references. I have a poor understanding of the subject so in the bottom I will describe my primitive model and viewing of the situation, maybe it will help to clarify something at this level.

The article about discovering of the effect has been published by Christian Andreas Doppler in 1842, which born in Austrian Empire. The meaning of the effect is in waves properties changing due to moving of the observer or the source of waves considering to the medium.

First we may imagine very simplified picture of the model of wave process which can be described by the equation of $$\large A \left(t \right) = \left|A_{max} \right| \sin{t},$$ where $\large A(t)$ — is somekind of property value of that 'waver' during time, for an example it can be the pressure in medium, $\large \left|A_{max} \right|$ — the maximum value of the property, which is constant. And we have set up frame and measure of distance in the way of sinus period, so the function is simple.

First we may answer on question: how to imagine the wave process in the simple case? Well, it can be barely done with the next modeling: imagine an observer, a source and the medium. The source is a straight plank with the length of $\large 2 \left|A_{max} \right|$, placed perpendicular to the distance line between observer and the source, that line hit the middle of the plank. Then let's imagine the holes on that plank, from which we can shoot with a small cores, which moving with constant velocity on trajectory of a straight line parallel to the distance line. The every core have some particular value inscribed on it, $\large A \nearrow$ or $\large A \searrow$, the arrow up when the closest previous by time neighborhood of the core have a lover value $\large A$ than a core, and closest next neighborhood have larger value than a current core, the arrow down when the opposite situation. In the case of the shooting holes placed on the edge of the plank, there will be no any arrow. We should consider that $\large A \left(t \right) \nearrow \neq \large A \left(t \right) \searrow$ even the values of our property is exactly the same.
Now we can launch the first core from the port on the middle, after some time the second core from the lower edge port and after the same period of time the middle port will shoot again, and so on. Cores is moving with the same and constant speed so the distance between them will be the same in the any time. When the first core will travel the some characterizing distance $\large 2cT$, where $\large c$ — is the speed of the core, $\large T$ — some characterizing time of launchung of the absolutely identical neighborhood in time core to the particular one, $\large A \nearrow = \large A \nearrow$ if inscribed $\large A$ is equal, the nine cores will be shot at all.

If we can make a very large amount of ports, and decrease the time interval between shots then we can obtain a smooth line that build from cores, this curve which consist of the values of $\large A$ will be dedicated to the timeline and a projection of this curve on a distance line between source and observer of waves in the medium will give to us somekind a picture of the wave propagation process.

For now will be interesting to imagine what will happs when the observer of the waves is resting due to frame of reference hard connected to the medium and the source of the waves (in our model it's a plank) is moving dedicated to this frame. The direction of this movement is straight into observer with the trajectory of the distance line between them.
Let imagine a shooting of the first core from the middle port, in the moment of time $\large t = 0$, in the zero point of our coordinates, after some time we shoot second core, but the problem is that by this time the plank has traveled distance to the observer which is equal $\large vt$, where $\large v$ — is the speed of the plank related to the frame of medium and it is constant. The first core will be on distance $\large ct$ from the zero point, where $\large c$ — is the speed of the core, and in the our case $\large c > 0$, $\large v > 0$, and $\large c > v$. When some characterizing time $\large 2T$ has passed, again will be launched a nine cores but the position of the plank will be far from the zero point (in the middle of the picture).

As we can see, in this case the place of the cores will be different compared to the situation when the source is in rest to the medium (and observer), and the characterizing distance between two closest in time, absolutely identical cores, fro and example cores number $\large 1 — 5 — 9$ will be different too. But this is continuous process actually, there is no any cores with inscribed values, so how we can imagine it . . . ? It's can be imagine like the sources is chasing the waves and in the same time producing the waves continuously.

We have done some thing with an imagination, so for now we should look what can give to use some formals and sign dedicated to it, we mean algebra of course. The characterizing time of absolute repeating is called period of wave process $\large T$, dedicated distance between two peaks of the value of the amplitude $\large A$ in waves is called the wavelength $\large \lambda$, the wave propagation speed $\large c$ is the property of medium itself, it's not depends on the frame of reference we choose. The frequency $\large \nu$ is the how many period of waves was in the unit of time, for an example we have forty periods on twenty seconds, how many periods will be on the one second? The answer is two periods per second so the frequency is two hertzs in SI system of units, $\large \nu = \dfrac{2} {1 \thinspace \text{sec}} = 2 \cdot 1 \thinspace \left(\text{sec} \right)^{-1}$. Esily to see that the frequency is reciprocal to the value of period measured in the time units.
From the picture we can notice that $\large \lambda = cT$ will decrease in case of moving source of the waves, on which value it will decrease? $$\large \bigtriangleup \lambda = \lambda_{0} - \lambda = cT - \left(c - v \right)T = vT$$ The $\large \lambda_{}0$ — is a wavelength in stationary source case. But if the wavelength is changed, and the speed of wave propagation is the same then due to their law of relationship must be changed the period $$\large \lambda = \lambda_{0} - \bigtriangleup \lambda = \left(c - v \right)T_{0}$$ $$\large \left(c - v \right)T_{0} = cT,$$ $\large T$ — period of waves when source is resting due to medium and observer, from this point we can show the new period in terms of the stationary case $$\large T = \dfrac{\left(c - v \right)T_{0}}{c} = \left(1 - \dfrac{v}{c} \right)T_{0},$$ and corresponding to, the new frequency will be $$\large \nu = \dfrac{1}{ \left(1 - \dfrac{v}{c} \right)T_{0}} = \dfrac{\nu_{0}}{\left(1 - \dfrac{v}{c} \right)},$$ as easily to see the frequency enlarging comparing to the resting source situation. If the source moving in the opposite direction of the observer which is resting in the frame of medium, the distance between them is continuously increasing, so the characterizing wavelength is increasing too, and will be $$\large \lambda = \left(c + v \right)T_{0},$$ and the corresponding frequency $$\large \nu = \dfrac{\nu_{0}}{\left(1 + \dfrac{v}{c} \right)},$$it will decrease corresponding to the rest case as easily to see.

Surprising and even shoking (to me at least) in so called Doppler's effect is that the case of resting source of waves due to frame of references of medium, and moving observer in this frame is totally different! Again our observer will be a plank, transparent plank that providing measurements without any interactions with a medium, the observer is moving trough medium right to the source of wave propagation, moving with constant speed with trajectory of line of distance between them.

As we can see from the picture the characterizing distance between cores after and before the observer plank is the same. The moving of the observer is not changing wavelength. The the period of time between two absolutely same values of waver property which observer will detect will change corresponding to the rest case. Why it will change? — Because observer is moving towards wave, and the each value of property is moving like a shooting cores with constant distance between them because the speed of propagation is the very property of the medium, so the characterizing time between two absolutely the same values will change, after the detection of the first peak, the observer will travel some distance further 'towards to closing' second peak by some time, and second peak (or the core in our case) will travel some distance too by the same time. It is easily to see that distance traveled by observer and by the core after detection first peak to the time of detection the second should be related in the next way $$\large vT_{r} + cT_{r} = \lambda,$$ where $\large T_{r}$ — is the time passed from registration of the first peak to the registration of the second. We know that $\large \lambda = cT$, so we can find the new 'period' reflated to the period in rest case, from this equation like that $$\large T_{r} = \dfrac{T}{1 + \dfrac{v}{c}},$$ the corresponding frequency which is based on period $$\large \nu_{r} = \left(1 + \dfrac{v}{c} \right) \cdot \nu,$$ and this is wondering asymmetry of the Doppler's effect. Because in general $$\large \nu_{r} \neq \nu$$ where $\nu$ — is the frequency from the case of resting observer and the moving source.

So the point is, if we have medium and Doppler's effect, we can distinguish which movement corresponding to the medium is taking place, observer or source. Also it's we should note that movement of observer is actually same as the movement of the medium in this effect, but movement of source of waves is not. Or I am talking something wrong?

