text:
# Tag Info

10

The rectangular prism is a rigid body. The equations of motion of a rigid body around its center of mass are given by: (Please, see for example: Marsden and Ratiu , (page 6). $$I_1\dot\Omega_1=(I_2-I_3)\Omega_2\Omega_3$$ $$I_2\dot\Omega_2=(I_3-I_1)\Omega_3\Omega_1$$ $$I_3\dot\Omega_3=(I_1-I_2)\Omega_1\Omega_2$$ Where $\Omega_1,_2,_3$ are the angular ...

9

The instability inherent in the medium length axis or $\prod_2$ as shown above is discussed in detail in Marsden and Ratiu, which is where the image is from. The unstable homoclinic orbit that connect the two unstable points have intersting features. Not only are they interesting because of the chaotic solutions via the Poincare-Melnikov method that ...

8

One may prove for an arbitrary rigid body (and wrt. to an arbitrary choice of pivotal point for the rigid body) that the three moments of inertia $I_x$, $I_y$, and $I_z$, around the three principal axes (which we will call $x$, $y$, and $z$) satisfy the triangle inequality, $$\tag{1} I_x +I_y ~\geq~ I_z, \qquad I_y +I_z ~\geq~ I_x, \qquad I_z +I_x ~\geq~ ... 7 You can always decompose a motion like this into two parts: (1) rolling without slipping and (2) slipping without rolling. What is slipping without rolling? It means the object moves uniformly in one direction along the surface, with no angular velocity about the object's own center of mass. For instance, a box that is pushed along the ground can easily ... 7 I think a reasonable first approximation can be made like this: choose an arbitrary orientation for the die, and figure out, if the die were released in that orientation with its lowermost point resting on a surface, which side would it fall on? That can be easily calculated; you just draw a line going straight down from the center of mass, and whichever ... 6 Here's a straightforward but somewhat computational way. There are two steps. (1) Show how to define the angular velocity vector in terms of rotation matrices. (2) Write a general rotation in terms of Euler angles. (3) Combine (1) and (2) to get an expression for the angular velocity vector in terms of Euler angles. Step 1. Recall that if \mathbf x(t) is ... 6 The moment of inertia is a rank 2 tensor not a scalar. You'll commonly see it written as a scalar, but this is because by choosing your axes to line up with the principal axes of the object the matrix representing the moment of inertia can be diagonalised:$$ {\bf I} = \left( \begin{matrix} I_{00} & 0 & 0 \\ 0 & I_{11} & 0 \\ 0 & 0 ...

5

Building up from the ground is essentially impossible. One reason is stability, as John Rennie points out in his answer, but a far more fundamental reason* has to do with compressive strength. When a space elevator is completed, the cable is under a lot of tension. However, if you build up from the ground then while you're building it it's under compression ...

5

You're correct that there is no such thing as a rigid body in reality. Any time a force is applied to an object at one point (such as a boulder being placed on one end of the see-saw), it only immediately applies to the molecules that it is touching. The displacement of those molecules propagates to the rest of the object as a "deformation wave," which is ...

5

For longitudinal waves, the effect moves with the speed of sound inside the matter which is equal to $$c=\sqrt{\frac{E}{\rho}}$$ where $E$ is the modulus of elasticity and $\rho$ is the mass density. For steel this is like $5000\;{\rm m/s}$. For beam transverse waves, it depends on which harmonic is excited and how many wavelengths fit in the length of the ...

5

You've duplicated constraints because if any one particle is constrainined in all three dimensions with all the other particles this constrains all the particles. The number of constraints is 3(N - 1). To give an example, take three particles a, b and c. If a is fixed relative to b and is also fixed relative to c, then b and c are fixed relative to each ...

4

This paper (http://www-stat.stanford.edu/~cgates/PERSI/papers/dyn_coin_07.pdf) shows that the probability distribution of getting a head, if I toss with the head side up is given by: $p(ψ, φ) =\frac{1}{2}+\frac{1}{\pi} \sin^{-1} (\cot(φ) \cot(ψ))$ if $(\cot φ)(\cot ψ) ≤ 1$, =1 if $\cot(φ) \cot(ψ) ≥ 1$ where $\phi, \psi$ are the Euler angles.

4

Every rigid body has 3 translational dof. In addition, there are 0, 2, or 3 rotational dof, depending on the geometry, giving a total of 3, 5, or 6 dof. A spherically symmetric rigid body has no other dof. A rigid body with rotational symmetry around an axis has 2 rotational dof, namely two angles for orienting the symmetry axis along a direction. All ...

4

I assume you know about rotation matrices, and so for a sequence rotations about Z-X-Z with angles $\phi$, $\theta$ and $\psi$ repsectively you have $$\vec{\omega} = \dot{\phi} \hat{z} + T_1 \left( \dot{\theta} \hat{x} + T_2 \left( \dot{\psi} \hat{z} \right) \right)$$ The logic here is apply a local spin of $\dot{\phi}$, $\dot{\theta}$ and $\dot{\psi}$ ...

3

Simply stated, in the area of contact dynamics, a unilateral (bilateral) constraint refers to a one-sided (two-sided) constraint, i.e. a constraint described$^1$ via an inequality (equality) of some constraint function $f(q,\dot{q},t)$, respectively. Here we are assuming that the variables $q^i$ are real (as opposed to complex). Technically, one demands ...

3

$\vec\omega = I^{-1} \vec L$, and $\vec L$ is constant in the absence of external forces. The bit that I think you're missing is that $I$ rotates with the rigid body, so it is not constant in general and neither is $\vec\omega$. I played with your online example, and the angular velocity does seem to always remain constant when I'm not poking the block, ...

3

Your statement is true. Proof: Let $\rho$ be the mass density of the rigid body. Remember that the tensor of inertia $I$ is given by: $$\vec{v}^t I \vec{w} = \int d^3b\, \rho(\vec{b}) (\vec{v} \cdot \vec{w} - (\vec{v}\cdot \vec{b})(\vec{w}\cdot \vec{b}))$$ for all $\vec{v},\vec{w} \in \mathbb{R}^3$. Now take an orthogonal matrix $O$ which ...

3

It will not rotate around A, since the centrifugal forces will make the body rotate about its center of mass. You can move the torque, it is not fixed to a given point.

3

The laws you are looking for are conservation of momentum and conservation of angular momentum. If you stick the two bodies together both laws still must be fulfilled (inelastic effects neglected). In the end you will have a compound single object. With the parallel axis theorem (wikipedia) you can calculate the mass moment of inertia and together with the ...

3

If want to describe the dynamics of the ball, you need to use the SO(3) matrix which describes the ball's orientation. This is a 3 by 3 matrix whose transpose is its inverse. These may be parametrized by Euler angles, and most of the literature on rigid rotating bodies uses this convention, but I think it is best just to use the matrix entries themselves ...

3

As a starting point, Wikipedia says on this issue: The principal axes are often aligned with the object's symmetry axes. If a rigid body has an axis of symmetry of order $m$, meaning it is symmetrical under rotations of 360°/$m$ about the given axis, that axis is a principal axis. When , the rigid body is a symmetrical top. If a rigid body has at least ...

3

You have already answered your own question! There is a force between the hinge and the door. If the door weren't attached to the hinge, it would start flying away in addition to spinning. The only error you have is a mistake in your integral. The net force on the door is $\frac{aML}{2}$ in your notation. (Note: it is probably best not to use $a$ for both ...

3

The trouble with building columns is that they are fundamentally unstable i.e. if you perturb them away from the vertical the perturbation grows and the column falls over. This problem is worse the higher the column relative to it's base, so for very high columnar structures you need extra butressing to keep the column stable. By contrast perturb a suspended ...

3

A rigid body has 6 configuration degrees of freedom because its most general configuration can be obtained by translating (3 degrees of freedom) and rotating (3 degrees of freedom) its initial configuration. A mathy way of saying this is that its configuration manifold is $\mathbb R^3\times \mathrm{SO}(3)$. However, you are right that the phase space of a ...

3

I'm guessing from your description that the left end of the rod is the end on contact with the ground, and the right end is the in the air at the point that the string is cut. I think that what will happen is this: When the string is cut, gravity will cause the rod to fall, such that its centre of gravity falls vertically. As the rod falls, it will rotate ...

2

So when we see an object rotating, its state of rotation is totally relative, as it happens for many other physical quantities... Is that correct? The state of rotation is not $totally$ relative; for example, the angular velocity of rotation is the same for all points of reference. It is true that you can use different point of reference for the ...

2

This is a well known problem. So, I will try to solve it in the general case. For a somewhat more detailed answer, please look at Chapter 9 of David Morin's Introduction to Classical Mechanics book. Also, since this looks like a homework, whenever you think you can do the rest of the problem yourself, stop reading and actually do it yourself! Let's first ...

2

The centre of the sphere is moving in a circle of radius R-r, as can be seen from a diagram very easily. Now, why we consider centre not any other point? The reason is that, first no other point on the sphere is moving in a circle. And secondly, Newton's laws for rigid body state that total force = mass * acceleration of centre of mass. Since centre of mass ...

2

I worked on a physics engine written in C# that does just this. Here are my notes on this topic. Objects have both translational and rotational momentum. When two objects collide, the overall algorithm goes like this: 1> Find the total momentum of both objects. Calculate the translational and rotational momentum, the vector sum of this is the total ...

