text: In OS X, the shortcut is Command-Shift-T by default. You can easily insert all manner of special characters or letters on a mac using simple shortcuts regardless of what application you are using. ... Mac Shortcut For Word Bullets. Section: Internet Tutorial: Greek Letters Fabulous Code Chart for Greek Letters & Symbols (ALT, HTML, and Unicode Codes) This chart provides ALT codes which can be entered into a variety of PC programs when the character is not on the keyboard. Formler i Word Når man bruger Word eller et tilsvarende tekstbehandlingsprogram til at skrive opgaver, rapporter eller noter, så bør man bruge lidt tid på at lære, hvordan man kan opstille tabeller, formler og lignende, så det ser ordentligt ud. Tick the box labelled Show Keyboard and Character Viewers in menu bar Ï : j : Chi : Î§ Ï : C c : Psi : Î¨ Ï : Y y : Omega : Î© Ï : W w : Inserting Math Symbols with Keyboard Shortcuts. For example, to use Command-C (copy), press and hold the Command key, then the C key, then release both keys. Insert sigma using the character map This method can be faster because it will allow you to search for a particular word. You'll find it in the Microsoft Office area of your Start menu. This will open Symbol utility having different special characters and symbols. Sigma Î£ is one of the most popular mathematic signs which means a summation of something. If you need help using alt codes find and note down the alt code you need then visit our instructions for using alt codes page. For e.g., to get Greek letter , you can type \alpha instead of â¦ Hi This feature was available in Word 2000 and 2007, I am shocked to not be able to find it in Word 2011: I was able to assign shortcuts to special characters (for example, a with a macron) using te 'Insert symbol' feature. How to insert Sigma Symbol with keyboard. Many of us use Microsoft Word and other word processing software to draft our documents and correspondences. The symbol (Ï) indicating the addition of the numbers or quantities indicated. 01.12.2016, 17:06. Select one or more characters. How To Get Microsoft Word On Mac Rip Dvd To Mp4 Mac X Mplayer2 Windows 10 ... 20:11:14 CST 2007 MS Word Doc Standard Deviation Symbol The usual symbol for standard deviation is a lower case Greek sigma ( You can get this either by typing a lower case 's' and formatting it with the Symbol font. To use a keyboard shortcut, press and hold one or more modifier keys and then press the last key of the shortcut. On Mac Excel Version. Click on a Sigma symbol below to copy it out to clipboard automatically. Shortcut (Word) 0394, Alt+X: Shortcut (Mac) Option+J: To type the Delta symbol (Î) in Word using the keyboard shortcut, first, type the Alt code (0394), select this code and then press Alt+X to convert the code into a Delta symbol. Sigma (uppercase Î£, lowercase Ï) is the 18th letter of the Modern Greek alphabet. 10/7/2019 Inserting Math Symbols with Keyboard Shortcuts. 2. Mac OS has a rather useful built-in utility called the Keyboard Viewer â an onscreen keyboard that displays many of the possible symbols. Word For Mac Sigma. Sigma Symbol in Greek Alphabet. 10.6.8 Snow Leopard with with MS Office for Mac 2011, Version 14.2.3. Controls the location at which the character is to appear. To see the full list of shortcuts select Help â Insert Greek Letters and Math menu item. 12/20/2020: New Page Word Shortcuts for Tables (win) created by max; 12/20/2020: New Page Word Shortcuts to Open, Close, Manage, and Print Documents (win) created by max; 12/20/2020: New Page Word Shortcuts to Find and Replace (win) created by max; 12/20/2020: New Page Word Shortcuts to Format Text Style and Align Text (win) created by max Novice users use the Graphical User Interface (GUI) method to insert Greek Alphabets. Word Mac Shortcuts For Symbols. Click on â¦ To Activate the Keyboard Viewer: 1. I also use F4 for applying bold to the first couple of words in each item in a bulleted list (easier on the fingers than Ctrl+B); for merging cells in several different rows; for making the Page Setup identical in two different sections of a. In Windows operating system, the uppercase sigma Î£ can be obtained by typing the numbers â2211â, followed by the keyboard shortcut âAlt+Xâ to get Î£. Thanks to missdona . Ein Word Spaltenumbruch sorgt dafür, dass der Text nach dem Umbruch in.. ... Sigma-Zeichen in Word, am PC und Mac schreiben. Amaya defines two kinds of keyboard shortcuts for Mac OS X: shortcuts using standard Apple modifier keys (ex. Cmd+C to copy the selection) and shortcuts using sequences (ex. Dear Sir or Madam, I am using an I Mac 27" (12.2), OX Ver. Click the radio button for âuse Math AutoCorrect rules outside of math regions.â Click Close to close this windows. Use the keyboard shortcut for mu: Alt + M. The "Alt" + "M" also works on the Mac. Dec 28, 2017 - Whether curious as to how Lean Six Sigma works, in training for certification or a very experienced champion, everyone will find this tool essential as the ultimate quick reference guide to the combined process improvement methods of Lean and Six Sigma. It also contains ASCII codes, both HTML character references (decimals) and entity references (symbolic names) if available. The 18th letter of the Greek alphabet, represented in the English alphabet as "s". These equation editor shortcut as termed as Math AutoCorrect and are available in versions of Microsoft Word 2007 and above. Title basically asks it; I have done the Mac OS X's built-in character viewer and also Insert>Symbol in Word, but cannot find the symbol. Search. To insert math symbol type Ctrl+M (Command M on Mac OS) and then type symbol mentioned in â¦ Sigma : Î£ Ï : S s : Tau : Î¤ Ï : T t : Upsilon : Î¥ Ï : U u : Phi : Î¦ Ï : F f : Phi (alt.) 2. Some symbols have shortcut keys. So you can the mu-characters in Word, Write on Mac and Co.: Starts the program in which you want to write the mu-symbol. The sigma summation symbol is known by most as a mathematical symbol that indicades the sum. So you think youâre fancy, huh? The facility is built into macOS. A quick Web search will produce a resource with a list of symbols and their corresponding codes. Just because you know how to copy and paste without the click of the mouse in Word. To insert math symbol type Ctrl+M ( Command M on Mac OS) and then type symbol mentioned in the table below. Welcome to Useful Shortcuts, THE Alt Code resource!. Home Word:mac FAQ Tutorials Find Help About Us Sitemap Search. * This may not work in Word X. Open Microsoft Word. Or look below to find out how to type sum symbol with keyboard using different techniques depending on your system. Dette dokument handler kun om formeleditoren i Word. Launch your Excel app and go to âInsert > Symbolsâ menu. The above table contains all you need to insert this symbol into your Word â¦ Windows. You can create a sigma sign by accessing the Character Palette, using a keyboard shortcut or by using the Special Characters menu in your current application. Thank you for any guidance you can lend. Any kind of chess players will find in Sigma Chess Lite a perfect rival for all their games. The sigma symbol provides the character used to denote the sum of an equation in mathematics. The number 2211 is magically transformed into the sigma character. I have found work arounds regarding using the unicode #305, but I tried it and the line does not center above the x when inserted. The alternative form of sigma (Ï) must be used in word-final position. Keyboard shortcut for the squared symbol How to Type the Squared Symbol on Microsoft Word and Google Docs. I found itâs an easy solution on Word for Mac and hope itâs the same for previous versions: select Word from the menu and go to Preferences. For example, the code for the sigma character is 2211: Type 2211 in your document and then press Alt+X. There are many ways to type Greek alphabet in Microsoft Word. Sigma symbol is now present on the sheet. So the keyboard shortcut for the squared symbol is Alt + 0178. They appear at the bottom of the Symbol dialog box. The result is like this: ². In Gematria it has the value of 200. To do so, open the Insert menu, select Symbol, and select the × symbol. This wikiHow teaches you how to insert the X-bar statistical symbol into a Microsoft Word document. The easiest way it to insert the the alpha symbol (Or any of hundreds of special characters and symbols.) Click the "Shortcut Key" button and choose a shortcut. is to find it among the available special symbols. Open System Preferences-> Keyboard. In Windows 7, you can find Character Map in Start All Programs Accessories System Tools Character Map. (Right-click the &Sigma button, choose Properties and click Keyboard to view the current setting). It involves navigating Insert Tab and selecting desired Greek symbol from Symbols. Mac menus and keyboards often use symbols for certain keys, including modifier keys: 730365Five Tips for Microsoft Word So you can write the mu-sign. I want to add math equations and be â¦ 1. Well, get ready to be even fancier (and more productive) because we've curated 99 of the best Word keyboard shortcuts. As Mac OS X users are not familiar with shortcut sequences in menu entries, only standard shortcuts are shown by default. Then select AutoCorrect. Ctrl-t Ctrl-t to create a table). Alternativet er at skrive i hånden. Microsoft Word shortcut for Greek Alphabet. 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Intersection of 2 visibility polygons