Related Classical Physics News on Phys.org

#### Dale

Mentor
My favorite reference on the Doppler effect is

First we may imagine very simplified picture of the model of wave process which can be described by the equation of $$\large A \left(t \right) = \left|A_{max} \right| \sin{t},$$ where $\large A(t)$ — is somekind of property value of that 'waver' during time
What you have described here is an oscillation, not a wave. To get a wave you need a function of time and space:
$$A(t,x)=A_{max}\sin(\omega t-k x)$$
Your whole plank and core thing confused me. I can’t help you with that. If you feel confused and you are using a confusing personal concept, the best approach is to discard the personal concept and learn standard concepts instead.

Without reference to the planks, in brief, what is your question?

#### frostysh

My favorite reference on the Doppler effect is

I have looked at it briefly and understand that it is for relativistic case, not the classical one, but I will read, thanx.

What you have described here is an oscillation, not a wave.
Me apologizing... Somehow not even saw such mistake. I just trying to self education and repeat my university program from long ago, so I may make such mistakes.
Your whole plank and core thing confused me. I can’t help you with that. If you feel confused and you are using a confusing personal concept, the best approach is to discard the personal concept and learn standard concepts instead.
I thought it will be more easily to imagine than a wave from a moving source.
Without reference to the planks, in brief, what is your question?
Is wavelength in the Doppler's effect changing or not? Is it changing in all variants of moving source, moving observer referred to the medium? Is Doppler effect absolute and not relative and using this effect we can distinguish what is actually moving referred to medium, observer or source?

For me understand for now, there is two cases, first moving source and there is actually appear physical wavelength change. Second case is a moving observer, which is not changing any wavelength. So the Doppler's effect is not relativistic in terms of classical relativism.

Last edited:

#### Dale

Mentor
I have looked at it briefly and understand that it is for relativistic case, not the classical one
It is for both and shows how both can be treated identically. That is why it is my favorite.

Is wavelength in the Doppler's effect changing or not? Is it changing in all variants of moving source, moving observer referred to the medium?
Yes, the wavelength changes, in general, in all cases.

Is Doppler effect absolute and not relative and using this effect we can distinguish what is actually moving referred to medium, observer or source?
All laws of physics are relative in the sense that they are the same in all reference frames. Therefore, you are always free to work the problem in the reference frame where it is simplest. For waves in a medium, this is usually the rest frame of the medium. Then, the question becomes: “in the frame of the medium, can we use the Doppler effect to unambiguously determine the speed of the emitter and the speed of the receiver?” Is this a fair restatement of the question?

#### A.T.

“in the frame of the medium, can we use the Doppler effect to unambiguously determine the speed of the emitter and the speed of the receiver?” Is this a fair restatement of the question?
Since it's the velocities that are frame dependent, not the Doppler shift, maybe better phrased as

Can we use the Doppler shift to unambiguously determine the velocities of the emitter and the receiver relative to the medium?

If that's the question, then the answer is no, because there are different combinations of emitter and receiver velocities relative to the medium, that give the same Doppler shift. But these combinations are not simply swapped velocities (no symmetry).

#### frostysh

It is for both and shows how both can be treated identically. That is why it is my favorite.
There is nothing about classic, as I can see, just a bold formula which is not giving any answers of the physical meaning of that, well at least me cannot see it there.
Yes, the wavelength changes, in general, in all cases.
It is impossible to change the wavelength without interraction with medium. Observer has no any interraction, it's a very different from the source of waves. We can imagine that like we are moving in medium near a wave in which the different values of the pressure is colored in the different colors, as we look from aside, there is distance between a colors will be the same as we are in rest correspondig to medium, but if the source of waves start to move corresponding to medium, the will be actual difference in wavelengths.
All laws of physics are relative in the sense that they are the same in all reference frames. Therefore, you are always free to work the problem in the reference frame where it is simplest. For waves in a medium, this is usually the rest frame of the medium. Then, the question becomes: “in the frame of the medium, can we use the Doppler effect to unambiguously determine the speed of the emitter and the speed of the receiver?” Is this a fair restatement of the question?
Actually I don't asked about the values of speed (which is obviously can be obtained from the formula), but something like that, you understand right.
The point is Doppler effect is not relative, it is absolute corresponding to medium, me think so, we can change frame of reference and the Doppler's effect will be not changed, the wavelength is absolute distance, it is an invariant. Actually me start to understand. The movement of source of waves is absolute in medium, like an 'ether' or something, using this movement we can distinguish absolute rest corresponding to the medium.

#### Dale

Mentor
It is confusingly phrased
Sorry about that. As near as I can tell the questions are identical, so if you think mine is confusing then I am happy using yours.

#### Dale

Mentor
It is impossible to change the wavelength without interraction with medium.
This is incorrect. The wavelength can be changed simply by changing reference frame of the analysis.

The point is Doppler effect is not relative, it is absolute corresponding to medium
Unfortunately, the word “absolute” has all sorts of negative connotations here. Can you express your question without it? I am pretty sure you do not intend it to have the negative connotation that it evokes.

#### A.T.

The point is Doppler effect is not relative, it is absolute corresponding to medium,
You have simply replaced "relative to..." with "absolute corresponding to...". What is the difference?

#### frostysh

If that's the question, then the answer is no, because there are different combinations of emitter and receiver velocities relative to the medium, that give the same Doppler shift. But these combinations are not simply swapped velocities (no symmetry).
Can you prove it? Me think it's terribly wrong, the point is we are measuring the wavelength, and definitely know the speed of the source of waves corresponding to medium. The speed of observer can do no change to the wavelength, only to detected period of wave.

Emmiter and reciever is not summetric, we cannot "switch" them in Doppler's effect and obtain the same effect. Or maybe me wrong... But it is interesting, indeed.

#### Dale

Mentor
Can we use the Doppler shift to unambiguously determine the velocities of the emitter and the receiver relative to the medium?

If that's the question, then the answer is no,
Can you prove it?
That the answer to the question formulated by @A.T. is “no” is almost trivial to prove. There are two unknowns and only one equation. There is generally no unique solution to one equation in two unknowns.

#### frostysh

This is incorrect. The wavelength can be changed simply by changing reference frame of the analysis.

Unfortunately, the word “absolute” has all sorts of negative connotations here. Can you express your question without it? I am pretty sure you do not intend it to have the negative connotation that it evokes.
It's simple: Doppler's effect is an invariant (if the medium is not changing), like a mass of a body, no matter the speed of frame of reference of the observer in which we will measure it.

Also I found that the Doppler's effect is an invariant to Galilean transformation, but the wavelength changing only in case of the source of waves moving.

#### A.T.

the point is we are measuring the wavelength,
When I say Doppler shift, then I mean the shift in frequency, and no info about the wavelength. If you additionally know the wavelength, then you can find both velocities for co-linear movement.

#### frostysh

That the answer to the question formulated by @A.T. is “no” is almost trivial to prove. There are two unknowns and only one equation. There is generally no unique solution to one equation in two unknowns.
I am not understanding of what you saying, but we can measure the wavelength in case of rest observer, and if we know it (and know it because we know the very feature of the medium $\large c$), and the achieving of the speed of the source of the wave is becoming trivial, there not only mathematics, there is physics. Sec I will post the prove which is I not understand but I googled, that Doppler's effect is an invariant.

#### A.T.

Sorry about that. As near as I can tell the questions are identical, so if you think mine is confusing then I am happy using yours.
I'm sorry for sounding too critical. I rephrased it as a suggestion.

#### A.T.

I am not understanding of what you saying, but we can measure the wavelength ...
See post #13. Doppler shift usually just means the shift in frequency. I did not assume we know the wavelength in that question.

#### frostysh

When I say Doppler shift, then I mean the shift in frequency, and no info about the wavelength. If you additionally know the wavelength, then you can find both velocities for co-linear movement.
If we know the characterizing feature of the medium, which is the speed of wave propagation there — $\large c$, we can found that source moving or not corresponding to medium, it is easily first we found the frequency (simple measuring), then we can measure wavelength of mechanical waves (it's simply too), and then just comparing wavelengths in case of rest to our case, if there are difference — source is moving, if there not, maybe moving observer or maybe medium. Something like that, but me can be wrong...