2

Let's look at the case of angular momentum. In physics, "continuous" mass distributions are usually specified by a mass density. The mass density is defined as the function $\rho:\mathbb R\times\mathbb R^3\to\mathbb R$ that specifies the mass density of the system at any time $t$ and any point $\mathbf x$ in space. This means that it satisfies the ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Re: post-review with clearcase

```I just replied to this in the other thread. There's a couple things that
could be causing this. Your request only appears to be hanging, because the
server is never responding, due to it being stuck, likely on the cat
process.```
```
Christian

--
Christian Hammond - chip...@chipx86.com
Review Board - http://www.reviewboard.org
VMware, Inc. - http://www.vmware.com

On Tue, Aug 17, 2010 at 3:03 AM, Shambhu <shambhu.1...@gmail.com> wrote:

> Hi,
>
>         I found the exact location where it is hanging. It hangs
> while
> r = urllib2.Request(url, body, headers) (in file postreview.py).
>
> I read about urllib2.Request, and it says that it requires 'https' to
> work. So does this mean that i have to create a https webui for
> reviewboard?
>
>
> Regards,
> Shambhu.
>
> On Aug 11, 4:10 pm, Shambhu <shambhu.1...@gmail.com> wrote:
> > Hi Dan,
> >
> >           I went through pervious post with same issue, but still i am
> > stuck. It would be great if you could provide me location of patches
> > which would be needed to make it working.
> >
> > Regards,
> > Shambhu.
> >
> > On Aug 10, 10:09 pm, Dan Savilonis <d...@n-cube.org> wrote:
> >
> > > Can you check the mailing lists and reviews.reviewboard.org? This
> > > sounds like something that came up before. Unfortunately post-review
> > > and Clearcase support are not in particularly good shape in the
> > > released version. It really needs to have some newer patches merged in
> > > to get things working more sensibly.
> >
> > > Dan
> >
> > > On Aug 9, 11:06 am, Shambhu <shambhu.1...@gmail.com> wrote:
> >
> > > > Hi,
> >
> > > >        After making some minor modification to resolve below error,
> > > > post-review script is able to proceed further. But now it hangs at
> > > > diff upload. It is not showing any error or warning. I tried to
> > > > diff generated by post-review through webui, but it hangs there also
> > > > without any error msg, it just shows 'Loading' and nothing happens.
> > > > Here is the debug message where it stucks:
> >
> > > > >>> Looking for 'reviewboard.test.com /' cookie in C:\Documents and
> > > > >>> Attempting to create review request on K for None
> > > > >>> HTTP POSTing tohttp://
> bnrpcwl0203.bnr.st.com/api/json/reviewrequests/new/:{'repository_path<http://bnrpcwl0203.bnr.st.com/api/json/reviewrequests/new/:%7B%27repository_path>':
> 'K'}
> > > > >>> Review request created
> > > > >>> HTTP POSTing tohttp://
> bnrpcwl0203.bnr.st.com/api/json/reviewrequests/16/diff/new/:{'basedir<http://bnrpcwl0203.bnr.st.com/api/json/reviewrequests/16/diff/new/:%7B%27basedir>':
> 'K'}
> >
> > > > And nothing happens after this. I checked server log and there also
> > > > nothing is mentioned. Here it is:
> > > > 20:23:53        DEBUG   DiffParser.parse: Beginning parse of diff,
> size =
> > > > 621
> > > > 20:23:53        DEBUG   DiffParser.parse: Finished parsing diff.
> > > > 20:24:41        DEBUG   DiffParser.parse: Beginning parse of diff,
> size = 620
> > > > 20:24:41        DEBUG   DiffParser.parse: Finished parsing diff.
> >
> > > > I didn't find any error or info in apache log also. Just to verify
> > > > whether i have correct directory permission of "media" directory, i
> > > > tried to upload screenshot, and that worked fine.
> >
> > > > Please suggest how to fix this and let me know if more info needed. I
> > > > think i am just one step away from using it, and it annoying me. :(
> >
> > > > Regards,
> > > > Shambhu.
> >
> > > > On Aug 9, 12:41 pm, Shambhu <shambhu.1...@gmail.com> wrote:
> >
> > > > > Hi,
> >
> > > > >        After checking with python-list i found that i was
> > > > > misinterpreting the output error message. The actual problem is
> post-
> > > > > review script is not able to access file "c:\docume~1\shambhu
> > > > > \locals~1\temp\4e0c6ccee4b4ee199cc18529c0bbf8c4" if this file is
> > > > > already present if there is failure in previous run.
> > > > > Now i am stuck again in function "do_diff" in post-review script.
> Here
> > > > > is piece of code:
> >
> > > > > for filenam in (onam, mnam) :
> > > > >                 if cpath.exists(filenam) and self.viewtype ==
> > > > > "dynamic":
> > > > >                     debug("Dynamic view Type")
> > > > >                     do_rem = False
> > > > >                     fn = filenam
> > > > >                 elif len(filenam) > 254 or self.viewtype ==
> > > > > "snapshot":
> > > > >                     debug("Snapshot View Type")
> > > > >                     fn = self.get_filename_hash(filenam)
> > > > >                     debug("FileName_Hash: %s" % fn)
> > > > >                     fn = cpath.join(tempfile.gettempdir(), fn)
> > > > >                     debug("TempFileTempdir: %s" % fn)
> > > > >                     do_rem = True
> > > > >                 fd = open(cpath.normpath(fn))
> > > > >                 fdata = fd.readlines()
> > > > >                 fd.close()
> > > > >                 file_data.append(fdata)
> > > > >                 # If the file was temp, it should be removed.
> > > > >                 if do_rem:
> > > > >                     os.remove(filenam)
> >
> > > > > Here i am getting error at last line "os.remove(filenam)", because
> > > > > filenam contains version extended path name and hence it is not
> able
> > > > > to access/remove windows command.
> >
> > > > > WindowsError: [Error 206] The filename or extension is too long:
> 'K:\
> > > > > \SHAMBHU_XXXXXXX\\YYYYYYYYYY\\@@\\main\\2\\abcabcabc\\@@\\main\
> > > > > \abcabcabc\\abcabcabc_r1\\xyzxyz\\1\\hello\\@@\\main\\abcabcabc\
> > > > > \abcabcabc_r1\\xyzxyz\\1\\hello.c@
> @\\@@\\main\\abcabcabc\\abcabcabc_r1\
> > > > > \xyzxyz\\xyzxyzxyz_1\\0'
> >
> > > > > Regards,
> > > > > Shambhu.
> >
> > > > > On Aug 7, 3:43 pm, Shambhu <shambhu.1...@gmail.com> wrote:
> >
> > > > > > Hi,
> >
> > > > > >       This time I tried post-review with checkedout file. I ran
> > > > > > command \$post-review -d <checkedout_Filename>
> > > > > > But even with checkedout file it is failing. Here is trace log:
> >
> > > > > > Traceback (most recent call last):
> > > > > >   File "C:\Python25\Scripts\post-review-script.py", line 8, in
> > > > > > <module>
> > > > > >     load_entry_point('rbtools==0.2.1alpha0.dev',
> 'console_scripts',
> > > > > > 'post-review')()
> > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line 2993,
> in
> > > > > > main
> > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line 1041,
> in
> > > > > > diff
> > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line 999,
> in
> > > > > > get_extended_namespace
> > > > > > WindowsError: [Error 5] Access is denied: 'c:\\docume~1\\shambhu\
> > > > > > \locals~1\\temp\\4e0c6ccee4b4ee199cc18529c0bbf8c4'
> >
> > > > > > After looking into postreview.py, i found that it is failing at
> > > > > > additional backslash "\" with the pathname and which is causing
> the
> > > > > > problem. I am able to access file
> 'c:\docume~1\shambhu\locals~1\temp
> > > > > > \4e0c6ccee4b4ee199cc18529c0bbf8c4' but not
> 'c:\\docume~1\\shambhu\
> > > > > > \locals~1\\temp\\4e0c6ccee4b4ee199cc18529c0bbf8c4'
> >
> > > > > > Please suggest how can i fix above issue. I tried a sample script
> > > > > > having "os.unlink" with Python3.1 and even with that i am getting
> same
> > > > > > issue of additional backslash "\".
> >
> > > > > > Regards,
> > > > > > Shambhu.
> >
> > > > > > On Aug 6, 2:00 pm, Shambhu <shambhu.1...@gmail.com> wrote:
> >
> > > > > > > Hi,
> >
> > > > > > >         I am new to ReviewBoard. I installed reviewboard verion
> 1.5rc1
> > > > > > > rbtools "0.2.1alpha0.dev" in windows machine. I am using
> clearcase as
> > > > > > > version control. When i use command "\$post-review -d file.name",
> i am
> > > > > > > getting file not found error, but the file is actually there. I
> am
> > > > > > > using dynamic view and the file mentioned below is checked-in.
> Here is
> > > > > > > log which i am getting:
> >
> > > > > > > K:\reviewboard_view\test_vob1\test_dir>post-review -d
> hello.c>>> cleartool pwv -short
> > > > > > > >>> repository info: Path: K, Base path: K, Supports
> changesets: False
> > > > > > > >>> cleartool desc -pre
> K:\reviewboard_view\test_vob1\test_dir\hello.c
> > > > > > > >>> cleartool desc -fmt %Vn K:\
> > > > > > > >>> cleartool desc -fmt %Vn K:\reviewboard_view
> > > > > > > >>> cleartool desc -fmt %Vn K:\reviewboard_view\test_vob1
> > > > > > > >>> cleartool desc -fmt %Vn
> K:\reviewboard_view\test_vob1\test_dir
> > > > > > > >>> cleartool desc -fmt %Vn K:\
> > > > > > > >>> cleartool desc -fmt %Vn K:\reviewboard_view
> > > > > > > >>> cleartool desc -fmt %Vn K:\reviewboard_view\test_vob1
> > > > > > > >>> cleartool desc -fmt %Vn
> K:\reviewboard_view\test_vob1\test_dir
> >
> > > > > > > ERROR: FILE NOT FOUND : K:\reviewboard_view\test_vob1\@@\main
> > > > > > > \2\test_dir\@@\main\3\hello.c@@\@@\main\4
> >
> > > > > > > If i just run \$post-review -d then i am getting following
> error:>>> cleartool pwv -short
> > > > > > > >>> repository info: Path: K, Base path: K, Supports
> changesets: False
> >
> > > > > > > Traceback (most recent call last):
> > > > > > >   File "C:\Python25\Scripts\post-review-script.py", line 8, in
> > > > > > > <module>
> > > > > > >     load_entry_point('rbtools==0.2.1alpha0.dev',
> 'console_scripts',
> > > > > > > 'post-review')()
> > > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line
> 2982, in
> > > > > > > main
> > > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line
> 1035, in
> > > > > > > diff
> > > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line 899,
> in
> > > > > > > get_extended_namespace
> > > > > > >   File "build\bdist.win32\egg\rbtools\postreview.py", line 890,
> in
> > > > > > > get_previous_version
> > > > > > > IndexError: list index out of range
> >
> > > > > > > Please let me know how to fix this issue or i have done some
> mistake
> > > > > > > in configuration.
> >
> > > > > > > Regards,
> > > > > > > Shambhu.
>
> --
> Want to help the Review Board project? Donate today at
> http://www.reviewboard.org/donate/
> Happy user? Let us know at http://www.reviewboard.org/users/
> -~----------~----~----~----~------~----~------~--~---
> To unsubscribe from this group, send email to
> For more options, visit this group at

format: plain


text:
• # question_answer If $z=1+i,$ then the multiplicative inverse of z2 is (where i = $\sqrt{-1}$) [Karnataka CET 1999] A) 2 si B) 1 - i C) - i/2 D) i/2