Let $P$ be a simple, closed and bounded polygon and $p_1,p_2 \in \mathrm{int}(P)$ be two points in its interior. Is it true that the intersection of the visibility polygons of $p_1$ and $p_2$ is connected?

The visibility polygon of a point $p\in P$ is the set of all $x \in P$ such that the line segment connecting $p$ and $x$ is contained in $P$.

It might be elementary, but we fail either finding a proof or a counterexample. Furthermore, in the literature I could only find details about the computational aspects of the visibility polygon, but not a single word about its properties. Any reference, example, sketch of proof etc. is welcomed!

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@Dror: You might also look at the work of Marilyn Breen, and the work she cites in her papers: informatik.uni-trier.de/~ley/pers/hd/b/Breen:Marilyn.html –  Joseph O'Rourke Apr 30 '13 at 19:41
The argument needs to use dimension 2 as there are analogous cases in 3 dimensions where the intersection is not connected. Gerhard "Ask Me About Blind Corners" Paseman, 2013.04.30 –  Gerhard Paseman Apr 30 '13 at 21:22

Here is an argument, a revision (and replacement) of one I sketched earlier.

Let $p_1$ and $p_2$ both see $a$ and $b$. I claim that every point along the shortest path $\sigma$ connecting $a$ to $b$ inside $P$ is visible to both $p_1$ and $p_2$. With this claim established, we know the intersection of the visibility polygons is connected.

Start turning/sweeping the rays $p_1 a$ and $p_2 a$ counterclockwise along $\sigma$ toward $b$, simultaneously tracking the same point along $\sigma$. If both rays remain unobstructed throughout the sweep, we are finished. So suppose otherwise. Then one or the other ray, say $p_2 a$, must encounter an obstruction, a reflex vertex $v$ hitting $p_2 a$, blocking the visibility to point $x \in \sigma$. Then we have some exterior points of the polygon enclosed within the closed path $p_2 x \cup \sigma(x,b) \cup b p_2$ of points interior to $P$, contradicting the simplicity of the polygon, i.e., the polygon has a hole:

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Great picture! –  Joel David Hamkins May 1 '13 at 13:46

The answer is yes. I do not see a clean proof. Here is a proof by case-checking. Consider two points $q$ and $q'$ that are visible from both $p_1$ and $p_2$. There are several cases:

1) Suppose four points $p_1$, $p_2$, $q$, $q'$ are in convex position, and points $p_1$, $p_2$ are opposite vertices of the convex hull. Then convex hull is completely inside the polygon, and in particular in the intersection of two visibility polygons. Thus, $q$ and $q'$ are in the same connected component.

2) Four points $p_1$, $p_2$, $q$, $q'$ are in convex position, and points $p_1$, $p_2$ are adjacent vertices of the convex hull. Without loss, assume that the order is $p_1$, $p_2$, $q$, $q'$. Let $r$ be the intersection point of line segments $p_1q$ and $p_2q'$. Then the line segments $qr$ and $q'r$ are contained in the intersection of visibility regions.

3) Point $q$ is in the convex hull of $p_1$, $p_2$ and $q'$. Then the nonconvex $4$-gon $p_1qp_2q'$ is in the intersection of visibility polygons, and line segment $qq'$ is completely contained in it.

4) Point $p_1$ is in the convex hull of $p_2$, $q$ and $q'$. In that case the line segments $qp_1$ and $q'p_1$ are in both visibility polygons. Again, $q$ and $q'$ are connected.

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Are you familiar with some references where these kind of things are shown/proven? There might be more things of that sort that will be useful for me. Thank any way! –  Dror Atariah Apr 30 '13 at 14:40
Well, Joseph O'Rourke wrote a book on art gallery theorems. :-) –  Boris Bukh Apr 30 '13 at 14:51
As far as I understood this book is mainly about the algorithms related to the art gallery, isn't it? Anyway, I'll have a closer look. –  Dror Atariah Apr 30 '13 at 19:01

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# A beam of unpolarised light is incident on a air-glass interface derive, using a suitable ray diagram that light reflected from the interface is completely polarised, when tan ip = ??

When an unpolarised light is incident on air-glass interface and some of the light reflected back to medium, some of the light refracts through the air-glass interface may be completely polarised (or) partially polarised (or) it can be unpolarised also it depends upon the angle of incidence for the angle of incidence of $(theta )=0{}^circ ,and,90{}^circ$ the reflected light remains unpolarised.

The angle of incidence at which the reflected light is completely plane polarised is known as polarization angle (or) Brewster’s angle.