#### frostysh

This is incorrect. The wavelength can be changed simply by changing reference frame of the analysis.
Me think you are totally, terribly wrong (me actually thought long ago too that change appear), and I have googled the prove of it. Well, me no good in mathematics and there, but even me can read English: "the wavelength is the same in both frames" — Galilean Transformation of Wave Velocity (page 2). The point is the wavelengths is only changing when source of waves is moving corresponding to the medium — this is mean the Doppler's effect is breaking relativity of frame of references of classical mechanics because wavelength is an invariant! This is can be feel on intuitive level, the length is actually invariant like a mass or like, I don't know, the volume.
See post #13. Doppler shift usually just means the shift in frequency. I did not assume we know the wavelength in that question.
Me stupid then, not understand, of course then in equation will be many unknowns. But in case of physics I have a no idea if we are in the medium, why we cannot measure it's features like characterizing speed of wave propagation in rest? Just take some medium in bottle and use sound waves on it... But if there medium with which we cannot interact, so there is no point to talk about any medium at all.

Mentor

#### A.T.

this is mean the Doppler's effect is breaking relativity of frame of references of classical mechanics because wavelength is an invariant!
How does the invariance of wavelengths break the relativity of frame of references of classical mechanics?

#### vanhees71

Gold Member
I'm a bit puzzled by this thread, because it simply answers the question about the Doppler effect for light in a vacuum. This is pretty simple when just writing a plane em. wave in a relativistic covariant way and then Lorentz boost to another frame of reference (or you write it covariantly to begin with by introducing the four-velocities of the source and the observer; I've to think about the details, how to really do this).

But since in the OP the question is about a medium, maybe the question was about the Doppler effect for sound? This can of course also be formulated relativistically, and it's quite illuminating since in contradistinction to em. waves in the vacuum here we indeed have a medium (the air for usual acoustic phenomena). Thus in this case we have even three four-velocities to consider: the four-velocities of the sound source, the observer, and of the medium.

#### frostysh

That is for the Galilean transformation. However, physics is governed by the Lorentz transform, not the Galilean transform.
What Lorentz's transformation? The same Lorentz's transformation which in the Special Relativity Theory kinematics? Well, me no understand what is mean "governed" in that case, I think old uncle Newton's model working perfectly in most of cases, in case of a classical Doppler's effect especially.
How does the invariance of wavelengths break the relativity of frame of references of classical mechanics?
I am apologizing, no good word 'break'... I mean we have two body moving, we don't know which body is 'actually' moving (with constant velocities relative to each other, so called inertial frames), this questions in relativity have no any sense, we can suggest that the first body moving and describe this movements and etc, you know... But in case of Doppler's effect appear, the movement of medium corresponding of source of waves and the movements of the source of waves corrpesponding to medium, is not the same, we cannot jump so easily, despite it's both inertial frames of references. At least on my present level of understanding of this curious phenomenon.
I'm a bit puzzled by this thread, because it simply answers the question about the Doppler effect for light in a vacuum. This is pretty simple when just writing a plane em. wave in a relativistic covariant way and then Lorentz boost to another frame of reference (or you write it covariantly to begin with by introducing the four-velocities of the source and the observer; I've to think about the details, how to really do this).

But since in the OP the question is about a medium, maybe the question was about the Doppler effect for sound? This can of course also be formulated relativistically, and it's quite illuminating since in contradistinction to em. waves in the vacuum here we indeed have a medium (the air for usual acoustic phenomena). Thus in this case we have even three four-velocities to consider: the four-velocities of the sound source, the observer, and of the medium.
Well I am totally not understood what you talking about...

1) There is classical kinematics, no any relativistic effects on model.

2) Medium is not a vacuum of course, this is true, despite in this case we characterizing the medium only by a speed of wave propagation $\large c$ and saying it is constant despite of frame of reference, this is still not a relativistic case, and this is still not the vacuum physical meaning, vacuum cannot moving for an example, we cannot connect to it any frame of reference, but to medium we can, to object we can, but I am not heard 'vacuum frame of reference'.

3) We have only three velocities, only three frame of references, the all is an inertial frames. We can make only two, hardly connect the observer to the medium for an example. The third frame of reference in formula in my topic included by constant $\large c$, as you may know saying 'speed' in classical relativity have no any sense, when we saying 'speed' we means corresponding to something, we means at least two frame of reference, this is because speed of propagation of waves in medium giving addition frame to the observer and the source frames.

4) If you about philosophical question: "How we can introduce the single inertial frame without defining another, and this another can be defined only by next one frame, and so on..." — this is the question from the mathematical logic and so called 'reversed mathematics' which is super incredibly abstract, and which almost totally unknown to me, so this question I cannot answer.

Just to clarify first post about Doppler's effect. I just curious if my states a true or not:

• Wavelength is the invariant corresponding to the observer inertial frame of references, so we cannot distinguish which movement appear, the medium moving or the observer of waves moving.
• The wavelength is changing by changing the velocity of the source of the waves (look at first post pictures) corresponding to the medium, and due to it's invariantcy in the frames of observer we can say that this is somekind of invariant property by which we can distinguish what is actually moving, medium or the source corresponding to the medium.
• This is means Doppler's effect in classical kinematics is not relative it is 'absolute' in medium.

Last edited:

#### A.T.

This is means Doppler's effect in classical kinematics is not relative it is 'absolute' in medium.
"Absolute in medium" is just a confusing way to say "relative to the medium", or simply "relative". It's not absolute if you have to reference it to something.

#### frostysh

"Absolute in medium" is just a confusing way to say "relative to the medium", or simply "relative". It's not absolute if you have to reference it to something.
The abstraction there is next: if medium exist then Doppler's effect can define motion in this medium regardles of the inertial frames, and this is me calling 'an absolute'.

#### Ibix

The abstraction there is next: if medium exist then Doppler's effect can define motion in this medium regardles of the inertial frames, and this is me callind 'an absolute'.
The wind allows you to detect motion with respect to a medium. It doesn't make the rest frame of the medium absolute - it's just the velocity with respect to the medium.

"Help with understanding the Doppler effect"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

format: plain


text:
# zbMATH — the first resource for mathematics

Rationality problems and conjectures of Milnor and Bloch-Kato. (English) Zbl 1279.14063
The classical Lüroth problem may be formulated as the question whether a unirational variety $$X/k$$ is in fact rational. It is known that in general the answer is negative. For $$k={\mathbb C}$$ the field of complex numbers M. Artin and D. Mumford [Proc. Lond. Math. Soc., III. Ser. 25, 75–95 (1972; Zbl 0244.14017)] following a suggestion of C. P. Ramanujam showed that for a smooth complex variety $$X$$ the torsion subgroup of the singular cohomology group $$H^{3}(X,{\mathbb Z})$$ is a birational invariant. By constructing a conic bundle over a rational surface and exhibiting a $$2$$-torsion class in the above group they found an example of a unirational variety that is not rational.
In the paper under review, the author uses unramified cohomology groups to detect counterexamples to the Lüroth problem. The unramified cohomology groups (for any $$i$$ and $$j$$) were defined By J.-L. Colliot-Thélène and M. Ojanguren [Invent. Math. 97, No. 1, 141–158 (1989; Zbl 0686.14050)] as the subgroups $$H^{i}_{ur}(L/k,{{\mu}_{n}^{{\otimes}j}})$$ of $$H^{i}_{\text{ét}}(L,{{\mu}_{n}^{{\otimes}j}})$$ consisting of the unramified elements at every discrete valuation of $$L$$ trivial on $$k.$$ Recall that a class $${\alpha}\in H^{i}_{\text{ét}}(L,{{\mu}_{n}^{{\otimes}j}})$$ is unramified at a discrete valuation $$\nu$$ of $$L/k$$ if $$\alpha$$ is in the image of the restriction map $$H^{i}_{\text{ét}}(A,{{\mu}_{n}^{{\otimes}j}})\rightarrow H^{i}_{\text{ét}}(L,{{\mu}_{n}^{{\otimes}j}})$$ , where $$A$$ is the valuation ring associated with $$\nu$$. The author generalizes the method of E. Peyre [Math. Ann. 296, No. 2, 247–268 (1993; Zbl 0790.12001)] and constructs for any prime $$l$$ and $$n\geq 2$$ a rationally connected, non-rational variety. The non-rationality of this variety is detected by a non-trivial class of degree $$n$$ in its unramified cohomology. By definition for a variety $$X$$, $$H^{i}_{ur}(X,{{\mu}_{n}^{{\otimes}j}}):= H^{i}_{ur}(k(X)/k,{{\mu}_{n}^{{\otimes}j}})$$. For $$l=2$$ these varieties are unirational and their non-rationality cannot be detected by a torsion unramified class of lower degree. The techniques used in the paper follow (to some extent) those used in Voevodsky’s proof of the Milnor conjecture and the Voevodsky-Rost proof of the Bloch-Kato conjecture.