Solution :

Given $z=1+i$ and $i=\sqrt{-1}.$ Squaring both sides, we get ${{z}^{2}}={{(1+i)}^{2}}=1+2i+{{i}^{2}}=1+2i-1$ or ${{z}^{2}}=2i.$ Since it is multiplicative identity, therefore multiplicative inverse of ${{z}^{2}}=\frac{1}{2i}\times \frac{i}{i}=\frac{i}{2{{i}^{2}}}=-\frac{i}{2}.$

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text:
nLab compact closed category

Context

Monoidal categories

monoidal categories

Contents

Definition

A compact closed category, or simply a compact category, is a symmetric monoidal category in which every object is dualizable, hence a rigid symmetric monoidal category.

In particular, a compact closed category is a closed monoidal category, with the internal hom given by $[A,B] = A^* \otimes B$ (where $A^*$ is the dual object of $A$).

More generally, if we drop the symmetry requirement, we obtain a rigid monoidal category, a.k.a. an autonomous category. Thus a compact category may also be called a rigid symmetric monoidal category or a symmetric autonomous category. A maximally clear, but rather verbose, term would be a symmetric monoidal category with duals for objects.

Properties

Relation to traced monoidal categories

Given a traced monoidal category $\mathcal{C}$, there is a free construction completion of it to a compact closed category $Int(\mathcal{C})$ (Joyal-Street-Verity 96):

the objects of $Int(\mathcal{C})$ are pairs $(A^+, A^-)$ of objects of $\mathcal{C}$, a morphism $(A^+ , A^-) \to (B^+ , B^-)$ in $Int(\mathcal{C})$ is given by a morphism of the form $A^+\otimes B^- \longrightarrow A^- \otimes B^+$ in $\mathcal{C}$, and composition of two such morphisms $(A^+ , A^-) \to (B^+ , B^-)$ and $(B^+ , B^-) \to (C^+ , C^-)$ is given by tracing out $B^+$ and $B^-$ in the evident way.

Relation to star-autnomous categories

A compact closed category is a star-autonomous category: the tensor unit is a dualizing object.

References

Discussion of coherence in compact closed catories is due to

• Max Kelly, M.L. Laplaza, Coherence for compact closed categories, Journal of Pure and Applied Algebra 19: 193–213 (1980)

The relation to quantum operations and completely positive maps is discussed in

• Peter Selinger, Dagger compact closed categories and completely positive maps. pdf

The relation to traced monoidal categories is discussed in

Revised on July 31, 2014 02:39:59 by Sam? (131.174.142.158)


text:
# Junk Drawer

For all those little papers scattered across your desk

# Re: Dumpster Diving through Dotfiles

D. Ben Knoble on 07 Nov 2019 in Blog

I learn a lot after some advice from thoughtbot.

Update 2019-11-19: slides for a presentation on this performance mystery

Update 2019-11-29: Both HTML traces are available on Google Drive: 1, 2

## Dumpster-diving?

Thoughtbot apparently started a new series on finding tricks in folks’ Dotfiles. As you may know by now, I maintain my own over on GitHub. I peruse others for fun and often learn a lot.

Well, in the course of adjusting their git-branches alias, I found a new trick.

## g for git

I have long had alias g='git' in my bash files, along with the appropriate completion definition. But I saw that thoughtbot had a g function which does a git-status if no arguments are provided! This is genius, says I, and I convert.

Aside: In doing so, I forgot to unalias g prior to reload my files. That caused the function definition g() { ... } to expand to git() { ... }—worse, since that definition calls git, I had made every invocation of git (including that of my PS1 prompt) a recursive stack overflow.

Lesson: prefer functions if the complexity can grow.

## More performance problems

Anyways, as you may remember from earlier, my Dotfiles repo is big. At time of writing:

λ g cstat count
1707
λ du -hd1 .git
16K    .git/gitweb
1,4M    .git/objects
0B    .git/rr-cache
8,0K    .git/info
84K    .git/logs
24K    .git/hooks
12K    .git/refs
40M    .git/modules
42M    .git

So the sucker is, well, large (and note how big .git/modules is—we’ll be coming back to that).

Testing out my new g function, I found that git status -sb was taking half a second to complete, where on other repos it ran 10-100x faster. What gives?

Naïvely, I tried git gc (even with --aggressive, which git admits you probably don’t need). This shaved off 6MB to get the numbers you see now. But the performance didn’t waver.

Thinking back to those numbers (and a trace of git code I’d accidentally done recently, wherein there were calls to submodule code), I remembered this little gem:

λ g submodule | wc -l
47

A quick experiment revealed the issue. After issuing git submodule deinit --all, speeds were back to normal. Having a lot of vim plugins is catching up to me…

Long-story short, turning off submodule stuff in the status brings me back down to the right time. You can do this with a flag on status, but I ended up doing

λ g config diff.ignoresubmodules all

So only my Dotfiles, where the submodules are a problem, ignores them.

Lesson: if your repo has a lot of submodules, you can speed up some operations with this local configuration. But be sure to check git submodule summary every now and then, just to be sure. In my workflow, I almost always only make changes by updating the submodules from upstream, so this can be less of an issue.


text:
Menu Outline Exercise Questions Appendices Lectures Student Projects Books Sections Introduction Atoms Molecules Crystal Structure Crystal Diffraction Crystal Binding Photons Phonons Electrons Band Model Crystal Physics Semiconductors

PHY.K02UF Molecular and Solid State Physics

## Introduction

Solid state physics relates the microscopic structure of a solid (the arrangement of the atoms) to its macroscopic properties (density, strength, electrical conductivity, thermal conductivity, optical properties, magnetism, color, etc.). Early in the history of solid state physics, basic properties of solids like density, color, hardness or yield strength were measured experimentally and tabulated. Experimental observations were used to formulate phenomenological laws. For instance, it is observed that the current that flows through a metal resistor is proportional to the voltage applied. From this observation Ohm postulated his phenomenological law, $V=IR$ (Voltage = Current* Resistance) without any deeper theoretical understanding.

As time went on and our theoretical understanding of solids improved, it became clear that every property of a solid can be calculated from the Schrödinger equation. This equation tells us which microscopic arrangement of the atoms in a solid has the lowest energy as well as the electrical, thermal, and optical properties of this arrangement of atoms. The only problem with this approach is that the Schrödinger equation is devilishly difficult to solve for many particle problems such as finding the quantum states for all electrons, protons, and neutrons in a solid.

In this course, approximations are introduced that make the Schrödinger equation easier to solve. In the section on molecules, sometimes we will neglect the electron-electron interactions which makes the Schrödinger equation much easier to solve. In the section on molecules we go further and neglect the electron-nuclei interactions as well as the electron-electron interactions. This results in the the famous "free electron model" is widely used to approximate the properties of metals and semiconductors. From this simple model, properties like the specific heat or the electrical conductivity can be calculated.

The lectures do not closely follow a book for the sections on atoms or molecules. There are online notes that can be found by following the links in the course outline. A longer explanation of these topics can be found in: Experimentalphysik 3: Atome, Moleküle und Festkörper by Demtröder, The Physics of Atoms and Quanta by H. Haken and H. C. Wolf, and Molecular Physics & Elementary of Quantum Chemistry, H. Haken un H. C. Wolf. See the section on text books for links to online versions of these books in German.

In the section of the course about solids, the lectures most closely follow Introduction to Solid State Physics by Charles Kittel. Other books that cover almost the same material are: Festkörperphysik by R. Gross and A. Marx, and Festkörperphysik by H. Ibach and H. Lüth. These books are also available online in the list of text books.

As part of the exercises that go with these lectures, every student must contribute something that will improve the course. This contribution should correspond to about 4 hours of work. It can be anything that you think will help students pass the exam. There is a list of suggested projects.


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# If sequence {x} is in l2, does x_n<k/n follow?

1. Feb 17, 2012

### jpe

1. The problem statement, all variables and given/known data
Suppose we have a sequence {x} = {x_1, x_2, ...} and we know that $\{x\}\in\ell^2$, i.e. $\sum^\infty x^2_n<\infty$. Does it follow that there exists a K>0 such that $x_n<K/n$ for all n?

2. Relevant equations
The converse is easy, $\sum 1/n^2 = \pi^2/6$, so there would be a finite upper bound for $\sum^\infty x^2_n<\infty$.

3. The attempt at a solution
I'm stuck. I cannot think of a counterexample and my hunch is that it's true. I was hoping that maybe from $\sum^\infty x^2_n=L$ for some L I could derive a bound for the elements of the sum involving the summation index, but to no avail so far.