When un polarised light is incident on the interface of Air-glass interface, the reflected light is polarised with its electric vector perpendicular to the plane of incidence. When the reflected and refracted light rays makes 90° with each other this angle of incidence is known as Brewster’s angle (or) angle of polarization. Refer the diagram

ip + r = 90°

from Snell’s law

μ1 sin i = μ2 = sin r

μ1 sin ip = μ2 sin r

where μ1 = 1 and μ2 = μ

ip + r = 90°

r = 90° – ip

sin ip = μ sin (90° – ip)

sin ip = μ cos ip

$frac{sin {{i}_{p}}}{cos {{i}_{p}}}=mu$

tan ip = μ

hence condition for polarization is proved.


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# Absolutely continuous and integration by parts

Let $f,g\in L^1([0,1])$. Suppose for all $\phi\in C^\infty[0,1]$ such that $\phi(0)=\phi(1)$ we have $$\int_0^1f(t)\phi^{\prime}(t)dt=-\int_0^1g(t)\phi(t)dt$$ Show that $f$ is absolutely continuous.

I tried to prove as this: absolutely continuous. However, the problem is not exactly same as we now require $\phi$ is smooth. So I want to know how to modify the construction of such $\phi_n$ to get the conclusion. Thanks for any hint.

• You can use almost the same construction as in the answer, but you have to use a Lipschitz function. This can be computed by using a smooth cut-off function. – gerw Jan 19 '16 at 20:26
• Yes. I tried leave a space such as $(1/n,2/n]$ and $(x-1/n,x]$ and etc to make function $\phi_n$ smooth. However, we also need to let $\int_{(1/n,2/n]}f\phi_n^{\prime}=0$ and etc. I am not sure how to write down them explicitly or show that such $\phi_n$ exist for all $f$. – Syoung Jan 19 '16 at 20:35


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# MVR

Joint adaptive mean-variance regularization and variance stabilization of high dimensional data The paper addresses a common problem in the analysis of high-dimensional high-throughput “omics” data, which is parameter estimation across multiple variables in a set of data where the number of variables is much larger than the sample size. Among the problems posed by this type of data are that variable-specific estimators of variances are not reliable and variable-wise tests statistics have low power, both due to a lack of degrees of freedom. In addition, it has been observed in this type of data that the variance increases as a function of the mean.par We introduce a nonparametric adaptive regularization procedure that is innovative in that (i) it employs a novel “similarity statistic”-based clustering technique to generate local-pooled or regularized shrinkage estimators of population parameters, (ii) the regularization is done jointly on population moments, benefiting from C. Stein’s result on inadmissibility, which implies that usual sample variance estimator is improved by a shrinkage estimator using information contained in the sample mean. From these joint regularized shrinkage estimators, we derived regularized $t$-like statistics and show in simulation studies that they offer more statistical power in hypothesis testing than their standard sample counterparts, or regular common value-shrinkage estimators, or when the information contained in the sample mean is simply ignored. Finally, we show that these estimators feature interesting properties of variance stabilization and normalization that can be used for preprocessing high-dimensional multivariate data. The method is available as an R package, called MVR’ (Mean-Variance Regularization’), downloadable from the CRAN website.

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Number Theory

# Euler's Totient Function

Given that $$30=2\times3\times5$$, what is the value of the Euler totient function of 30, i.e. what is $$\phi(30)$$?

Given that the only prime factors of a certain positive integer $$n$$ are 2 and 3, find (in terms of $$n$$) the number of positive integers less than or equal to $$n$$ that are coprime to $$n$$.

$\dfrac1{24} , \dfrac{2}{24}, \dfrac{3}{24}, \ldots , \dfrac{23}{24}, \dfrac{24}{24}$

How many of the fractions above cannot be reduced?

$\dfrac1{32} , \dfrac{2}{32}, \dfrac{3}{32}, \ldots , \dfrac{31}{32}, \dfrac{32}{32}$

Which of the following is true regarding the 32 fractions above?

Statement 1: The number of fractions that cannot be reduced is less than the number of fractions that can be reduced.

Statement 2: The number of fractions that cannot be reduced is equal to the number of fractions that can be reduced.

Statement 3: The number of fractions that cannot be reduced is greater than the number of fractions that can be reduced.

Let $$A$$ denote the number of positive integers less than or equal to 11 that are coprime with 11.

Let $$B$$ denote the number of positive integers less than or equal to 12 that are coprime with 12.

Which one is larger, $$A$$ or $$B$$?

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# How do I generate a sparse invertible 10000 by 10000 binary matrix with 30 to 50 non-zeros per row?

How do I generate a sparse invertible 10000 by 10000 binary matrix with 30 to 50 non-zeros per row(uniform distribution)?

What sort of algorithm should I use to do this task?

Brute Force algorithm- Using a random generator, create a such a matrix, and test for invertibility by finding its determinant/Gaussian Elimination.

(I tried this approach, the algorithm never completes within 1 hour, so I gaved up)

Reverse ERO approach- Starting with an identity matrix, do repeated Elementary Row Operations on it until the above is fulfiled.

(I haven't tried this approach yet, it is possible that it will work, but there is simply no way to guarantee that every row will have 30-50 non-zero entries)

Upper triangular approach- Starting with an identity matrix, choose 30-50 random entries in the upper triangular part to be non-zeros, then do row swaps to make them look random

(I tried this approach, but the matrices produced turned out to look very skewed to the right.)

Can anyone think up of any other possible approaches to this problem?

• How about the Upper-Triangular approach, but with random row and column swaps? – Blue Jul 2 '15 at 4:24
• Will column swaps preserve the invertibility? – Yellow Skies Jul 2 '15 at 4:28
• Yes, column swaps preserve invertibility, just like row swaps. The reason is the same. For the determinant to be zero, the rows or columns must be linearly dependent. The rank-nullity theorem says these are equivalent. Swapping columns cannot change the dependence. – Ross Millikan Jul 2 '15 at 4:32
• Column swaps are just row swaps of the transpose. – Blue Jul 2 '15 at 4:33
• ah! haha! thanks! – Yellow Skies Jul 2 '15 at 4:33

Do you want an invertible matrix $A$ over $\mathbb{Z}/2\mathbb{Z}$ or over $\mathbb{R}$ ? In the first case, the Blue's method seems to be good. Yet, in the second case, it is not, because $\det(A)=\pm 1$ that is far from random.
EDIT. I assume that you want (although my post does not seem to excite you) an invertible matrix over $\mathbb{Q}$. That follows is a better method than above:
STEP 1. We seek randomly a matrix $B$ as you want and s.t., for every $i$, $B[i,i]=0$. Such a matrix has a non-negligible probability of being singular. Fortunately $C=B+I$ is "almost certainly" invertible; yet $C$ often admits the eigenvalue $1$.
STEP 2. Swap rows and swap columns; then the characteristic polynomial of the obtained matrix $A=PCQ$ is "almost certainly" irreducible over $\mathbb{Q}$ and, in particular, $A$ is invertible.
Note that the permutations $P,Q$ must be "dense", otherwise there remain too much $"1"$ on the diagonal and, consequently, your matrix is not random. Write each permutation as a product of $k<n$ transpositions; then the complexity of the calculation of $PC$ (for instance) is the complexity of $n$ swaps, that is $O(n^2)$. On the other hand, I do not know the complexity of the choice of a random permutation.