##### MSC:
 14M20 Rational and unirational varieties 19D45 Higher symbols, Milnor $$K$$-theory 11E81 Algebraic theory of quadratic forms; Witt groups and rings 12G05 Galois cohomology 14F42 Motivic cohomology; motivic homotopy theory
Full Text:
##### References:
 [1] doi:10.1007/BF01425486 · Zbl 0199.55501 · doi:10.1007/BF01425486 [2] doi:10.1007/978-3-642-01200-6_6 · Zbl 1244.19003 · doi:10.1007/978-3-642-01200-6_6 [4] doi:10.4007/annals.2011.174.1.11 · Zbl 1236.14026 · doi:10.4007/annals.2011.174.1.11 [6] doi:10.1007/978-94-011-4098-0_5 · doi:10.1007/978-94-011-4098-0_5 [7] doi:10.1016/j.jpaa.2005.12.012 · Zbl 1091.19002 · doi:10.1016/j.jpaa.2005.12.012 [9] doi:10.1016/0021-8693(85)90073-0 · Zbl 0586.13005 · doi:10.1016/0021-8693(85)90073-0 [10] doi:10.1007/BF01389135 · Zbl 0546.14014 · doi:10.1007/BF01389135 [11] doi:10.1007/s100970000015 · Zbl 1066.11015 · doi:10.1007/s100970000015 [12] doi:10.1007/978-3-662-03276-3 · doi:10.1007/978-3-662-03276-3 [16] doi:10.1215/00127094-1548389 · Zbl 1244.14010 · doi:10.1215/00127094-1548389 [17] doi:10.1007/BF01393696 · Zbl 0685.10015 · doi:10.1007/BF01393696 [18] doi:10.1007/BF01850658 · Zbl 0686.14050 · doi:10.1007/BF01850658 [19] doi:10.2307/3062141 · Zbl 0998.11015 · doi:10.2307/3062141 [24] doi:10.1090/S0894-0347-02-00402-2 · Zbl 1092.14063 · doi:10.1090/S0894-0347-02-00402-2 [25] doi:10.1016/j.aim.2011.04.009 · Zbl 1255.14018 · doi:10.1016/j.aim.2011.04.009 [26] doi:10.1112/plms/s3-25.1.75 · Zbl 0244.14017 · doi:10.1112/plms/s3-25.1.75 [27] doi:10.1016/0021-8693(75)90145-3 · Zbl 0314.12104 · doi:10.1016/0021-8693(75)90145-3 [29] doi:10.1007/BF01445105 · Zbl 0790.12001 · doi:10.1007/BF01445105 [30] doi:10.4007/annals.2007.165.1 · Zbl 1124.14017 · doi:10.4007/annals.2007.165.1 [32] doi:10.1007/s10977-005-1562-7 · Zbl 1117.14023 · doi:10.1007/s10977-005-1562-7 [33] doi:10.1016/j.jpaa.2010.02.006 · Zbl 1200.14041 · doi:10.1016/j.jpaa.2010.02.006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# Ex.15.1 Q19 Probability Solution - NCERT Maths Class 10

Go back to  'Ex.15.1'

## Question

A child has a die whose six faces show the letters as given below:

 A B C D E A

The die is thrown once. What is the probability of getting

(i) $$\rm A?$$

(ii) $$\rm D?$$

## Text Solution

What is known?

A die has six faces which show the letters as shown in the diagram and it is thrown once.

 A B C D E A

What is unknown?

The probability of getting (i) $$\rm A?$$ (ii) $$\rm D?$$

Steps:

Total number of outcomes = $$6$$

(i) Probability of getting $$\rm A$$

\begin{align}& =\frac{\text{Number of possible outcomes}}{\text{No of favourable outcomes}} \\& =\frac{2}{6} \\\end{align}

(ii) Probability of getting $$\rm D$$

\begin{align}& =\frac{\text{Number of possible outcomes}}{\text{No of favourable outcomes}} \\ & =\frac{1}{6} \\\end{align}

The probability of getting $$\rm A$$ and $$\rm D$$ is \begin{align}\frac{2}{6}\text{ and }\frac{1}{6}\end{align}

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school


text:
DocumentTools - Maple Programming Help

Home : Support : Online Help : Programming : Document Tools : DocumentTools/GetDocumentProperty

DocumentTools

 GetDocumentProperty
 Query property/properties of a document

 Calling Sequence GetDocumentProperty(all) GetDocumentProperty(attr)

Parameters

 attr - name ; property of the document that is to be queried

Description

 • The GetDocumentProperty function queries the document for the value of a property, or all properties.

Examples

Suppose that your document has an Author property. To retrieve the value of this property, you can do this:

 > $\mathrm{with}\left(\mathrm{DocumentTools}\right):$
 > $\mathrm{GetDocumentProperty}\left('\mathrm{Author}'\right)$
 ${"Maplesoft"}$ (1)


text:
# Adaptive Hash Functions: How to tell how many iterations were used?

If an adaptive hash function like bcrypt or PBKDF2 is used in hashing passwords, the number of iterations used in the hashing process can be configured.

For a penetration tester or a malicious hacker, what are the ways to determine how many iterations were used in hashing passwords, assuming that they do not have access to source codes, only a database dump of the password hashes.

-
I still think this fits security.SE better than crypto.SE. –  CodesInChaos Jul 27 '12 at 11:12

## migrated from security.stackexchange.comJul 27 '12 at 10:55

This question came from our site for Information security professionals.

The plain hash itself does not give any indication of the number of iterations. But with practical schemes, such as most crypt based ones, the number of iterations is stored alongside hash and salt in the database.

Keeping the number of iterations secret doesn't gain you much security in practice. Figuring out the number of iterations isn't that hard in practice. Choose a few users who probably have weak passwords, and compare after each iteration. Or if you can register your own accounts, you can simply attack that single user whose password you know.

If you want to improve security in a scenario where the attacker obtains only the database, but not the source-code/config file, there are much better techniques than a secret number of iteration. For example you could concatenate the salt with a secret key, or encrypt the hash. That way an attacker has no chance of attacking the hashes without gaining access to the place where you store the key.

-


text:
## integration of exponential functions

I have a test tomorrow and I am hoping someone can help me with the following two integrals:

1. $$\int$$ye^$$^{-y^{2}}$$/2dy

For this one I am using substition with u=-y$$^{2}$$/2 and du = -y/4

What I don't understand is how we account for the first y in this integral.

2. $$\int$$(1/$${\sqrt{2}$$)e^$$^{-1/6(y-1)^{2}}$$dy

If I'm having trouble with the first one, you can assume I'm not getting far on this one either.

 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
 you're problem is unclear. can you re-type that plz.
 sure. one moment...

## integration of exponential functions

 Quote by Snarf du = -y/4
That is not right. Check the derivative of the y2 and then find du/dy.

 2. $$\int$$(1/$${\sqrt{2}$$)e^$$^{-1/6(y-1)^{2}}$$dy
This one's a bit unclear. Is it $$\exp\left(\frac{-1}{6}(y-1)^2\right)$$ or $$\exp\left(\frac{-1}{6(y-1)^2}\right)$$? Also should there be another y term in the integral somewhere?

 Recognitions: Gold Member Homework Help The first one is probably a lot easier than you think. When I see integrals like these, I always solve the derivative of a the exponential part and see what it looks like. What's the derivative of e^(-y^2)?

 Quote by neutrino That is not right. Check the derivative of the y2 and then find du/dy. This one's a bit unclear. Is it $$\exp\left(\frac{-1}{6}(y-1)^2\right)$$ or $$\exp\left(\frac{-1}{6(y-1)^2}\right)$$? Also should there be another y term in the integral somewhere?
The first one $$\exp\left(\frac{-1}{6}(y-1)^2\right)$$

 Quote by JasonRox The first one is probably a lot easier than you think. When I see integrals like these, I always solve the derivative of a the exponential part and see what it looks like. What's the derivative of e^(-y^2)?
-2ye^(-y^2) ?