2. Feb 17, 2012

### jbunniii

If you had something like $x_n = 1/\sqrt{n}$, there would be no such $K$, right? Of course $\sum x_n^2$ doesn't converge in that case, but can you replace enough of the $x_n$'s with 0 to achieve convergence?

3. Feb 17, 2012

### LCKurtz

When you think about the p series$$\sum_1^\infty \frac 1 {n^p}$$you know that p=1 is the dividing line between convergence and divergence. So as soon as p > 1 even a little, you get convergence. You might be lulled into thinking that anything bigger than n in the denominator will give convergence because of this. But that is wrong because the series$$\sum_2^\infty \frac 1 {n\ln n}$$also diverges. The logarithm grows so slowly that it doesn't help enough to get convergence.

This is a roundabout way of suggesting that if you are looking for counterexamples right on the edge of convergence-divergence, a judicious use of logarithms in the formula might help.

4. Feb 17, 2012

### Dick

I like jbunnii's suggestion better. Make a lot of terms in your series 0.

5. Feb 17, 2012

### jpe

Yeah, that was a good suggestion indeed, it seems almost trivial now. Let {x} be given by
$x_n=1/\sqrt{n}$ if $n=m^2$ for some m, 0 else. So we would have x={1,0,0,1/2,0,0,0,0,1/3,0, ...} for the first few terms. Then:
$\sum_{n=1}^\infty x_n^2 = \sum_{m=1}^\infty (1/\sqrt{m^2})^2=\sum 1/m^2=\pi^2/6$, so $x\in\ell^2$. However, assume there is a bound $x_n\leq K/n$ for all n. Look at the element with $n=(K+1)^2$:
$x_{(K+1)^2}=1/(K+1)=(K+1)/(K+1)^2>K/(K+1)^2$. Thus, K cannot have been a bound. Since K is arbitrary, no such K can exist, and we have found a counterexample!

Thanks for the input guys!


text:
### Browse by

Workshop organitzat pel grup GAECE (Grup de recerca en accionaments amb commutació electrònica), celebrat a l'EPSEVG el 2 de febrer de 2018

### Summary

• #### Are SRM drives a real alternative for EV powertrain? : Conclusions of the Workshop

(2018-02)
Conference report
Open Access
This paper is a summary of the debate that took place in the round tables: - What is slowing down the application of SRM drivesfor road vehicle electrification? - Where should research and development focus toboost application ...
• #### A novel topology of high-speed SRM for high-performance traction applications

(2018-02)
Conference report
Open Access
A novel topology of high-speed Switched Reluctance Machine (SRM) for high-performance traction applications is presented in this article. The target application, a Hybrid Electric Vehicle (HEV) in the sport segment poses ...
• #### In-wheel axial-flux SRM drive for light electric vehicles

(2018-02)
Conference report
Open Access
Revenues from global sales of light electric vehicles are expected to grow from $9.3 billion in 2017 to$ 23.9 billion in 2025. In order to boost this growth electric drives with better features and lower costs have to ...
• #### Torque control strategy for an axial flux switched reluctance machine

(2018-02)
Conference report
Open Access
This paper reflects the work done to design a torque control strategy for an axial flux switched reluctance machine. The general electrical model is first presented but as the switched reluctance machine behaves nonlinearly1 ...
• #### Modular switched reluctance machines to be used in automotive applications

(2018-02)
Conference report
Open Access
In the last decades industry, including also that of electrical machines and drives, was pushed near to its limits by the high market demands and fierce competition. As a response to the demanding challenges, improvements ...
• #### Powder metallurgical materials and processes for soft magnetic applications

(2018-02)
Conference report
Open Access
For many designers of electrical machines, the term “soft magnetic materials” automatically means laminated electrical sheet. This is unfortunate, since for many applications, particularly at low frequencies, laminated ...
• #### SRM drives an alternative for E-traction : Presentation of the workshop

(2018-02)
Conference report
Open Access
Electrification of road vehicles is one of the most consistent initiatives to achieve a clean, environmentally friendly and efficient transport system. The choice of the electric machine for the powertrain is an important ...
• #### Workshop SRM Drives an Alternative for E‐Traction : Proceedings

(2018-02)
Conference report
Open Access
Electrification of road vehicles is one of the most consistent initiatives to achieve a clean, environmentally friendly and efficient transport system. The choice of the electric machine for the powertrain is an important ...


text:
# How do you find the derivative of  1/t^2?

Aug 30, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{2}{t} ^ 3$

#### Explanation:

Given -

$y = \frac{1}{t} ^ 2$

It can be written as -

$y = {t}^{-} 2$

Then apply the differentiation rule to differentiate

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 2 {t}^{-} 3$

This can be written as -

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{2}{t} ^ 3$


text:
- 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
 On fixed points on compact Riemann surfaces Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 1015-1021 https://doi.org/10.4134/BKMS.2011.48.5.1015Printed September 1, 2011 Grzegorz Gromadzki University of Gda\'nsk Abstract : A point of a Riemann surface $X$ is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set ${\rm Fix}(X)$ of fixed points of a Riemann surface $X$ of genus $g\geq 2$ has at most $82(g-1)$ elements and this bound is attained just for $X$ having a Hurwitz group of automorphisms, i.e., a group of order $84(g-1)$. The set of such points is invariant under the group of holomorphic automorphisms of $X$ and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient conditions for its faithfulness. Keywords : automorphisms of Riemann surfaces, fixed point, Fuchsian groups, symmetric representation MSC numbers : Primary 30F10; Secondary 14H37, 14H55, 20B25 Downloads: Full-text PDF


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# Definition of conjugate momentum on a manifold

I have trouble understanding this definition:

Let $$Q$$ be some manifold and $$L: TQ \to \mathbb{R}$$ a smooth function. Then for some local coordinates $$(q, \dot{q})$$ on $$TQ$$ the conjugated momentum is defined as $$\frac{\partial L}{\partial \dot{q}}$$, which is an element of the co-tangential bundle $$T^{*}Q$$.

How is the expression $$\frac{\partial L}{\partial \dot{q}}$$ to be interpreted? If one simply expresses $$L$$ in local coordinates by $$L \circ(q^{-1}, \dot{q}^{-1}): \mathbb{R}^{2n} \to \mathbb{R}$$ and differentiates it with respect to the second variable one gets a function $$\mathbb{R}^n \to \mathbb{R}$$ and not an element of the co-tangential bundle $$T^{*}Q$$. Is the correct expression $$\partial_2 ( L \circ(q^{-1}, \dot{q}^{-1}))\circ (q, \dot{q}) \in T^{*}Q\ ?$$

• yes, the issue is that the derivatives you get away from $0 \in \Bbb R^n$ are not actually independent of the choice of local coordinates in any reasonable sense. The only invariant data is what you're writing down along the 0-section. – user98602 Dec 31 '18 at 0:39

The notation $$\partial L/\partial\dot{q}$$ is no more than a symbol that denotes the Frechet derivative of $$L$$ with respect to $$\dot{q}$$. More precisely, let $$L:Q\times TQ\to\mathbb{R}.$$ Then for all $$x\in Q$$, $$T_xQ$$ is a vector space equipped with the norm induced by the metric on $$Q$$. In this sense, one may define a bounded linear operator $$A:TQ\to\mathbb{R}$$, such that $$\lim_{Y\to 0}\frac{\left\|L(x,X+Y)-L(x,X)-A(Y)\right\|_{\mathbb{R}}}{\left\|Y\right\|_{T_xQ}}=0$$ for a given $$x\in Q$$ and a given $$X\in T_xQ$$. This linear operator $$A$$, if it exists, is called the partial derivative of $$L$$ with respect to $$X$$, also denoted by $$\partial L/\partial X$$ for intuition. Further, if one considers a trajectory $$q:\mathbb{R}\to Q$$, we have $$\dot{q}:\mathbb{R}\to T_{q}Q$$. Hence when considering the special form $$L(q,\dot{q})$$, we also take $$\partial L/\partial\dot{q}$$ instead of $$\partial L/\partial X$$, again, for intuition.
Finally, whatever the notation is assigned to the operator defined above, either $$A$$ or $$\partial L/\partial X$$ or $$\partial L/\partial\dot{q}$$, it is (1) linear and is (2) from $$TQ$$ to $$\mathbb{R}$$. On the other hand, the collection of all linear operators from $$TQ$$ to $$\mathbb{R}$$ is definitely $$T^*Q$$. Therefore, it follows that $$A\in T^*Q,\quad\text{or}\quad\frac{\partial L}{\partial X}\in T^*Q,\quad\text{or}\quad\frac{\partial L}{\partial\dot{q}}\in T^*Q.$$


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2.10

## The University of Warwick

Skip to 0 minutes and 9 secondsWelcome back. So last session, we saw that Wikipedia actually makes information available on how many people have viewed different pages. So for example, if you go to stats.grok.se, and you type in the name of the page, like Friday, then you get a nice graph which looks a little bit like this. Now the good news is that you can actually get the raw data if you want to analyse this information, not just plot graphs on the website. You can get that data by clicking on this page in JSON format down here. Unfortunately, what turns up is not a nice table as you might hope, of data which is really easy to analyse.

Skip to 0 minutes and 51 secondsInstead what you get is a lot of strange punctuation symbols, so funny brackets and colons and things. Now thankfully, it's not actually that difficult to take this data and turn it into a table that you can work with. What we need to do is get this information out of the web browser and into a programme which can understand it. Now to do our data analysis here and throughout the rest of the course, we're going to use R. Now, R is an industry leading package for analysing data. And conveniently, thanks to the generosity of the many programmers who've contributed to it, it's free.