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Question

# As part of a probability experiment, Elliott is to answer 4- multiple choice questions. For each question, there are 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly?A. $\dfrac{{27}}{{81}}$B. $\dfrac{{12}}{{81}}$C. $\dfrac{4}{{81}}$D. $\dfrac{3}{{81}}$E. $\dfrac{1}{{81}}$

Probability of choosing correct option for each of the 4 questions $= {\rm{p = }}{{\rm{p}}_{Q1}} = {{\rm{p}}_{Q2}} = {{\rm{p}}_{Q3}} = {{\rm{p}}_{Q4}} = \dfrac{1}{3}$.
${\rm{p}}\left( {{{\rm{Q}}_1} \cap {{\rm{Q}}_2} \cap {{\rm{Q}}_3} \cap {{\rm{Q}}_4}} \right) = {\rm{p}}\left( {{{\rm{Q}}_1}} \right){\rm{p}}\left( {{{\rm{Q}}_2}} \right){\rm{p}}\left( {{{\rm{Q}}_3}} \right){\rm{p}}\left( {{{\rm{Q}}_4}} \right)$ [since all event are independent]
$= \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3} = \dfrac{1}{{81}}$
Thus the required probability is $\left( {\rm{D}} \right)\dfrac{1}{{81}}$


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Revision history [back]

Loading things up in gazebo isn't exactly a walk in the park it seems they need things to be in a very specific layout which I detail below.

└── simple_box
├── model.config
├── simple_box.dae
├── simple_box.sdf
└── simple_box.urdf

The following gazebo command will convert files, provide warnings about what is wrong, and print a converted file out on the command line:

gz-8.1.1 sdf -p ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf

The printout which can be redirected to overwrite the original sdf file, for example:

gz-8.1.1 sdf -p ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf >  ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf

Models

Here are some very simple models I've compressed for convenience, plus an updated simple_box.zip, these all load in both gazebo and V-REP except V-REP doesn't seem to support textures: - simple_box.zip your simple_box updated to load in gazebo and V-REP - ball_bearing.zip should be dark gray, has a material definition (a V-REP option), and is otherwise very simple - bookshelf.zip includes a texture and is composed of several simple boxes - cinder_block.zip includes a collada mesh

The materials spec they have also seems to be important if there is to be a shelf made of wood:

    <material>
<script>
<uri>file://media/materials/scripts/gazebo.material</uri>
<name>Gazebo/Wood</name>
</script>
</material>

And gazebo won't load model/mesh files next to the sdf file unless it is specified with model://model_folder_name/model_mesh_file.dae, as you can see in this working version of simple_box.dae:

<sdf version='1.6'>
<model name='cube'>
<pose frame=''>0 0 0 0 -0 0</pose>
<inertial>
<pose frame=''>0 0 0 0 -0 0</pose>
<mass>1</mass>
<inertia>
<ixx>1</ixx>
<ixy>0</ixy>
<ixz>0</ixz>
<iyy>1</iyy>
<iyz>0</iyz>
<izz>1</izz>
</inertia>
</inertial>
<pose frame=''>0 0 0 0 -0 0</pose>
<geometry>
<box>
<size>1 1 1</size>
</box>
</geometry>
</collision>
<pose frame=''>0 0 0 0 -0 0</pose>
<geometry>
<mesh>
<scale>1 1 1</scale>
<uri>model://simple_box/simple_box.dae</uri>
</mesh>
</geometry>
</visual>
</model>
</sdf>

It seems part of the solution is that the models don't need to define the world, they can simply be a model like the files above. An additional requirement for gazebo is the model.config file, which specifies the name of the object and the path to the sdf file. Gazebo also requires model file (like collada).

Simulations aka World

The world definition is what has all those extra requirements such as specifying gravity, light sources, simulation refresh rate, etc. You may want to support simulation definitions, but it should likely not be used for simple model definitions.

Here is everything needed for a basic simulation world definition but note that there seems to be a small bug in the saved vs loaded dimensions as specified in gazebo 8.1.1.

Loading things up in gazebo isn't exactly a walk in the park it seems they need things to be in a very specific layout which I detail below.

└── simple_box
├── model.config
├── simple_box.dae
├── simple_box.sdf
└── simple_box.urdf

The following gazebo command will convert files, provide warnings about what is wrong, and print a converted file out on the command line:

gz-8.1.1 sdf -p ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf
~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.urdf

The printout which can be redirected to overwrite the original sdf file, for example:

gz-8.1.1 sdf -p ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.urdf >  ~/src/bullet3/data/kuka_iiwa/kuka_with_gripper.sdf

Models

Here are some very simple models I've compressed for convenience, plus an updated simple_box.zip, these all load in both gazebo and V-REP except V-REP doesn't seem to support textures: - simple_box.zip your simple_box updated to load in gazebo and V-REP - ball_bearing.zip should be dark gray, has a material definition (a V-REP option), and is otherwise very simple - bookshelf.zip includes a texture and is composed of several simple boxes - cinder_block.zip includes a collada mesh

The materials spec they have also seems to be important if there is to be a shelf made of wood:

    <material>
<script>
<uri>file://media/materials/scripts/gazebo.material</uri>
<name>Gazebo/Wood</name>
</script>
</material>

And gazebo won't load model/mesh files next to the sdf file unless it is specified with model://model_folder_name/model_mesh_file.dae, as you can see in this working version of simple_box.dae:

<sdf version='1.6'>
<model name='cube'>
<pose frame=''>0 0 0 0 -0 0</pose>
<inertial>
<pose frame=''>0 0 0 0 -0 0</pose>
<mass>1</mass>
<inertia>
<ixx>1</ixx>
<ixy>0</ixy>
<ixz>0</ixz>
<iyy>1</iyy>
<iyz>0</iyz>
<izz>1</izz>
</inertia>
</inertial>
<pose frame=''>0 0 0 0 -0 0</pose>
<geometry>
<box>
<size>1 1 1</size>
</box>
</geometry>
</collision>
<pose frame=''>0 0 0 0 -0 0</pose>
<geometry>
<mesh>
<scale>1 1 1</scale>
<uri>model://simple_box/simple_box.dae</uri>
</mesh>
</geometry>
</visual>

It seems part of the solution is that the models don't need to define the world, they can simply be a model like the files above. An additional requirement for gazebo is the model.config file, which specifies the name of the object and the path to the sdf file. Gazebo also requires model file (like collada).
The world definition is what has all those extra requirements such as specifying gravity, light sources, simulation refresh rate, etc. You may want to support simulation definitions, but it should likely not be used for simple model definitions.


text:
## The Seckel Pear

I wrote about our pear trees a few years ago.  At that time, if you check out the post (there’s a time-lapsed video of myself picking up pears), you will notice that the ground is more or less thick with pears.  That year, we picked up (and composted) push-carts full of pears — hundreds of pounds.  This year, it was a ho-hum year for fruit (and nuts) in general.