 Quote by Snarf The first one $$\exp\left(\frac{-1}{6}(y-1)^2\right)$$
I don't think it's possible to solve the second integral in terms of elementary functions.

 neutrino the derivative of -y^2/2 would be -y?

 Quote by neutrino I don't think it's possible to solve the second integral in terms of elementary functions.
Would it help if it was being integrated from negative infinity to infinity?

Should have put that up initially

 So... for the first one would the answer be -2ye^(-y/2)?

 Quote by Snarf Would it help if it was being integrated from negative infinity to infinity? Should have put that up initially
Ah. There are some ways of dealing with that.

 or is it -2ye^(y^2)?

 Quote by Snarf So... for the first one would the answer be -2ye^(-y/2)?
 Quote by Snarf or is it -2ye^(y^2)?
Neither. The derivative of $$e^{-\frac{y^2}{2}}$$, with respect to y, $$-ye^{-\frac{y^2}{2}}$$.

 Quote by neutrino Neither. The derivative of $$e^{-\frac{y^2}{2}}$$, with respect to y, $$-ye^{-\frac{y^2}{2}}$$.
Oh. Now I see why you gave me that great hint.

Now as far as your hint on the second one... very interesting, but a bit complex for me. The last time I took a calc class was about three years ago.

Does this look like I'm getting close?

$$=\int_{0}^{\infty}\int_{0}^{\infty} e^{-{(1/6(y-1)^2+1/6(x-1)^2)}} dxdy$$

 You could use a sub. like u = (1/6)(y-1) to simplify things.


text:
# Find the Area of Sector Whose Central Angle and Radius Are 60o and 21 Cm Respectively. (Pi = 22/7) - Geometry

Diagram

Find the area of sector whose central angle and radius are 60o and 21 cm respectively.
(pi = 22/7)

#### Solution

Area =theta/360 xx pi"r"^2

⇒ A = 60/360 xx 22/7 xx 21^2

⇒ A = 1/6 xx 22/7 xx 21 xx 21

⇒ A = 11 × 21

⇒ A = 231 cm2

Concept: Tangent to a Circle
Is there an error in this question or solution?


text:
# How to plot changes as a result of a parameter?

Hi,

I am new to Sage, with a Mathematica background, and am finding my way through things but am stumped on two problems and would be gladly pointed in the right direction.

What I want to do is plot how changing a parameter, in this case k (the domain of the graph), affects the accuracy of an approximation. My definition of accuracy in this case is simply the integral of the difference of the functions, which works for the purpose I have.

a = point2d((k, N(integrate(abs(nsin(x)-sin(x)),x,-k,k))) for k in range(-5, 5))
a

I have defined nsin(x) as

nsin(x)=x-x^3/factorial(3)+x^5/factorial(5)

I would also like to be able to define an error function so that I could instead write:

   error(function1, function2, xmin,xmax) = N(integrate(abs(function1-function2),x,-xmin,xmax)))

but I haven't figured out how to pass a function as an argument within a function.

Any help appreciated.

For context, I am a high school mathematics teacher and I am working with a group of enrichment students to compare the accuracy of some approximations of the Gaussian function to the analytical form.

edit retag close merge delete

Note e.g. for $k=-5$ you integrate from $-(-5)=5$ to $-5$ (i.e. the interval $[-5,5]$ with the reversed orientation), hence the "error" is negative; it would be reasonable to restrict to positive $k$.

( 2021-10-20 11:47:55 +0200 )edit

Good point. We are moving towards looking at the skew normal and approximations of the skew normal, neither of which are symmetric. I can just add an abs function as needed.

( 2021-10-21 03:31:51 +0200 )edit

Sort by » oldest newest most voted

The syntax f(x) = x^2 defines a callable symbolic expression f. Callable symbolic expressions are limited in the type of arguments they can take; in particular they cannot take functions as arguments.

But you can define an ordinary Python function instead:

def error(function1, function2, xmin, xmax):
x = var('x')
return N(integrate(abs(function1(x)-function2(x)),x,xmin,xmax))

and then:

sage: nsin(x)=x-x^3/factorial(3)+x^5/factorial(5)
sage: point2d((k, error(nsin,sin,-k,k)) for k in range(-5, 5))

In the error function I defined the local variable x to be the symbolic variable named x, to avoid relying on the assumption that the variable x has already been defined that way elsewhere. It is defined that way by default in a fresh SageMath session, but it's not uncommon to re-define x, and we should allow that without breaking our function. To solve the issue in a different way, you could also add x as a (third) parameter in the error function instead.

more

Thank you. This was very helpful.