Skip to 1 minute and 30 secondsHere, I'm going to assume you've already followed the instructions that we've made available for installing R and RStudio. Go and have a look at the course website if not. So let's open RStudio. I've opened it in the background already. Here we go. Now, lots of people have actually already written programmes which can help us solve parts of our problem. For example, there's already a package, or in other words, a collection of programmes which will let us download data from the web and get it into R. This package is called RCurl. So let's install it. We can use a command called install.packages.

Skip to 2 minutes and 52 secondsSo if we go back to the web browser, copy the URL, take it back to RStudio, and then we can type in a function called getURL and just paste in that URL between quotes. If you hit Enter, there you go. Excellent. So good news is that R has successfully managed to get the data. The bad news is it pretty much looks exactly like what we had in the browser. And possibly even worse. We've got some further strange slash symbols in there. Okay. So let's try and turn this information into a table which we can understand. Now in order to help us work with this data, we want to save it somewhere rather than just printing it to the screen.

Skip to 3 minutes and 40 secondsWhat we're looking at here is what we call raw data. Data which we haven't processed at all. So let's label the place we're going to save it "rawData." So here we go. Let's type in raw data and put some information in there using the arrow symbol. And then we type in getURL, as we did before, and paste in the URL. There we go. Excellent. So it seems to have done something. If we type in raw data, we can see what it's done. Brilliant. It's there, just like it was before. So let's try and turn this into a table. Now the good news is this strange looking format is actually a very well-known format. It's called JSON.

Skip to 4 minutes and 23 secondsAnd other people have written programmes which will read the information you can see on your screen and turn it into a table that you can work with in a much easier fashion. So first we need to install one of these programmes for parsing this data. So parsing is basically interpreting this format and turning it into a different format that we can work with more easily. So let's install this package. Again, you only need to do this once on the computer you're working on.

Skip to 4 minutes and 56 secondsAnd the package is called RJSONIO. There we go. Excellent. It's installed. And now, again as before, we need to load it. This is a bit you have to do every time you want to use this package in R. Again, without quotes.

Skip to 5 minutes and 14 secondsBrilliant. Okay. So in order to turn that strange looking data into a table, in fact we just need one function called fromJSON, which we write like this. And we pass the information we saved before in "rawData" to this function. Like that, just by putting in the brackets afterwards. If we press Enter, then you can see that what comes out is looking a lot easier to understand. There's still some strange complicated bits there, but we can see at the top, especially under "$daily_views," there's something which looks a bit like a table, which we might be able to work with. So as we did before, let's try and save this data somewhere. Now, we've parsed the data, as we were discussing before. Skip to 6 minutes and 2 secondsSo rather than calling it "raw data," let's call it "parsed data" now. So type in parsed data. And if I just type in exactly what I typed in before, instead of printing the parsed data to the screen, it'll save it in "parsedData," another variable. Let's check what's there, make sure it's worked. There you go. Excellent. Printed the same thing to the screen. So how do we get access to that bit of the data which is labelled "$data_views?" Well, let's try typing this in. The place we just saved it is called "Parsed Data." And now let's type dollar daily underscore views.

Skip to 6 minutes and 45 secondsThere you go. There's the table. So we've got something which looks like it might be a bit easier to work with. It'd be nice if we could make a graph of our own to see what's going on. So next week, we'll have a look at how to do this. See you then.

# Finding out what people are looking for on Wikipedia using R

Note: In order to see the details of the commands and screen-based information it is best to view this video full screen and in HD. However, if you’d like to have a go yourself, we strongly recommend you follow the instructions in the text below, where we tell you what the commands in the video are. You’ll probably find this a lot easier than copying the commands from the video.

Welcome to this first exercise of the Big Data course. The exercises in this course are designed for you to follow and run yourself in RStudio and R.

The video above is a representation, a walkthrough, of the full exercise below. You can watch the video to gain an understanding of the use of data and R or, if you are interested in trying the processes for yourself, then follow the exercise text below that will guide you through the various steps.

Last session we saw that Wikipedia makes information available on how many people have viewed a given page. We visited the site http://stats.grok.se/ and accessed data on how often people had viewed different Wikipedia pages.

To recap, let’s try finding out how often people look at the “Friday” page on Wikipedia. On the http://stats.grok.se/ website, type in “Friday”.

Note: there is a known issue with some recent downloads of the data. http://stats.grok.se/en/201603/friday- Internet Server Error http://stats.grok.se/en/201602/friday - Internet Server Error http://stats.grok.se/en/201601/friday - OK

To get hold of this data to do our own analysis, we can click on the little link at the bottom of the page: “This page in json format”, which brings us to this page: http://stats.grok.se/json/en/201504/Friday

Unfortunately, we find that the data does not come in a nice table that we can work with easily! Instead, you get a page full of funny brackets, colons, and other punctuation signs.

The good news is that it’s not so hard to turn this strange looking information into a table.

We need to get this information out of the web browser and into a program, which is going to help us analyse it.

We are going to use R, which is an industry leading environment for analysing data, with the excellent editor program RStudio. Conveniently, thanks to the generosity of the many programmers who have contributed to R and RStudio, they are both free!

Let’s open RStudio. These exercises, one per week except in Week 5, have instructions, followed by commands you can type into the window labelled “Console”, or copy from here:

    cat("Hello, World...")

You can ignore anything on a line written after a # sign – this is just a comment. There is no need to copy this across – although if you do, R will ignore it too. Try it out:

    cat("Hello again, World!")  # This is a comment

This exercise aims to explain a lot of the commands used. However, R has some great built in help too. If you would like to learn more about a command (for example, “install.packages”), try the R ? feature:

    ?install.packages

So, back to our original problem. How do we use R to find out what people are looking for on Wikipedia?

Now, lots of people have already written programs which can help us solve parts of our problem. In R, these are made available in “packages”. For example, there is already a package which will let us download data from the web, and get it into R. This package is called “RCurl”. Let’s install it.

This command installs the package for you - you only ever need to run it once on the computer you are using right now:

    install.packages("RCurl")

This command loads the package for you. You need to run this command every time you open R and want to use this package:

    library(RCurl)

    getURL("http://stats.grok.se/json/en/201410/Friday")

The good news is that we’ve got the data! The bad news is that it still looks like the strange format we saw in the web browser.

So we can try and turn this information into a table which we can understand, let’s save the information.

This is what we would call “raw data”, data which we haven’t processed at all, so let’s label the place we are saving the information “rawData”.

Put the result of getURL in “rawData”:

    rawData <- getURL("http://stats.grok.se/json/en/201410/Friday")

The place we are saving the information, “rawData”, is called a variable. It’s just like a box where you can keep information you’d like to do something with later.

Let’s have a look at what’s now in rawData, by typing the variable name into the Console:

    rawData

OK – this looks like what we had before!

Now let’s try and turn this dataset into a table.

This format is actually a well known format called “JSON”. We can install a program which can read this data. This program is called a “parser”.

Again, there is already a “package” which will help R to read JSON data.. This package is called “RJSONIO”. Let’s install it:

    install.packages("RJSONIO")  # Install the JSON parser
library(RJSONIO)  # Load the JSON parser

Note: where the code consists of more than one line of code you must hit ‘Enter’ at the end of each line.

To parse the JSON, we can use a function called “fromJSON”:

    fromJSON(rawData)

What comes out of this function looks a bit more understandable, particularly the bit under “$daily_views”. Let’s save the parsed data in a variable called “parsedData”:  parsedData <- fromJSON(rawData)  Let’s check what’s now saved in parsedData, by typing the variable name into the Console:  parsedData  … looks good. How can we access the information in the variable labelled “$daily_views”? Try typing this in

    parsedData\$daily_views

OK - it looks like we’ve got something which is a bit more like a table!


text:
The manager of a local monopoly estimates that the elasticity

The manager of a local monopoly estimates that the elasticity of demand for its product is constant and equal to –4. The firm’s marginal cost is constant at $10 per unit. a. Express the firm’s marginal revenue as a function of its price. b. Determine the profit-maximizing price. 1 Approved Answer Related Questions in Others - Others • 1. Ten firms compete in a market to sell product X. The total sales of all... (Solved) August 01, 2015 1. Ten firms compete in a market to sell product X. The total sales of all firms selling the product are$1,000,000. Ranking the firms’ sales from highest to lowest, we...
a prototype automobile that could be driven 180 miles on a single gallon of unleaded gasoline. They estimated that in mass production that care would cost $40,000... Solution Preview : Assignment here are the problems for exam 2: Do the applied problems only. Make sure to type the problem and then answer it. There is a tab for the home work problem portion of the test in... • 100 multiple choice about encomics for leadership (Solved) March 03, 2014 100 multiple choice about encomics for leadership for graduate student Solution Preview : NEW ENGLAND COLLEGE SCHOOL OF GRADUATE AND PROFESSIONAL STUDIES TAKE HOME TEST SPRING 2014 There are one hundred questions in this test and you should answer all of them. Please read each... • Monopoly taxation (14 points) Suppose the marginal cost of producing... (Solved) April 18, 2017 Monopoly taxation (14 points) Suppose the marginal cost of producing onesies for adults is constant , where MC = m, and m is a positive number. The demand curve for... Solution Preview : Monopoly taxation (14 points) Suppose the marginal cost of producing onesies for adults is constant, where MC = m, and m is a positive number. The demand curve for adult onesies is given by... • Managerial Economics Questionsntw (Solved) March 09, 2015 I have three questions, is a big file because I had to copy a photo of the graph involved to get the whole thing to transfer over. Solution Preview : A firm sells its product in a perfectly competitive market where other firms charge a price of$90 per unit. The firm’s total costs are C(Q) = 40 + 10Q + 2Q2. What price and output would...