On the apple front, we are down to a single, mature apple tree.   The crabapple tree next our house was taken down in the spring.  The roofing company that redid our roof recommended that it be taken down as it was too close to the house and the roof.  It was likely a great move.  The heartwood of the trunk, about 12 inches above the ground was rotted and about half of the sapwood was intact; there were also many, many dead branches.  The other apple tree to come down was the tree we had gathered apples from for the cyser last season.  The heartwood on this tree was long gone and the entire weight of the tree was supported by the sapwood, which was beginning to give under the stress.  That said, if the cyser turns out, and we do not have need to make 5 gallons of vinegar, it will be a sort of unique, never-to-be-produce-exactly-again beverage.  The other apple tree that I gave little attention to, resided in the way-back woods behind our main yard.  It was tucked along our property line, behind a buckthorn thicket.  That tree died over the winter.  With one, mature tree, we have had zero useable apples.

The walnut trees on the property had a crumby year, as well.  Melissa is pleased that the dogs are not bringing in greasy-black bits of walnut husk, but it is sad to have not seen all the small green orbs growing over the course of the summer.  I suspect that at the peak time when the catkins on the trees were just right for pollination, it rained heavily and for an extended period and washed the pollen into the ground. In fact, a quick survey of the neighborhood walnut trees also show no nuts.  It will be a sparse winter for the squirrels; we will need to keep an eye on the chicken coop this winter for squirrels raiding the feed.

The cherry tree we planted the year after we moved into our house had a good year, a good for a tree just beginning to produce useable quantities of cherries.  We also had no plums this year.

But, back to the pears.  There was not a heavy load of pears on the two trees this year.  The east-tree, which I have yet to identify the variety of, had an alright year.  We have not had to pickup many, if any, of the fruit from the ground.   The west-tree, which, as best as I can tell is a Seckel pear tree, produced a decent amount of fruit.  About 82 pounds worth of fruit.  With mead and cyser in carboys, we decided to branch out into the more fruit-based hard beverages and less honey-based.  We’re going to tackle making a perry (pear cider) this winter.  The 82 pounds of pears are currently taking up space in one of the freezers.  There are still fruit on the tree; we’re hopeful to make the total an even 100 pounds before it is too late.

As I worked in the yard today, near the pear trees, I started thinking about the Seckel.  I thought about curious size of the fruit – quite small.  I thought about the particulars of this one tree – how old was it, who planted it, why was it planted in the location it resides in?  On a short break from the work I was attending to in the yard, I searched the internet for history of the seckel pear.  I knew that I would not find results on our Seckel, but I might find more information on the origins of the Seckel variety.  The results returned included a few tree nurseries that carry Seckel trees – many of the nurseries’ online catalogs all have very similar text that spins the mysterious origins of the Seckel.  Other results that were returned from the search included recipes that use pears as a primary ingredient in a dish.  Amongst the results was an article from a horticultural and rural life journal from 1880.  The Gardener’s Monthly and Horticulturist Devoted to Horticulture, Arboriculture and Rural Affairs, Volume XXII, 1880.  The seckel is actually mentioned a number of times in this issue.  There is, however, an entire article on the seckel; titled: THE OLD SECKEL PEAR.

There is a print of an engraving of the the old seckel pear tree in the journal — surprisingly, our pear tree has the same harrowed look, complete with droopy, arching downward-swept branches.

So, for the reader’s amusement and enjoyment, the following the article.

THE OLD SECKEL PEAR.

BY JAFET.

I had heard from a friend, of the old, original
accidental seedling, the parent stock of all of that
ilk extant, and the story gradually infected my
imagination. It began to haunt me. I saw it –”

” In my mind’s eye, Horatio,” –”

standing like a sentinel down there in ” The
Neck ” among the dikes and ditches ; living
through slow and patient history; watching
through its ” two hundred years,” so the story
goes, and listening to the hum and stir of distant
life in the Quaker metropolis, and the growing
traffic of the two rivers that washed the meadow’s
foot more than one hundred and fifty years from
this 31st day of July, 1880.

” More than one hundred and fifty years ago”
–”say the “Neckers” –” the first dike was thrown
up to reclaini the meadows on which they and
their fathers’ fiithers have lived and moved and
had their being; fighting the waves at spring tides,
and the rheumatiz’ nipre at their leisure ; but
never much troubled with a dry time, even
though there be but a fraction of an inch of rain-
fall in a month, or a whole dry summer never so
long.

It is a fat land down there, and has its bless-
ings and its drawbacks like other places. A
hardy race grows and thrives, and feeds others
out of the rich alluvial, but lays its bones away
on higher ground, for

And SO they lay them down at last, on green
and gravelly slopes, afiir from the music of the
singing birds of their household groves ; and so
their sons and sons’ sons have come and warmed
the old homes and kept the old names and man-
sions awhile in the meadows, and then followed
on to the narrow house in the higher ground.
But this is wandering from the old Pear tree.
That, I had some trouble to find, of which more
anon.

The ” facts” above stated, expressed more in
the local vernacular, I had from an old Necker,
who did not dream himself, but set his listener
dreaming.

Who munched the pear, and thoughtlessly
dropped the core over the side of what vessel, as
she passed the “Back Channel? And when?
It must have been between 1682 and 1720 ; for
that core floated to fast land, seeded and inaugu-
rated its celebrated distinct vai-iety far inside the
old dike that more than one hundred and fifty
years ago first barred back the waters from their
accustomed flats. May it not as likely have
been in the first named year as at any time
in the interval between that and the latter? For
what is thirty-eight years, more or less, in the
life of a pear tree, whose ” more than one hun-
dred and fifty years” have to-day been resolved
out of its indefinite past? And who shall say it
was not Penu himself, as likely as any of his
fellow-voyagers, –” or as those in the few following
years, –” who cast overboard the unconscious seed
of the land-mark of the two centuries then to
come?