( 2021-10-21 03:32:09 +0200 )edit

## Stats

Seen: 81 times

Last updated: Oct 20 '21


text:
## Check If A Number Is Power Of 2 In C

The program below takes two integers from the user (a base number and an exponent) and calculates the power. Secure your home or business with the best alarm systems and monitoring from ADT Security. Data Structure with C. Unplug this product from wall outlets before cleaning. In the 3DS version, these extra hearts are stored separately from the regenerating hearts (as of Version 1. Taxpayers can check the status of their tax refund. This approach reduces the problem of finding a n to problem of finding a n-1 till exponent becomes 0. Under this system, banks can continue to use the existing account numbers, and where necessary the number will be padded with zeros to make the length of 18 digits as required. So count the no. Using this virtualization feature, the SAN HBA port utilization can be increased and based on the. ) q for "quantile", the inverse c. Aside from straitening a bent pin or cleaning out some dirt, you'll probably need to seek the services of a professional computer repair service to correct any major problems you see here. Cummins will provide the entire electrified power solution, as well as some of the most critical components that have the largest impact on performance, quality and power of the. The rest of the factors of the perfect number 2^(n-1) * (2^n -1) are each of the above factors multiplied by the prime 2^(n-1). Example on how to calculate the power of a number if the exponent is an integer. This is a genuine Hitachi replacement part, they are sold as a pair (2). The expressed voltage gain in dB (voltage amplification) at the cutoff frequency f c is. Find Power of any Number in C++. How to find whether a number is power of two or not. Find power of a number using recursion using c program Guys it would be better if you check for any idiot entering 0 as one of the two numbers, in that case it. Modern computers adopt IEEE 754 standard for representing floating-point numbers. See also isalnum Check if character is alphanumeric (function ) isalpha Check if character is alphabetic (function ). Write a program to check whether the given number is even or odd. In mathematics, a power of two is a number of the form 2 n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. The second two characters are numbers that indicate the age of the car. Step 1: Write the Source Code: Enter the following source codes using a programming text editor (such as NotePad++ for Windows or gedit for UNIX/Linux/Mac) or an Interactive Development. Cummins will be the leading provider of electrified power in our commercial and industrial markets just as we are the leader in diesel and natural gas powered products. Switch to DISH to enjoy the best value in TV with a 2-year price guarantee, award winning technology, and satellite television's top-rated customer service. It means a prime number is only divisible by 1 and itself, and it start from 2. Breaking news and analysis on politics, business, world national news, entertainment more. Java Program to Check Whether Given String is a Palindrome - This Java program is used to demonstrate whether the given string is a palindrome or not. If it is, it prints a statement stating it is as well as prints out the exponent of three that would give me the integer input. Visit your local ACE store today for check cashing!. The DSC Resources for VMware version 2. Official MapQuest website, find driving directions, maps, live traffic updates and road conditions. are not powers of 10. C program to calculate factorial of a number using loop. For instance you want to print the same words ten times. Check whether x % 2 is not equal to zero and x not equal to 1 which indicates x is not power of 2 otherwise if x becomes 1 then it is the power of 2. Passport photo-copies of the Executants (Person/s who have created the POA) in the Power Of Attorney. It also covers Prime Number Definition, prime factorization, calculating prime factors, finding all prime numbers between 1 and 100 in a simple way, list of all prime numbers upto 1000. 3(B)(1) and 300. Advanced power management products offer more power and functionality in less space Shakopee, Minn. The market can be dominated by as few as two firms or as many as twenty, and still be considered oligopoly. The power expression "x**y" means that x is multiplied by itself y times, where y is a natural numebr. Cummins will be the leading provider of electrified power in our commercial and industrial markets just as we are the leader in diesel and natural gas powered products. MSN India offers latest national and World news, with the best of Cricket, Bollywood, Business, Lifestyle and more. The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and the C language complex number types (and arrays thereof), which have an identical object representation requirement. Automobile manufacturers hide the true potential of their engines to create cost savings, emission controls, and universal operation in all conditions. The Bureau of Labor Statistics is the principal fact-finding agency for the Federal Government in the broad field of labor economics and statistics. Etsy is a global online marketplace, where people come together to make, sell, buy, and collect unique items. Play FREE online games!Welcome to Pogo. Online Check-in Opens To check in, just enter your Reservation Code (PNR) and surname using your mobile or the above ‘Check-in’ section before arriving at the airport. Write a program to check whether the given number is even or odd. Start a free trial to create a beautiful website, buy a domain name, fast hosting, online marketing and award-winning 24/7 support. " In the same way we saw that only the square roots of square numbers are rational, we could prove that only the nth roots of nth powers are rational. This C program for power of a number allows the user to enter Number and an exponent value. GPU math libraries for FFT, BLAS, sparse matrix, dense and sparse direct solvers, random number generation, and more. If the original number was a power of 2, then the decrement will reduce it to one less, so that we round up to the same original value. e:if its less than 24hours only its showing correctly if its more than one ay its considering only hours but not dates technically i should date and time right. In binary, for instance, the maximum possible sum of three single-bit numbers is 3, which is a 2-bit number. Report a power outage, tree down, or streetlight outage, view outages by list or map, and get information on restoration efforts and resources. Play FREE online games!Welcome to Pogo. (2) For the purposes of this regulation 1 square metre (m 2) is equivalent to 10. Note: Zero (0) and 1 are not considered as prime numbers. The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and the C language complex number types (and arrays thereof), which have an identical object representation requirement. Windows 10 update resulted in corrupt BIOS, computer is now left unbootable. Oligopoly is a market structure characterized by a small number of relatively large firms that dominate an industry. Apply for Assistance. Do not install or use this product near water. If count is 1 then N is power of 2. From([End]-[Start])) for my data. Here's a C program to calculate the sine series with output. For the other cases the num & (num - 1) comes into play: That's saying if you take any number, and mask off the bits from one lower, you'll get one of two cases: if the number is a power of two already, then one less will result in a binary number that only has the lower-order bits set. Two (2) is the only one even prime number because all the numbers can be divided by 2. com(with details). If we subtract a power of 2 numbers by 1 then all unset bits after the only set bit become set; and the set bit become unset. The power operator ** binds less tightly than an arithmetic or bitwise unary operator on its right, that is, 2**-1 is 0. Never use an E85 fuel or a mixture of oil and gasoline designated for two cycle engines. For calculating the power of any number user have four possibilities to input values. There is a root name, for example, the root name for the normal distribution is norm. In this article, we will show you, How to Write a Program for Armstrong Number in C using While Loop, For Loop, Functions and Recursion. Here's how to stay safe around power lines and during monsoon storms. Our mission is to ensure that Utah Power Credit Union creates financial power with our members by providing excellent value and lifelong relationships. Etsy is a global online marketplace, where people come together to make, sell, buy, and collect unique items. Web Design HTML Tutorials Online HTML, CSS and JS Editor Bootstrap 4 Tutorials. federal legislative information. It is a bit different if you are (me include) coming from a C language background like javascript, php or some other similar ones … So the syntax is as follows:. are not powers of 10. Start a free trial to create a beautiful website, buy a domain name, fast hosting, online marketing and award-winning 24/7 support. C program to check if a number is a power of 2 using bitwise operation. Do not install or use this product near water. Who is my supplier? Your electricity supplier is the company you choose to buy your electricity from, and who you pay your bills to. We’ll help you find the right plan for your home. This article explains the steps for Power Systems SAN multipath configuration using the SAN port virtualization feature NPIV. #1 Wireless Network Quality, Verizon Wireless received the highest score in Volumes 1 & 2 of the J. PPL Corporation and the PPL family of companies power the lives and businesses of more than 10 million customers in the United States and the United Kingdom. Public Service Commission's web pages on Consumer Retail Choice and Consumer Suppliers' Offers. com, your headquarters for everything OBD-II related. Only 6174? The digits of any four digit number can be arranged into a maximum number by putting the digits in descending order, and a minimum number by putting them in ascending order. At Bank of America, our purpose is to help make financial lives better through the power of every connection. For example reverse of 839 is 938. Write a program that takes five integer command-line arguments and prints the median (the third largest one). Discussion forums for IT professionals and programmers. This C program to count digits in a number allows the user to enter any positive integer. SURGE TANK. This program calculates the power of a number using recursion where base and exponent is entered by the user. This is the number 32 -- in fact, left shifting is the equivalent of multiplying by a power of two. This is the number 32 -- in fact, left shifting is the equivalent of multiplying by a power of two. Detection techniques can be used to detect if the parameter is a certain value or if it is parenthesis. For example, I want to find out if "TRF" is in column. 1 is also 0-th power of 10. c's, ("stock" can vary 6 to 8 c. You’ll be able to check if your number can be transferred using the Keep Your Phone Number tool found in the tools module near the bottom of every plan page. This C program allows the user to enter the number (n) he wishes to calculate the average and sum. Deep Discounts on Hotels, Flights and Rental Cars. For Canada, please visit uww. The program is same as first program where we're using (**) sign to find out the square root but only different is this that here we're using a predefined method pow() instead of (**) sign to get the power of that number. We can use recursion to calculate power of a number because it follows recursive sub-problem structure. \$2^0 = 1\$; Looping up to number is very inefficient. Note When the system is powered with a 4200 W power supply either in 110 V or 220 V combined mode operation, the available power is determined by the configuration of the system (the type of line cards, the number of line cards, number of ports consuming inline power etc. From solar to wind power, you can go green with ease. Given a positive integer n, find if it can be expressed as x y where y > 1 and x > 0. I also guide them in doing their final year projects. Power Cool can be identified by it’s purple color. ) Strictly, 1 is not a power of 10. Well, it means 2 raised to some power. How you contact the national authorities varies from country to country. An automatic standby generator is a back-up electrical system that operates whether you are home or away. Returns e raised to the power of number. For example, I want to find out if "TRF" is in column. Embassy or Consulate and request it be forwarded to CIA. Learn how to prepare for storms. Shop new & used cars, research & compare models, find local dealers/sellers, calculate payments, value your car, sell/trade in your car & more at Cars. Shop online for all your home improvement needs: appliances, bathroom decorating ideas, kitchen remodeling, patio furniture, power tools, bbq grills, carpeting, lumber, concrete, lighting, ceiling fans and more at The Home Depot. This program allows the user to enter an integer value and then finds the square of that number using Arithmetic Operator. Support independent creators There’s no Etsy warehouse – just millions of people selling the things they love. c FW Math 321, 2012/12/11 Elements of Complex Calculus 1 Basics of Series and Complex Numbers 1. Given an integer, write a function to determine if it is a power of two. To understand this code you need good knowledge of For Loop in C++. In-depth DC, Virginia, Maryland news coverage including traffic, weather, crime, education, restaurant. For Calculate Power of any number, multiply particular number by itself on the basis of power. To find factorial of a number in C++ programming, you have to ask to the user to enter the number to find the factorial of the number using the for loop and display the factorial result of the number on the output screen as shown here in the following program. Here is one if we would want to avoid CPU-branching, which would be nice in compiled languages like C or C++ for CPUs which have broad instruction pipelines. 1234567890 to the 10th power of 10 (in base 10). Shared amperage means multiple ports share the amperage available. Arizona Millionaire's Club is the newest $30 Scratchers from the Arizona Lottery with more million dollar prizes than ever before! Learn More Did you know your non-winning tickets could be worth big bucks?. The C SERIES power banks feature advanced second generation power bank technology. Statements: (1) The measured number 2. REScheck-Web simplifies residential energy code compliance by automating trade-off calculations for the IECC and a number of state-specific codes. 1 and before, if both arguments were of integer types and the second argument was negative, an exception was raised. Apply for Power of Attorney. er tool or these instructions to operate the power tool. Power BI is a business analytics service that delivers insights to enable fast, informed decisions. This program allows the user to enter an integer value and then finds the square of that number using Arithmetic Operator. More C Programs. The idea is simple try all numbers x starting from 2 to square root of n (given number). Any whole number which is greater than 1 and has only two factors that is 1 and the number itself, is called a prime number. The power expression "x**y" means that x is multiplied by itself y times, where y is a natural numebr. Further adding to the beauty of accepted answer above -. " In the same way we saw that only the square roots of square numbers are rational, we could prove that only the nth roots of nth powers are rational. If either of these is the case, call the number below. By supplying your home telephone or account number we will be able to get you to the right location. We incorporate and dissolve limited companies. Start typing in your model number (i. Report a power outage, tree down, or streetlight outage, view outages by list or map, and get information on restoration efforts and resources. Brink's, Incorporated provides U. The New York Times: Find breaking news, multimedia, reviews & opinion on Washington, business, sports, movies, travel, books, jobs, education, real estate, cars. For all real numbers a, b, and c, a = b if and only if a + c = b + c. As Fred Brooks observed in The Mythical Man-Month, "Representation is the essence of programming. c program to check whether a number is power of 2 or not with out using loop. C++ program to find Square Root of a Number For calculate Square Root of a number we multiply number by 0. Thus, the 5th root of 32 is rational, because 32 is a 5th power, namely the 5th power of 2. There is a root name, for example, the root name for the normal distribution is norm. ) if, in order to reduce or eliminate induc-tive heating, the raceway is nonmetallic or nonmagnetic and the installation complies with 300. This program calculates the power of a number using recursion where base and exponent is entered by the user. Write a C program to find power of a number using loop. [email protected] In the olden days when computing resources were scarce, every programmer probably knew about this shortcut and others like it, these days – not so much. Citation Machine™ helps students and professionals properly credit the information that they use. In situations where you can't check these dimensions we suggest you check your cylinder cranking pressure. But (-1) is not in the range 0 and 2 (divisor -1). But what power? Well, the exponent for 2 contains some arithmetic which itself contains a raise to the power operation. 