text:
# Heavy-quark opportunities and challenges at FCC-ee

@inproceedings{Monteil2021HeavyquarkOA,
title={Heavy-quark opportunities and challenges at FCC-ee},
author={St'ephane Monteil and G. R. Wilkinson},
year={2021}
}
• Published 2021
• Physics
The abundant production of beauty and charm hadrons in the 5 × 10 Z decays expected at FCC-ee offers outstanding opportunities in flavour physics that in general exceed those available at Belle II, and are complementary to the heavy-flavour programme of the LHC. A wide range of measurements will be possible in heavy-flavour spectroscopy, rare decays of heavy-flavoured particles and CP -violation studies, which will benefit from the low-background experimental environment, the high Lorentz boost… Expand
1 Citations

#### Figures and Tables from this paper

Hunt for rare processes and long-lived particles at FCC-ee
• Physics
• 2021
In this essay we discuss the possibilities and associated challenges concerning beyond the Standard Model searches at FCC-ee, such as rare decays of heavy-flavoured particles and long-livedExpand

#### References

SHOWING 1-10 OF 63 REFERENCES
Opportunities in Flavour Physics at the HL-LHC and HE-LHC
Motivated by the success of the flavour physics programme carried out over the last decade at the Large Hadron Collider (LHC), we characterize in detail the physics potential of its High-LuminosityExpand
Prospects for B + c → τ + ν τ at FCC-ee
This paper presents the prospects for a precise measurement of the branching fraction of the leptonic B+ c → τντ decay at the Future Circular Collider (FCC-ee) running at the Z-pole. A detailedExpand
FCC Physics Opportunities
We review the physics opportunities of the Future Circular Collider, covering its e+e-, pp, ep and heavy ion programmes. We describe the measurement capabilities of each FCC component, addressing theExpand
Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era
The LHCb Upgrade II will fully exploit the flavour-physics opportunities of the HL-LHC, and study additional physics topics that take advantage of the forward acceptance of the LHCb spectrometer. TheExpand
Low-energy signatures of the PS3 model: from B-physics anomalies to LFV
• Physics
• 2018
A bstractThe three-site Pati-Salam gauge model provides a consistent description for the hints of lepton-flavor non-universality observed in B decays, connecting the present pattern of “anomalies” toExpand
Clues for flavor from rare lepton and quark decays
• Physics
• 2015
A bstractFlavor symmetries successfully explain lepton and quark masses and mixings yet it is usually hard to distinguish different models that predict the same mixing angles. Further experimentalExpand
The Belle II Physics Book
We present the physics program of the Belle II experiment, located on the intensity frontier SuperKEKB e+e- collider. Belle II collected its first collisions in 2018, and is expected to operate forExpand
A method to determine |Vcb| at the weak scale in top decays at the LHC
• Physics
• 2018
A bstractUntil now, the Cabibbo Kobayashi Maskawa matrix element, |Vcb|, has always been measured in B decays, i.e. at an energy scale qb∼mb2$${q}_b\sim \frac{m_b}{2}$$, far below the weak scale.Expand
Lepton polarization asymmetries in rare semi-tauonic $$b \rightarrow s$$b→s exclusive decays at FCC-ee
• Physics
• 2017
We consider measurements of exclusive rare semi-tauonic b-hadron decays, mediated by the $$b \rightarrow s \tau ^+ \tau ^-$$b→sτ+τ- transition, at a future high-energy circular electron–positronExpand
Power-enhanced leading-logarithmic QED corrections to Bq→ μ+μ−
• Physics
• Journal of High Energy Physics
• 2019
A bstractWe provide a systematic treatment of the previously discovered power- enhanced QED corrections to the leptonic decay Bq→ μ+μ− (q = d, s) in the frame- work of soft-collinear effective theoryExpand


text:
Calculating Factor of Safety

1. Apr 28, 2017

AutumnBeds

1. The problem statement, all variables and given/known data

The 14mm diameter steel bolt with modulus of elasticity of 210GPa and modulus of rigidity of 85 GPa shown in the diagram below holds two components together. The thickness of the bolted interface of the components is 18mm. To 2 decimal places, for the given loading;

Assuming the ultimate tensile stress is 490MN/m2 and the ultimate shear stress is 290MN/m2 determine the factor of safety in operation.

Forces - http://imgur.com/mbTD0Xg

2. Relevant equations

Assuming the ultimate tensile stress is 490MN/m2 and the ultimate shear stress is 290MN/m2 determine the factor of safety in operation.

3. The attempt at a solution

I have resolves the forces and found the following

Direct Stress 35.12 Mpa
Tensile Stress 0.17 Mpa (I think something may be amiss here)
Sheet Stress 26.24 Mpa

But for the factor of safety the notes I have been given say to divide the UTS by the direct stress,

So 490/35.12 = 13.95 (seems rather high). But then do I repeat for the Ultimate sheer stress?

So again 290/35.12 = 8.26.

Then is the lower of the two value?

Any help is greatly appreciated.

2. Apr 29, 2017

tech99

No one answered. I think you have two modes of failure, each having its own FoS. The lowest must be the relevant one.

3. Apr 29, 2017

4. May 1, 2017

PhanthomJay

Bolts subjected to both shear and tension forces have allowable stresses governed by shear-tension interaction equations specified by applicable loads. The safety factor depends on what the results of the interaction equation show. It could be quite less than the safety factor for tension alone or shear alone. As requested, please show your work.

5. May 9, 2017

AutumnBeds

6. May 10, 2017

PhanthomJay

The terms 'direct' stress and 'tensile' stress need definition. Direct stress is tensile stress if no shear stresses exist. Tensile stress is the actual tensile stress on the bolt. In your first image, you are calculating the tensile stress, which you did correctly , except you transposed some numbers it should be 5734, you wrote 5374.

In the 2nd image, you are calculating tensile strain, not stress, and strain is a dimensionless number. I am unsure why you are doing this, though.

In the third image, you have calculated the shear stress correctly.

Now in the 4th image, you calculate a safety factor for tension stress and a safety factor for shear stress, and both are rather large safety factors, but you really can't look at the overall safety factor of the bolt without calculating the effects of both tensile and shear loads applied at the same time, because the shear stress reduces the allowable tensile stress in the bolt, using a combined tension and shear stress formula to determine the allowable tensile stress. Only then can you calculate the safety factor, which will be the lowest of the 3 safety factors so calculated. Are you familiar with combined shear and tension stress formulas? I suspect that the safety factor for shear alone will control, because your actual stresses are rather low, but generally speaking, when shear and tensile stresses are high, the combined stress safety factor will be a lot less than the individual tension and shear alone safety factors.

7. May 10, 2017

AutumnBeds

Thanks,

1. Will redo the calculation and transpose the numbers correctly

2. This most likely just a written error on my behalf

3. Thanks - occasionally I get things correct.

4. No - nothing in the course notes gives guidance on the using the columbines stresses to calculate the fos. If you can offer any guidance on this I would be grateful.

Thanks again.

8. May 11, 2017

PhanthomJay

I
If it's not in your notes, I guess they are not looking for a combined stress formula, which probably isn't necessary on this problem where stresses are rather low and shear alone safety factor controls.
A combined stress formula for bolts might look like ( approxomTely...don't use it at face value $F_t = 1.3 F_u - 5 f_v </= F_u$ where
F_u = max direct tensile syress at failure
F_t = max allowed tensile failure stress
f_v = applied shear load shear stress

If stresses are low then individual shear or tension safety factors control, but when stresses are high, the combined stress governs and must be used.

Last edited: May 12, 2017


text:
• N S Mondal

Articles written in Pramana – Journal of Physics

• Effect of next-nearest-neighbour interaction on $d_{x^{2}−y^{2}}$ -wave superconducting phase in 2D t-J model

n exact diagonalization calculation of the t-J model on 2D square cluster has been studied for the ground state properties of HTSC. Effect of next-nearest-neighbour hopping and magnetic (both antiferromagnetic and ferromagnetic) interaction on $d_{x^{2} −y^{2}}$-wave pairing has been shown. Relative strength of the next-nearest-neighbour interaction with respect to that of near-neighbour interaction for the strongest $d_{x^{2} −y^{2}}$-wave pairing has been estimated. A schematic phase diagram is shown. It is shown that a two-sublattice model with antiferromagnetic interaction between them and a small intra-ferromagnetic-type interaction in one sublattice favours $d_{x^{2} −y^{2}}$-wave superconductivity and moderate negative type NNN hopping adds flavours to this phase.

• Role of next-nearest-neighbour hopping in the internal structure of the ground state and finite temperature quantities of 2D t-J model

An exact diagonalization calculation for a small cluster in the two-dimensional t-J model has been studied to calculate two-hole correlation. Calculations reveal dominant hole–hole correlation for holes sitting on next-nearest-neighbour (NNN) sites and critical coupling occurs at $J/t = 0.8$. With the increase in negative-type NNN hopping, correlation decreases at NNN sites whereas it increases at other sites. The thermodynamic properties such as entropy and specific heat are studied as functions of temperature with various NNN hopping strength. Results show that with the inclusion of negative NNN hopping, the system becomes more ordered. A qualitative transition temperature region has been estimated. It is shown that with the increase in NNN hopping strength, $T_{c}$ increases. Specific heat results show non-Fermi liquid-type behaviour of the system. All our calculations establish the importance of negative-type NNN hopping.

• Role of correlated hopping in mixed valence phenomena

Role of correlated hopping is studied using extended Falicov–Kimball model in a small cluster. A discontinuous insulator-to-metal transition is observed at a critical 𝑓-level energy. Transition is sharper for larger correlated hopping. In the specific heat curves a two-peak structure consisting of a sharp peak followed by a Schottky-type broad peak is exhibited. In a limited parameter region, some heavy-fermion like characteristics have been observed

• # Pramana – Journal of Physics

Volume 94, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text:
# Statistics - Venn Diagram

Venn diagram is a way to visually represents relationship between groups of entities or objects. Venn diagrams are comprised of circles where each circle represents a whole set. Venn diagram can have unlimited circles but generally two or three circles are preferred otherwise the diagram becomes too complex.