Up to the day noted in the first paragraph, I
had never seen the object of my lately awakened
enthusiasm. Nothing would do until I could set
eyes on it, if yet standing ; and if not, alas what
My friend had described it as ” still standing
fifteen years ago, but with one-half decayed ofi”
the trunk, the balance a mere shell, supported
by props, and piously guarded with posts and
rails,” ready to fall and pass away forever. He
gave me a verbal notion of the direction and dis-
tance, relying more upon a reference for par-
ticulars to his description of his own visit
published long ago in the Gardener’s Monthly.
Neglecting this at the lime, I was not aware of
its more particular reference to exact locality.

His interesting article is well worth reading, and

will be found in vol. 7, page 44, Feb. 1865.

I had, therefore, a loose notion of the general
locality, comprising, perhaps, a couple of square
miles, anywhere within which it might be, and
over which I might have to roam vaguely and
guessingly. In that area there were, possibly,
many descendants of the old patriarch pear,
themselves aged; and one might risk being
sentimental over some decayed sample of several
generations later than the real, simon-pure-
great-great-grandfather of them all. My friend’s
verbal directions were months old, and, refracted
by my own unsafe keeping, were, as a guide,
about as reliable as young Launcelot’s directions
to Old Gobbo.

” Old Gobbo–” faster young gentleman, I pray yoa
which is the way to Master Jew’s?

Launcelot –” Turn up on your right hand, at the next
turning, but at the next turning of all, on your left;
–” marry, at the very next turning turn of no hand, but
turn down indirectly to the Jew’s house.”

Thus prepared (?) for the search, I started for
it overland, on the hottest day of this hottest of
Julys ; but was driven back by the heat, fotigue
and uncertainty of location, reinforced by grow-
ing lateness of the hour. So on the last day of
July I tried my second parallel, and attempted
to flank the position by water, taking the little
steamer at foot of Chestnut street, Schuylkill.
Making a demoralized landing at a rotten, half
burnt, plankless oil wharf, I reached land by
perilous gymnastics over the tops of bare wharf
piles, and formed again in good order. But a
Necker’s ” half mile” is a full mile and a half I
walked to and fro four miles, prospecting around,
and brought up* at a country hotel on the ” Old
don’t try my route, but take the one I found out
since. It is very simple. A stage from Peter
“Wright & Sons, 307 Walnut street, goes all the
way twice a day, passing this point ; fare 75 cts.
round trip. And so cut your eye teeth on my
experience. It is easier.

A busy ostler was sponging a critter at a

Jafet –” How long have you lived in these parts ?

Ostler –” Boy an’ man, all my life, –” some forty
year.

Jafet –” Then perhaps you know of a very old
pear tree somewhere in this region.

Ostler –” The old Seckel d’ye mean ! Know it?
Ish’d think I orter; many’s the pear I’ve had
ofl’n it too. D’ye see that lane right wher’ yer
standin’? That big yaller house down ther’s John
Bastian’s, and he has the old Seckel, if’t has’nt
blowed over. But stop, mister, tha’ don’t ripen
jist yit, if that’s wot yer goin’ fer.

To think I should reach Mecca in this unsenti-
mental way, and not on a cloud, or the back of
a camel !

I found Mr. Bastian sitting on his porch. He
received me very kindly, and directed me to the
identical spot. Sure enough, there stood the
ancient of days and its surroundings, ” the old
stone house, the sloping meadow and the ditch.”
Eureka !

The half trunk was a mere shell when Mr.
Bastian first knew it forty years ago, and he says
it was “much the same as now.” At least half
the circumference is gone. At 3 feet 6 inches
from the ground, it measures 5 feet 4 J inches
around the half trunk and across the exposed
diameter. The diameter, Irom bark to bark
is 23j inches. I estimate the full circumfer-
ence when whole and sound, as having been
at least 6 feet 6 inches, 3J feet from the ground.
The fraction of all that remains of the old storm-
beaten, ancestral Seckel Pear is 26 feet in height.

The old stone house must be one hundred and
fifty years old. It is of one storj” and attic, and
the walls are like a fort in thickness. Mr. Bas-
tian now lives in his more commodious mansion
near by on a rising ground. His son, who was
born in the old stone homestead, lives there now
with his family. There are many very old
homesteads all through the Neck. They are
perhaps, with the exception of the old Swedes
Church, among the oldest buildings remaining
in the city. Mr. Bastian has ‘owned the old
Seckel farm forty years. At the time he moved
there the late Thomas P. Cope told him that the
Seckel family had known the old tree for eighty
jears. Eighty plus forty makes one hundred
and twenty years to begin on. Perhaps some
earlier experience, going backward from the
year 1760, which this gives us, –” and so verify the
tradition of ” more than one hundred and fifty
years and perhaps two hundred.”

Other issues of The Garden’s Monthly can be found on archive.org.

If you’re interested the origin story of the pear (from species-specific perspective), check out Origin, Domestication, and Dispersing of Pear (Pyrus spp.)  (pdf)

## Black Walnuts

Growing up in Hibbing and specifically on the block I grew up on, I did not pay much attention to the large walnut tree that grew (it is still there) in Frank Pascuzzi’s backyard.  Every fall, the alley would be littered with husks from the tree’s seeds – green-husked, tennis-balled shaped-and-sized things; squirrels could be see carrying husk-less nuts in their mouths while run down the low-slung electrical wires above the alley.

My mother would yell at me, “don’t touch the husks, they’ll turn your hands black!”  I never really figured out what the big damn deal was with the husks; it is not like the husks were the walnut-equivalent of Charlie and the Chocolate Factory’s Violet Beauregarde‘s three-course-meal-chewing-gum; I wasn’t going to turn into a black-and-green-husked walnut.  My hands would just be stained for a short while.

Even with the threat of stained hands, the walnuts made fantastic weapons.  Pegging your friend (or enemy) in the head with a thing that looked like a tennis ball but felt like a baseball was awesome.

But, there was one thing that I did not realize until late last fall.  That the walnut tree (and now, a likely offspring of that tree growing in a yard across the alley) should not be growing in Hibbing.  This is not some political should not or a moral should not, this is more of an oddity should not.  Black walnut trees (Juglans nigra) generally can be found as far north in Minnesota as the Twin Cities.  Even then, looking at the map, walnut trees are a southern Minnesota thing.  The walnut tree in Hibbing is effectively 200 miles too far north.

As the USDA lays out on their website, “Many . . .  environmental factors, in addition to hardiness zones, contribute to the success or failure of plants. Wind, soil type, soil moisture, humidity, pollution, snow, and winter sunshine can greatly affect the survival of plants. The way plants are placed in the landscape, how they are planted, and their size and health might also influence their survival.” It is very much possible to have isolated populations – like the small patch of them, indicated on the map, in South Dakota.