3(B)(1) and 300. !!! Programs : 1. C program to find area. Online systems to check for VAT registration. SURGE TANK. Routing Number: This is the routing number of the bank that facilitates electronic clearing of the check. leaking fittings while maintaining a constant check on the reservoir fluid level. Welcome to OBD-Codes. Logic to find power of a number without using pow() function in C programming. This is written in any of the ways shown below. This means your data is securely handled by only two parties - VitalChek and the government agency issuing your requested certificate. After utility power returns, the generator shuts itself off and waits for the next outage. I have used this tool several times to run a burn in read and write test on USB drives. That’s why Walbro high-performance fuel pumps and modules are developed and built specifically to meet the demands of today’s high-pressure and high-flow engines with efficient and durable performance. A failure in the power steering system, such as a broken hose, broken power steering pump drive belt, or failed pump, would result in a loss of pressure to both the hydro-boost and steering gear. 40V, set the voltage to 14. Here is the microprocessor 8086 assembly language program to check whether the given number is prime or not. If you need to calculate the power of a number raised to a decimal value, you can use pow() library function. Can I switch to AT&T but keep the phone number I already have from another carrier? A. @helios Just a typo: The first 'x' you have must be your number and the rest 'x's the number of decimals points you want. The task is to check if N is a power of 2. com is over 10 years old. This C program to count digits in a number allows the user to enter any positive integer. Shop iPhone cases & accessories made from the finest materials. Perfect number is a positive number which sum of all positive divisors excluding that number is equal to that number. Scosche PowerVolt Power Delivery Dual 18W USB-C Car Charger (CPDC8C8) The best car charger with two USB-C ports. If it is signed by two witnesses, they must witness either (1) the signing of the power of attorney or (2) the principal’s signing or acknowledgment of his or her signature. which is sometimes rounded off to: 1 Mbd = 2 quad/yr. How to check a standard relay. Use only a grounded electrical outlet when connecting the device to a power source. Congress is composed of two parts: the Senate and the House of Representatives. Thank you for your patience during the merger process. C Program to Check whether the Given Number is a Prime ; C Program to Find the Greatest Among Ten Numbers ; C Program to Find the Greatest Number of Three Numbers ; C Program to Asks the User For a Number Between 1 to 9 ; C Program to Check Whether the Given Number is Even or Odd ; C Program to Swapping Two Numbers Using Bitwise Operators ; C. Reverse of number means reverse the position of all digits of any number. Download the GPS traffic app, powered by community. The only exception is the Match 5 prize of$1 million, which becomes $2 million for Power Play ticket holders, no matter which number is drawn. , for the annual open streets event that takes place along 5 miles of Tacoma’s waterfront. Quick Q: How to square numbers??? Quick Q: How to square numbers??? InclinedToFall. Before relying on this information, you should be aware of the following limitations. So I tried "square()" with no luck. 2 Mana Regenerated per Second per Power Charge "Creation is the act of making the intangible tangible. User declares double type variable or float and int. I really dont know whats so great in it. In most cases you can keep your current phone number. Java Program to Check Whether Given String is a Palindrome - This Java program is used to demonstrate whether the given string is a palindrome or not. Next: Write a Python program to check if an integer is the power of another integer. : Scout knows his way to hundreds of e-bills… he’ll fetch yours right now at no charge!. For Calculate Power of any number, multiply particular number by itself on the basis of power. This tells you where to start testing. Easy Tutor says. This selection will show you how to add two numbers together. Decimal number system is a base 10 number system using digits for 0 to 9 whereas binary number system is base 2 and uses 0 and 1. com is a huge collection of song lyrics, album information and featured video clips for a seemingly endless array of artists — collaboratively assembled by contributing editors. 1K Beer Run and Block Party is the perfect race for those who enjoy athletics along with McFadden's and Pizza Bar! More Info » Buy Tickets ». python tip trick Recently I found this simple one liner which can save your time & can be efficient to check if number is power of 2. 2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. And our student credit cards can help you start out right. The Bowden cable system is fast becoming the mechanism of choice by most of the auto manufacturers. How would I go about counting the number of characters in this string, without including the commas, semicolons, spaces, and periods. A matrix is like a vector in that it is a list of numbers, but it is different in that you can have both rows and columns of numbers. – July 12, 2019 – Cyber Power Systems (USA), Inc. Note: Zero (0) and 1 are not considered as prime numbers. It will also show the S. I came up with this simple algorithm: private bool. C program to check whether an Integer Number is power of two (2) or Not - This program will read an integer number and check this number is the power of two (2) or not. A simple solution is to repeatedly compute powers of x. Find out more about Petrosoft's technology and business partners. It is often useful to find a formula for a sequence of numbers. 410 × 10-3 contains three significant figures. federal legislative information. This program allows the user to enter an integer value and then finds the square of that number using Arithmetic Operator. two variables temp and expo assigned value 1. As CenturyLink and Qwest merge companies, we are working hard to combine our systems. C Program to Check Whether a Number can be Expressed as Sum of Two Prime Numbers Example to check if an integer (entered by the user) can be expressed as the sum of two prime numbers of all possible combinations with the use of functions. Load more Load more Only on CFAX 1070. We offer free demos on new arrivals so you can review the item before purchase. Online Check-in Opens To check in, just enter your Reservation Code (PNR) and surname using your mobile or the above ‘Check-in’ section before arriving at the airport. Burbank Water and Power - Call (818) 238-3700. Suppose you want to calculate 2^3 is 2*2*2=8. The second two characters are numbers that indicate the age of the car. Citation Machine™ helps students and professionals properly credit the information that they use. Combine and save with a flight + car package, plus, enjoy 7 days UK car hire for the price of 5 when you book before 26 August 2019. Find Power of any Number in C++. The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and the C language complex number types (and arrays thereof), which have an identical object representation requirement. Check if a number is a power of another number. This approach can be extended to cases where y is some larger power of 2. The constant e equals 2. Easy Tutor says. wake me next time you want to know if a number is a multiple of 2 rather than a power of 2. C++ program to check whether a number is palindrome number or not. C pointers questions; Check given number is prime number or not. A reserved word always appears in lowercase and can only be used for the purpose, which has. Redeem for cash back as a deposit into Bank of America ® checking or savings accounts, for credit to eligible Merrill accounts including 529 accounts, as a statement credit to your credit card, or for gift cards and purchases at the Bank of America Travel Center; Preferred Rewards members earn 25%-75% more points on every purchase. Best Answer: *Class 2 compliance requires a maximum power output availability of less than 100 watts for the component. Perform one or more of the following tasks to check the operation of the AC power adapter. The program also uses C's math. Sign in to queue. Read this guide on finding the right charger or power adapter. Write C code to check if an integer is a power of 2 or not in a single line? Even this is one of the most frequently asked interview questions. Fidelity Investments offers Financial Planning and Advice, Retirement Plans, Wealth Management Services, Trading and Brokerage services, and a wide range of investment products including Mutual Funds, ETFs, Fixed income Bonds and CDs and much more. Write a program to find factorial of the given number 2. \$2^0 = 1\$; Looping up to number is very inefficient. If you have only five digits of precision, the number becomes 123460000 (rounding up). Does this mean I'm done showing it is not the sum of two squares? c)$34300 = 7^3 \cdot 5^2 \cdot 2^2\$; again the power of 7 is not even. Ranking Data In Lists. As CenturyLink and Qwest merge companies, we are working hard to combine our systems. Look up your code definition. If this Form is a post-effective amendment filed pursuant to Rule 462(c) under the Securities Act, check the following box and list the Securities Act registration statement number of the earlier effective registration statement for the same offering. Then, after you combine those, take your new number and refer to the following chart to determine the type: According to the table, the binary number 0100, or 4, is the number for a Rock type attack. Check a Number's Primality A simple routine to check most small numbers for primality. The R Language. Search web. The battery is also submitted to short duration charging and discharging pulses of about 2 milliseconds to check that the unit accepts and can deliver charge. how to check if Integer number is power of two in Java is one of the frequently asked coding question. Numbers, Characters, and Strings. Given a positive integer n, find if it can be expressed as x y where y > 1 and x > 0. It means a prime number is only divisible by 1 and itself, and it start from 2. Collaborate for free with online versions of Microsoft Word, PowerPoint, Excel, and OneNote. All PATC performance torque converters are manufactured in-house. This is the first time since. Shop online for all your home improvement needs: appliances, bathroom decorating ideas, kitchen remodeling, patio furniture, power tools, bbq grills, carpeting, lumber, concrete, lighting, ceiling fans and more at The Home Depot. How to check if a number is a Perfect Square Squares of all integers are known as perfect squares. Use default argument of 2 for p, so that if this argument is omitted the number will be squared. This C program to count digits in a number allows the user to enter any positive integer. 1) The best example of an effective payroll transaction file hash total would most likely be A) sum of net pay. C++ program to check for the power of two using function. Would like to display the number result in a label. We can use recursion to calculate power of a number because it follows recursive sub-problem structure. Unless the power of attorney otherwise provides, language in a power of attorney granting general authority with respect to real property authorizes the agent to do all of the following: (A) Demand, buy, lease, receive, accept as a gift or as security for an extension of credit,. ] The number of barrels of crude oil per tonne varies widely, depending upon the source. You’ll be able to check if your number can be transferred using the Keep Your Phone Number tool found in the tools module near the bottom of every plan page. Here is one if we would want to avoid CPU-branching, which would be nice in compiled languages like C or C++ for CPUs which have broad instruction pipelines. I had a number of remote-access sessions with Microsoft Support. in raceway 2, etc. Power Cool can be identified by it’s purple color. Form an LLC, incorporate a business, make a will, register a trademark, get legal advice, and more online. During a P-state, the processor is still executing instructions, whereas during a C-state (other than C0), the processor is idle, meaning that nothing is executing. Here, we are using different 4 methods to check it. In order to check whether a number is a perfect cube or not, we find its prime factors and group together triplets of the prime factors. The algorithm needs to be: Simple Correct for any ulong value. This approach can be extended to cases where y is some larger power of 2. Taxpayer must sign and date this form on page 2, line 7. Household Indoor ExercisesFitness gyms are great for stormy days or weeks and additionally harmful weather. Raising a number to a power p is the same as multiplying n by itself p times. Our mission is to ensure that Utah Power Credit Union creates financial power with our members by providing excellent value and lifelong relationships. Download a NEW Norton™ 360 plan - protect your devices against viruses, ransomware, malware and other online threats. Select the charge current according to battery size. Thus, the numbers which, squared and added, produce a prime, can be found here as p and q. 1 is also 0-th power of 10. Find power of a number using recursion using c program; Find gcd of a number using recursion in c program; Factorial program in c using recursion; To implement Tower Of Hanoi using C; write a c program which produces its own source code as its output; C program to print hello world without using semicolon; To Find Factorial Of A Number Using C. Career Waypoints (C-WAY) FAQs for Extension of Enlistments to Complete Prescribed Sea Tour for First Term Personnel The Career Waypoints (C-WAY) system is a corporate Information Technology system which provides a mechanism for matching personnel inventory to requirements with the best performing Sailors. It counts all non-zeros and ones in base 10. With fewer than two firms, the industry is monopoly. Play It Again ® with an eligible Silverado ® scratch ticket! Read more. We have just launched a brand new range of power banks called the C SERIES. GPU math libraries for FFT, BLAS, sparse matrix, dense and sparse direct solvers, random number generation, and more. and 50box betting. Example: If num = 64, return true. For Calculate Power of any number, multiply particular number by itself on the basis of power. Check the power icon in the system tray. Below you can find 5 different solutions - all of them correct, but some of them more efficient than others. C program to check whether number is Armstrong or Not - C program for Armstrong - C programming Example. Here, we will also show you, C Program for Armstrong Number between 1 to n. C Program to find Power of a Number Using For Loop. power_of_2 = 1 while power_of_2 <= n: if power_of_2 == n: return True power_of_2 *= 2 return False simply compares your number to all smaller-or-equal powers of two. Expression. We have just launched a brand new range of power banks called the C SERIES. Parcel: 1300 724 491 / Remittance: 02 98202645 Manila Contact: 02 6188650/09178256546. Passport photo-copies of the Executants (Person/s who have created the POA) in the Power Of Attorney. The C++ compiler classifies these words into different categories: Reserved words: A reserved is a word that has a special meaning in C++. You can use the #define directive to define a constant using an expression. !!! Programs : 1.