## Steps to draw a Venn Diagram

Consider the following sets of people:

1. Cricket Players - $C = \{ Ram, Shyam, Mohan, Rohan, Ramesh, Suresh \}$

2. Hockey Players - $H = \{ Ramesh, Naresh, Mahesh, Leela, Sunita \}$

Step 1: Draw a rectangle and label it as players.

Step 2: Draw two circles and label them as Cricket and Hockey. Make sure that circles are overlapping each other.

Step 3: Write Names inside the circle as relevant. Common name(s) should fall within common region.

## Union

Union ($\cup$) represents a set where items are present in all categories but are not repeated.

### Example

Problem Statement:

Draw a Venn diagram of $C \cup H$.

Solution:

Step 1: Determine players who are either playing cricket or hockey. Draw them as following:

$C \cup H = \{ Ram, Shyam, Mohan, Rohan, Ramesh, Suresh, Naresh, Mahesh, Leela, Sunita \}$.

## Intersection

Intersection ($\cap$) represents a set where items are present in both categories.

### Example

Problem Statement:

Draw a Venn diagram of $C \cap H$.

Solution:

Step 1: Determine players who are playing cricket and hockey both. Draw them as following:

$C \cap H = \{ Ramesh \}$.

## Difference

Difference ($-$) represents a set where items are present only in one category and not in other one.

### Example

Problem Statement:

Draw a Venn diagram of $C - H$.

Solution:

Step 1: Determine players who are playing cricket only. Draw them as following:

$C - H = \{ Ram, Shyam, Mohan, Rohan, Suresh \}$.


text:
Tsinghua Science and Technology  2019, Vol. 24 Issue (06): 706-715    doi: 10.26599/TST.2018.9010092
 REGULAR ARTICLES
Residuals-Based Deep Least Square Support Vector Machine with Redundancy Test Based Model Selection to Predict Time Series
Yanhua Yu*, Jie Li
∙ Yanhua Yu and Jie Li are with the School of Computer, Beijing University of Posts and Telecommunications, Beijing 100876, China. E-mail: jli@bupt.edu.cn.

Abstract

In this paper, we propose a novel Residuals-Based Deep Least Squares Support Vector Machine (RBD-LSSVM). In the RBD-LSSVM, multiple LSSVMs are sequentially connected. The second LSSVM uses the fitting residuals of the first LSSVM as input time series, and the third LSSVM trains the residuals of the second, and so on. The original time series is the input of the first LSSVM. Additionally, to obtain the best hyper-parameters for the RBD-LSSVM, we propose a model validation method based on redundancy test using Omni-Directional Correlation Function (ODCF). This method is based on the fact when a model is appropriate for a given time series, there should be no information or correlation in the residuals. We propose the use of ODCF as a statistic to detect nonlinear correlation between two random variables. Thus, we can select hyper-parameters without encountering overfitting, which cannot be avoided by only cross validation using the validation set. We conducted experiments on two time series: annual sunspot number series and monthly Total Column Ozone (TCO) series in New Delhi. Analysis of the prediction results and comparisons with recent and past studies demonstrate the promising performance of the proposed RBD-LSSVM approach with redundancy test based model selection method for modeling and predicting nonlinear time series.

Received: 10 January 2018      Published: 15 March 2018
Corresponding Authors: Yanhua Yu


text:
Owen wrote:

> I would answer "\$$\mathbb{Z}/2\$$" to both Puzzle 102' and Puzzle 102''—but I would mean the group under addition in the first case, and the monoid under multiplication in the second!

Okay, good! If you want to be polite to mathematicians, you should say \$$(\mathbb{Z}/2, +) \$$ as your answer to Puzzle 102\$${}^\prime\$$ and
\$$(\mathbb{Z}/2, \cdot ) \$$ as your answer to Puzzle 102\$${}^{\prime\prime}\$$ - that's how mathematicians distinguish between the same set made into monoids with two different operations.

If you just write \$$\mathbb{Z}/2\$$, all mathematicians will assume you mean the group \$$(\mathbb{Z}/2, +) \$$.

Another nice name for the monoid \$$( \mathbb{Z}/2, \cdot ) \$$ is \$$(\textbf{Bool}, \wedge) \$$, since we can think of 0 as "false" and 1 as "true", and then multiplication becomes "and".

This monoid is also isomorphic to \$$(\textbf{Bool}, \vee) \$$, but now the identity element is "false", not "true"!

Another nice name for the group \$$(\mathbb{Z}/2, +) \$$ is \$$(\textbf{Bool}, \mathrm{XOR}) \$$, since ["exclusive or"](https://en.wikipedia.org/wiki/Exclusive_or) makes the Booleans into a group that's isomorphic to \$$(\mathbb{Z}/2, +) \$$.

And finally, if you make \$$\mathbb{Z}/2\$$ into a _ring_ with both addition and multiplication as its operations, mathematicians often call it \$$\mathbb{F}_2\$$, because it's the [field with two elements](https://en.wikipedia.org/wiki/GF(2)). You can also think of this field as the Booleans with "exclusive or" as addition and "and" as multiplication.


text:
# Mental Arithmetic

#### Question No 1

A motorcyclist travels 200 Km in 1 hr. How many minutes if would take him to travel 120 Km?

#### Select the correct answer

Solution!
200 Km distance covered in minutes = 60

1 Km distance covered in minutes = 60/200 = 3/10

120 Km distance covered in minutes = (3/10) * 120 = 36 minutes.

2664/12/6=?

#### Select the correct answer

Solution!
(2664/12) * (1/6) = 37.

#### Question No 3

What is 8/40 expressed as a decimal?

#### Select the correct answer

Solution!
Simple way is

(8/4) * (1/10) = 2 * 0.1 = 0.2.

#### Question No 4

John can read 8 pages of a book in 7 minutes, how long will he take to read 40 pages?

#### Select the correct answer

Solution!
40/8 = 5

As pages are increased 5 times. So minutes will also increase 5 time.

7 * 5 = 35.

#### Question No 5

If the number 5r2 is divisible by 6, then r = ?

#### Select the correct answer

Solution!
572 is completely divisible by 6..

#### Question No 6

What must be added to each numerator and denominator of 13/29 so that it becomes 1/2

#### Select the correct answer

Solution!
(13+3)/(29+3) = 1/2.

#### Question No 7

At a particular time shadow of a pole 40m long is measured to be 30m. If the length of a plaza is 200m then how long would the shadow be at about the same time?

#### Select the correct answer

Solution!
Shadow of 40m pole = 30m

Shadow of 1m pole = 30/40m

Shadow of 200m plaza = (30/40)*200 = 150m.

#### Question No 8

Subtract 369 from 1250.

#### Select the correct answer

Solution!
1250 - 369 = 881.

#### Question No 9

If n is not equal to 0, Which of the following must be greater than n? (1) 2n (2) n^2 (3) 2-n

#### Select the correct answer

Solution!
Square of every non zero integer is grater than the orignal number.

*Note that multiple of 2 of negative numbers are lesser than the orignal number..

#### Question No 10

If the number 481z673 is completely divisible by 9, what is the the smallest whole number in place of z?

#### Select the correct answer

Solution!
Select answer from options

4817673 is completely devisible by 9..

#### Question No 11

Deduct 7.3 from 34.2.

#### Select the correct answer

Solution!
34.2 - 7.3 = 26.9.

100/101 = ?

#### Select the correct answer

Solution!
100/101 = 0.990099.

#### Question No 13

What is 10 less 5/9 of 117?

Solution!
(5/9) * 117 = 65

65 - 10 = 55.

#### Question No 14

Divide 672 by 12.

Solution!
672 / 12 = 56.

#### Question No 15

The side of a square is 2. What is the area of the square?

#### Select the correct answer

Solution!
Area of square is
2 * (any side)
= 2 * (2) = 4 square units.

#### Question No 16

The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg.Find the average weights of all the boys in the class.

#### Select the correct answer

Solution!

In this question weighted average is calculated rather than simple average

(50.25*16 + 45.15*8)/(16+8) = 48.55.

#### Question No 17

If the product of 4 consecutive integers is 120, which is greater?

Solution!
5*4*3*2 = 120.

#### Question No 18

7/21 in lowest term is?

Solution!
7/21 = 1/3.

#### Question No 19

If average of 8, 7, 12, 15 and x is 11 what is x?

#### Select the correct answer

Solution!
(8+7+12+15+x)/5 = 11

42+x = 55

x = 55-42
=13.

#### Question No 20

The average of five numbers is 27.If one number is excluded the average becomes 25.What is the excluded number?

#### Select the correct answer

Solution!
No answer description available for this question..

#### Question No 21

Divide 52 by 4 and add 17 multiplied by 3.

Solution!
52 / 4 = 13

17 * 3 = 51

13 + 51 = 64.

#### Question No 22

What is 126 divided by 3?

Solution!
126 / 3 = 42.

#### Question No 23

If n is even, Which of the following cannot be odd? (1) n+3 (2) 3n (3) n^2 - 1

#### Select the correct answer

Solution!
3n and n^2 - 1 will always odd so in case of 3n answers will be even..

#### Question No 24

A number is thrift if it is a multiple of 2 or 3. How many thrift numbers are there between 0 and 15?

#### Select the correct answer

Solution!
Thrift numbers between 0 and 15 are following

2,3,4,6,8,9,10,12,14.

#### Question No 25

If the sum of three consecutive whole numbers is 15, what is the largest of the three numbers?

Solution!
6+5+4 = 15.

#### Question No 26

Ali can type at a speed of 25 words per minute. How many words he can type in one hour?

#### Select the correct answer

Solution!
Typed words in 1 minute = 25
Typed words in 60 minutes = 60 * 25 = 1500.

#### Question No 27

16 men dig a ditch in 10 days. How many men would be required to complete the job in half the time?

#### Select the correct answer

Solution!
Double number of men are required to complete the job in half time..

#### Question No 28

What is average of 12 , 15 and 18?