Microclimates abound as do odd strains of genetics.  A tree growing in Eureka, Missouri may be a Juglans nigra, but it might not be able to survive a winter in Hibbing.  Likewise, a black walnut from Hibbing might not be able to survive the summers of east-central Missouri.

Trees and particularly fruit trees, have piqued my interest for a while; a year or two before leaving Proctor, I had planted several cherry and apple trees at that house.  Our first spring here in Saint Paul, on our acre-of-earth, we planted cherry trees, apple trees, plum trees, and a hardy peach tree.  This was in addition to the existing pear and apple trees at our place.  Adding to that list of trees, we also have several large black walnut trees, mulberry trees, hackberry trees, and dozens of understory trees, like buckthorn, lilac, and ironwood, in the forest that covers the back of our property.

In addition to the penchant for trees, I have beeing tossing around a bit of an oddball idea: buy tax forfeited property and then plant trees on it.  Minnesota’s more heavily forested counties tend to have many pieces of land available for purchase (or here).  It is a bit of a goofy idea and there are bound to be hiccups with such an idea.  None of my friends that I have run the idea past, have seemed interested or enthusiastic.  You could grow fruit trees, but there is predation by those pesky ruminants that are spread throughout the state.  Though, that is often an issue with young trees no matter what they end up bearing.

Last fall, I was looking out at the back yard, looking at the walnut trees with their clusters of tennis-ball-sized-green-husked nuts, and it occurred to me that I could grow my own trees from seeds.  Mentally, I have connected my crazy buy-tax-forfeited-land with collecting-tree-seeds-to-be-planted.

There is a proverb floating out on the Internet, often attributed to being of Chinese origins, that says, “The best time to plant a tree is 20 years ago.  The second best time is now.”  This could also just be metaphorical in the sense that you should do something soon rather than later.  So, with that in mind, I started to collect tree seeds.

Melissa called me a human-squirrel.  We would be in a park or at the highway rest area, and if there was a nut tree with seeds under it, I would start to gather up nuts.  I gathered walnut seeds in St. Paul, Blue Earth, Iowa City, Eureka, MO, and Racine, MN.  Unfortunately, I did not get up to Hibbing in time to gather walnut seeds there.  I branched out from walnuts and collected oak acorns, too.  Hastings, Winona, St. Paul, and Rochester, MN.  I collected bur oak, swamp white oak, white oak, and red oak seeds.

Generally, these seeds to be stratified in order for them to begin growing into trees.  Stratification is the process of chilling seeds for an extended period of time; in the real world, this is generally called winter, but for the seeds I gathered, this was the wine-chilling drawer in our refrigerator.  But before going into the shallow-freeze, I needed to get a better handle on whether the seeds were actually viable enough to be likely to grow.

That’s where the float test comes into play.  In the case of the walnuts, the husks needed to be removed first.  I let the seeds sit for a few days in a cool, dry place before attempting to remove the husks.  Removing the husks involved latex gloves and serrated knife.  Once the husks had been removed, you can try the float test.  Fill a jar or tall glass with water and just place a nut in the water.  If it floats, your nut is bad.  If it sinks, you have a slightly more viable candidate-nut.  Floating means there is air trapped inside the nut.  Air in a nut is an indication that there is likely a worm in the nut.

The nuts that passed the float-test (or failed to float in the float-test) were put into ziplock bags filled with damp sawdust and placed into the refrigerator.  The length of stratification varied from 137 days for the walnuts picked up in Racine, MN, to 196 days for the Quercus macrocarpa (bur oak) picked up in Rochester, MN.

### We waited.  And, we waited.

With some of the seeds in the refrigerator for over six months, Melissa, at times, became annoyed that I had all these bags seeds and wet sawdust in there taking up space.  The bags of wet sawdust with seeds, each bag being marked with species and date of collection, stayed in the refrigerator until late March (2014), I started to catalog the seeds in a Google Doc’s spreadsheet, writing the encoded identifier on the plastic or wood markers, and then plant the seeds in small pots.  Eventually, little tiny trees began to poke through the soil. Black walnut seeds from Blue Earth, MN, were the first to nudge through to the surface.  Walnuts from Racine, MN were followed by St. Paul and Iowa City.  Eureka, MO, is the hold out; I think, though, that are one or two nuts from there are about to sprout.

Oaks, as it would seem, have a slightly different sprout-timing.  While the walnuts have been pushing up tiny trunks, an equally tiny tap-root has been pushing downward.  The oak acorns that are sprouting, are busy pushing down a tap root – their tiny trunks will be pushed skyward later.

Getting these seeds to grow seems to have relatively straightforward; next, will be getting these little trees through the summer and into the fall.  Then, I’ll start to collect nuts, again, as I travel here and there — hopefully collecting some from the trees in Hibbing.

http://esp.cr.usgs.gov/data/little/

http://www.fs.fed.us/database/feis/plants/tree/index.html

## Apple Seedling

In an earlier post, I had mentioned an apple seed that I had stuck in the of dirt of a flower pot in the kitchen; the seed sprouted and I had the photo-snapping-rig setup to capture the little guy grow.

Well, the seedling did not make it – it died.  But, I managed to capture all but the very first day of the seedling. The video takes about nine days of photos and compresses it down into about 30 seconds.

## Time Lapse

I will apologize a head of time for this posting.  It takes a bit of a dive into nerdom with some technical specifications, talk of Linux, servers, a mentioning of a thing called firewire and, at the end, there is information on the software that I am using to make time lapse videos.  But, interspersed between bits of this and that are some time lapse videos as well as some other nice photos.

Around five years ago, I made a time lapse video from a series of photographs.  The photographs, all 4,748 of them, were taken using a JVC MiniDV camcorder. The camera was tethered to a PowerBook (running Linux) via a firewire cable; the laptop would trigger the camera and then download the still-frame every 15 minutes.  Each photo was then uploaded to a server that was running in the basement.  The original video that was produced was over ten minutes long – the above video is a reprocessed version sped-up by four times.

Using a bit of software that I wrote, each photo was analyzed to determine if it was “too dark”. The analysis consisted of averaging the value of all the colors contained in a given photo; if the average was too close to black, the photo was rejected.  Another bit of processing involved inserting text, a timestamp and a watermark into the photo being processed.  Given the tools I was working with – a crufty PowerBook (held together with duct tape) running Linux and a MiniDV camera – embedding the text, timestamp and watermark as part of the photo/image made sense to me at the time.  Looking back, it would have been more useful to not have embedded that information into the images; some other location – either an ancillary place or even within each JPEG.