text:
Lesson 2

Scale Factors and Making Scaled Copies

Lesson Narrative

This lesson develops the vocabulary for talking about scaling and scaled copies more precisely (MP6), and identifying the structures in common between two figures (MP7).

Specifically, students begin to describe the numerical relationship between the corresponding lengths in two figures using a scale factor. They see that when two figures are scaled copies of one another, the same scale factor relates their corresponding lengths. They practice identifying scale factors.

Students then draw scaled copies of simple shapes off a grid with a focus on strengthening their understanding that the relationship between scaled copies is multiplicative, not additive. Students make careful arguments about the scaling process (MP3), have opportunities to use tools like tracing paper or index cards strategically (MP5).

As students draw scaled copies and analyze scaled relationships more closely, encourage them to continue using the terms scale factor and corresponding in their reasoning.

Learning Goals

Teacher Facing

• Comprehend the phrase “scale factor” and explain (orally) how it relates corresponding lengths of a figure and its scaled copy.
• Critique (orally and in writing) different strategies (expressed in words and through other representations) for creating scaled copies of a figure.
• Draw a scaled copy of a given figure using a given scale factor.
• Generalize (orally and in writing) that the relationship between the side lengths of a figure and its scaled copy is multiplicative, not additive.

Student Facing

Let’s draw scaled copies.

Required Preparation

Make sure students have access to their geometry toolkits, especially tracing paper and index cards.

Student Facing

• I can describe what the scale factor has to do with a figure and its scaled copy.
• I can draw a scaled copy of a figure using a given scale factor.
• I know what operation to use on the side lengths of a figure to produce a scaled copy.

Building On

Building Towards

Glossary Entries

• scale factor

To create a scaled copy, we multiply all the lengths in the original figure by the same number. This number is called the scale factor.

In this example, the scale factor is 1.5, because $$4 \boldcdot (1.5) = 6$$, $$5 \boldcdot (1.5)=7.5$$, and $$6 \boldcdot (1.5)=9$$.