#### Select the correct answer

Solution!
(12+15+18)/3 = 45/3 = 15.

#### Question No 29

What is 3206 divided by 7?

#### Select the correct answer

Solution!
3206 / 7 = 458

No need to perform complete devision first digit comes 4 after devision and there is only one option in which first digit is 4..

#### Question No 30

Which is greater, (A) 5/8 of 112 , (B) 7/8 of 88?

#### Select the correct answer

Solution!
(5/8) * 112 = 70

and
(7/8) * 88 = 77

Hence, (7/8) of 88 is greater..

#### Question No 31

When R is divided by 7 remainder is 3. What is the remainder when 3R is divided by 7?

#### Select the correct answer

Solution!
No answer description is available for this question..

#### Question No 32

What is the difference of the product and the quotient of 8 and 8?

Solution!
8*8 = 64
and
8/8 = 1
So,
64 - 1 = 63.

#### Question No 33

What is the average of 8, 13, 25, 43, and 11?

#### Select the correct answer

Solution!
(8+13+25+43+11)/5 = 100/5
= 20.

#### Question No 34

Which of the following is the least number which is divisible by both 12 and 18?

#### Select the correct answer

Solution!
Least common multiple of 12 and 18 is 36.

#### Question No 35

What is average of 2, 5 , 6 , 9 and 18?

#### Select the correct answer

Solution!
(2+5+6+9+18)/5 = 40/5 = 8.

#### Question No 36

Which of the following is a prime number?

#### Select the correct answer

Solution!
A prime number is the number which is divisible by 1 and by itself only

and 2 is the only one even number which is prime..

#### Question No 37

What is 9 multiplied by 8?

Solution!
9 * 8 = 72.

#### Question No 38

A coach trip starts at nine fifty.It lasts twenty-five minutes.At what time does it finish?

#### Select the correct answer

Solution!
No answer description available for this question..

#### Question No 39

Ahmad reads 24 pages of a book in 15 minutes. The rate of pages read per minute by him will be

Solution!
24/15 = 8/5
8/5 = 1.6.

#### Question No 40

A cycle costs $170.Jane saves$50 each week.How many weeks will it be before she can buy it?

#### Select the correct answer

Solution!
170 / 50 = 3.4
But 3.4 is not in options so nearest Option is 4.

#### Question No 41

If m is an even integer and 3m < 48 and 2m > 24 then m = ?

#### Select the correct answer

Solution!
3*14 = 42 (lesser than 48)
and
2*14 = 28 (greater than 24)..

#### Question No 42

Multiply 15 by 6 and subtract 29.

Solution!
15 * 6 = 90

90 - 29 = 61.

#### Question No 43

Add 2/5 of 90 to 5/6 of 78.

Solution!
(2/5) * 90 = 36

(5/6) * 78 = 65

36 + 65 = 101.

Or

Solution!

#### Select the correct answer

Solution!
A will get half amount which B got.So if A's amount is 40, B's amount will be 80 (double of A's amount)..

#### Question No 79

In a Zoo deers and lions are in ratio of 5/2. If there are 20 deers how many lion are there?

#### Select the correct answer

Solution!
20 is 4 times of 5 So in this way 4 times of 2 will be 8..

#### Question No 80

What is the largest 4 digit number exactly divisible by 88?

#### Select the correct answer

Solution!
No answer description available for this question..

#### Question No 81

49/10 + 49/10 + 49/10 = ?

#### Select the correct answer

Solution!
By taking LCM of these three terms we have

(49+49+49)/10 = 147/10.

#### Question No 82

Multiply 6.85 by 7.

#### Select the correct answer

Solution!
6.85 * 7 = 47.95.

#### Question No 83

What is 45% of 300?

#### Select the correct answer

Solution!
45 * (300/100) = 135

Quick way to find answer from options is

50% of 300 is 150 so 45% of 300 should be less than 150

So, it may be 149 or 135
149 is very close to 150 which is not possible

Hence, 135 is correct answer..

#### Question No 84

Average of 3 numbers is 15. What is the sum of 3 numbers?

Solution!
Let sum is x.

x/3 = 15
x = 15*3 = 45.

2+2*2?

#### Select the correct answer

Solution!
2 + (2 * 2) = 6

Multiplication is performed first and subtraction afterwards.

Sequence of solving operators is
/
*
+
-.

#### Question No 86

What is average of 2 , 5 and 8?

#### Select the correct answer

Solution!
(2+5+8)/3 = 15/3 = 5.

#### Question No 87

What is 5/8 of 240?

#### Select the correct answer

Solution!
(5/8) * 240 = 150.

#### Question No 88

What is the sum of first 5 positive even integers?

Solution!
2+4+6+8+10 = 30.

#### Question No 89

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?

#### Select the correct answer

Solution!
Weighted average will be more close to the average of that batch which has maximum number of students so aanswer is 54.68

If you want to calculate it by formula then solution is

(55*50 + 60*55 + 45*60)/(55 + 60 + 45) = 54.68.

#### Question No 90

15 men were hired to plough a piece of land in 10 days. How many more men will be required to do the same job in 3 days?

#### Select the correct answer

Solution!
x/15 = 10/3

x = (10/3)*15
x = 50.

So more number of men required = 50-15 = 35.

#### Question No 91

What is 35% of 250?

#### Select the correct answer

Solution!
35 * (250/100) = 87.5

Quick way to find answer from options is

33% of 250 is nearly 83(250/3 = 83.3)

So, answer should be in 80's which is only one option 87.5.

#### Question No 92

Multiply 86 by 9 and add to 13 multiplied by 6.

Solution!
86 * 9 = 774

13 * 6 = 78

774 + 78 = 852.

#### Question No 93

If p is and odd integer and 7p > 50 and 3p < 35 then p is?

#### Select the correct answer

Solution!
7*11 = 77 (greater than 35) and 3*7 = 33 (lesser than 35)

*Note that 8 is also true but in question it is explicitly said that integer must be odd..

#### Question No 94

What is 3/4 of 92 plus 13?

Solution!
(3/4) * 92 = 69

69 + 13 = 82.

#### Question No 95

If A/B is 2/3 and difference between values of A and B is 10 What is value of B?

#### Select the correct answer

Solution!
If B is 30, A is 20 so difference of 10 is maintained..

#### Question No 96

A bus covers a distance of 60 Km in 1.5 hr. How far it would travel in half hour.

#### Select the correct answer

Solution!
Distance covered in 1.5 hr = 60

Distance covered in 1 hr = 60/1.5 = 40 Km

Distance Covered in 0.5 hr = 40 * 0.5 = 20.

#### Question No 97

Subtract eight and nine from twenty-five.

Solution!
25 - 8 - 9 = 8.

#### Question No 98

A cigarette case is full of cigars and cigarettes, probability of a cigarette is 8/15. What is the ratio of cigars to cigarettes.

#### Select the correct answer

Solution!
In 15 cigars and cigarettes there are 8 cigarettes So ratio between cigars and cigarettes is 8/7. Which means there are 8 cigarettes and 7 cigars..

#### Question No 99

What is average of 3, 5 and 10?

#### Select the correct answer

Solution!
(3+5+10)/3 = 18/3 = 6.

#### Question No 100

What is 55% of 320?

#### Select the correct answer

Solution!
55 * (320 / 100) = 176

Quick way to find answer from options is

50% of 320 is 160 so answer should be greater than 160
Only one option is greater than 160 which is 176..
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100


text:
# Density Functional Theory studies of cluster states in nuclei

Abstract : The framework of nuclear energy density functionals is applied to a study of the formation and evolution of cluster states in nuclei. The relativistic functional DD-ME2 is used in triaxial and reflection-asymmetric relativistic Hartree-Bogoliubov calculations of relatively light $N = Z$ and neutron-rich nuclei. The role of deformation and degeneracy of single-nucleon states in the formation of clusters is analysed, and interesting cluster structures are predicted in excited configurations of Be, C, O, Ne, Mg, Si, S, Ar and Ca $N = Z$ nuclei. Cluster phenomena in neutron-rich nuclei are discussed, and it is shown that in neutron-rich Be and C nuclei cluster states occur as a result of molecular bonding of $\alpha$-particles by the excess neutrons, and also that proton covalent bonding can occur in $^{10}$C.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-01012018
Contributor : Sophie Heurteau Connect in order to contact the contributor
Submitted on : Wednesday, June 25, 2014 - 11:22:55 AM
Last modification on : Tuesday, November 30, 2021 - 8:32:05 AM

### Citation

J. P. Ebran, E. Khan, T. Niksic, D. Vretenar. Density Functional Theory studies of cluster states in nuclei. Physical Review C, American Physical Society, 2014, 90, pp.054329. ⟨10.1103/PhysRevC.90.054329⟩. ⟨in2p3-01012018⟩

### Metrics

Les métriques sont temporairement indisponibles


text:
# [Tex/LaTex] Caption text and label size to only one figure

captionsfloatsfontsize

Could I change caption text size and label size to only one figure?

I've seen in other questions that:

\captionsetup[figure]{font=footnotesize,labelfont=footnotesize}

can be used to change sizes in captions, but that is for the whole document and I would like to do this for only one figure; could this be possible?

Best regards and thank you so much.

Local changes to a specific caption can be done within the figure or table environment, if \captionsetup is used in the relevant environment. See the example of the 2nd figure environment -- the change of settings does not leak outside and has no effect on the third figure caption.

Make sure to remove the optional argument [figure] or [table], otherwise caption complains and does not apply the local changes at all.

\documentclass{article}

\usepackage{caption}

\begin{document}

\begin{figure}
\caption{Foo figure}
\end{figure}

\begin{figure}
\captionsetup{font=footnotesize,labelfont=footnotesize}
\caption{Foobar figure}
\end{figure}

\begin{figure}
\caption{other Foo figure}
\end{figure}

\end{document}