This go around, I am still using a nine year old camera (in 2009, the camera I used was from 2000), but a nine year old in 2014 is a different bit of technology than a nine year old camera in 2009.  The new camera is a Nikon D50 with a 35-70mm lens.  The camera body, lens, DC power adapter, and USB cable came to a total of about $225. The laptop that is effectively acting as an intervalometer would likely sell for another$225 (or less), but since the laptop is one that I have had for a long while and no longer actively use it, it is plausible to think of it as having no cost for me.

If you are still unclear as to what I am talking about with intervalometers, laptops and Nikon cameras, the basic idea is making a camera take a picture again and again and again at a regular interval.  It is kind of like regular motion pictures but on a much slower pace.  Instead of having 24 or 30 frames per second (as with a typical motion picture), there is only one frame every fifteen minutes.  Fifteen minutes is about the closest interval between photos that does not cause a tremendous waste of disk space and, in my case, you are able to capture enough difference in plant growth that it is noticeable; at 5 megabytes per photo, it amounts to a little less than half a gigabyte per day – with the particular laptop, I could safely shoot 140 days of photos.  Add a tweak to the software mix – and push the photos else where – like Amazon S3 – and you have an unlimited number of days.

Once I have a pile of photos, they need to be strung together into a video. In the Apple ecosystem, there is iMovie.  It is relatively inexpensive and is fairly easy to use.  This is what I use.  If you are hellbent on free or open source – checkout ffmpeg.

But that does not actually clear-up getting photos from the Nikon to the laptop; it also does not clear-up getting the laptop to trigger the camera at regular intervals.

I am using gphoto2.  This is a bit of open source software.  It took a bit of wrangling to get it to work, but it is quite robust and, so far, is quite reliable.  At the end of this posting, there are some random notes and a link to a bit of software I wrote to make it easier to trigger, download from the camera, and rename the photos in a consistent manner.

I am not sure why I like making or even watching time lapse videos of plants growing.  Maybe it has to do with being able to visualize something that ordinarily takes too long to be noticed by the human eye.

Maybe, I just feel a bit like Art Clokey.

Currently, the photo-snapping-rig is busy taking photos of a seedling started from a seed I pulled from a Braeburn apple.  The seedling is about an inch tall; its cotyledons have spread and the second set of leaves are little tiny spikes just above the stem.  I plan to photograph it for a couple weeks, or until the tripod the camera is attached to gets bumped.

Notes for a deep dive into nerdom:

If you are using Windows, you are on your own – I have not been an active or engaged Windows user for years. You’ll likely need cygwin in order to get gphoto2 working.  If you are using a Mac, I found it easiest to use homebrew.  Install homebrew, and then a simple brew install gphoto2 did the trick to get it installed.  I also installed ufraw for processing Nikon Raw format photos, but this is not necessary if you are using other Apple pieces of software for knitting your photos into movies (e.g. iMovie).

The camera needs to be in “PTP Mode” to communicate over USB; this is done by actually changing a setting on the camera – most likely by changing a setting from USB Mass Storage to PTP Mode. Once you have done that, with the camera connected to the computer, issue the command:

gphoto2 –auto-detect.

#> gphoto2 --auto-detect
Model                          Port
----------------------------------------------------------
Nikon D50 (PTP mode)           usb:253,003

If you are on a Mac, you will likely get an error at this point – instead of getting the listing of the attached camera.  Apple has a “helper process” that may latch onto the USB of the attached camera.  This will prevent gphoto2 from being able to communicate with it.

My solution was a bit of a big hammer.  I moved the offending program out of the way so it could be executed to latch onto the USB.  Another approach would be to terminate the process.  The program is called “PTPCamera”; if you would like to use the small-hammer approach, terminating it from a command line can be done like this:

ps -ax | grep PTPCamera | grep -v ' grep ' | awk '{print \$1}' | xargs kill -9

Or the big-hammer approach:

sudo mv /System/Library/Image\ Capture/Devices/PTPCamera.app /tmp

You might still need to terminate the process even if you move the program out of the way.

Once you have the PTPCamera process terminate/moved, try running gphoto2, again.

#> gphoto2 --summary
Camera summary:
Manufacturer: Nikon Corporation
Model: D50
Version: V1.00
Vendor Extension ID: 0xa (1.0)
Vendor Extension Description: Nikon PTP Extensions

Capture Formats: JPEG Undefined Type
Display Formats: Undefined Type, Association/Directory, TIFF, JPEG, DPOF, Script

Device Capabilities:
Generic Image Capture, No Open Capture, Nikon Capture 1

Storage Devices Summary:
store_00010001:
StorageDescription: None
VolumeLabel: NIKON D50
Storage Type: Removable RAM (memory card)
Filesystemtype: Digital Camera Layout (DCIM)
Access Capability: Read Only with Object deletion
Maximum Capability: 2014969856 (1921 MB)
Free Space (Bytes): 2009399296 (1916 MB)
Free Space (Images): 267

Device Property Summary:
Battery Level(0x5001):(read only) (type=0x2) Range [0 - 100, step 1] value: 100% (100)
'3008x2000',
'2256x1496',
'1504x1000'
] value: '1504x1000'
Compression Setting(0x5004):(readwrite) (type=0x2) Enumeration [0,1,2,4,5] value: RAW (4)
White Balance(0x5005):(readwrite) (type=0x4) Enumeration [2,4,5,6,7,32784,32785,32787] value: Automatic (2)
F-Number(0x5007):(readwrite) (type=0x4) Enumeration [450,500,560,630,710,800,900,1000,1100,1300,1400,1600,1800,2000,2200,2500,2900,3200] value: f/4.5 (450)
Focal Length(0x5008):(read only) (type=0x6) Range [3500 - 7000, step 1] value: 70 mm (7000)
Focus Mode(0x500a):(read only) (type=0x4) Enumeration [1,32784,32785,32786] value: Manual Focus (1)
Exposure Metering Mode(0x500b):(readwrite) (type=0x4) Enumeration [2,3,4] value: Multi-spot (3)
Flash Mode(0x500c):(readwrite) (type=0x4) Enumeration [2,4,32784] value: Auto (32784)
Exposure Time(0x500d):(read only) (type=0x6) Enumeration [20,25,31,40,50,62,80,100,125,166,200,250,333] value: 0.0017 sec (166)
Exposure Program Mode(0x500e):(read only) (type=0x4) Enumeration [1,2,3,4,32784,32785,32786,32787,32788,32789,32791] value: Auto (32784)
Exposure Index (film speed ISO)(0x500f):(readwrite) (type=0x4) Enumeration [200,400,800,1600] value: ISO 200 (200)
Exposure Bias Compensation(0x5010):(readwrite) (type=0x3) Enumeration [-5000,-4666,-4333,-4000,-3666,-3333,-3000,-2666,-2333,-2000,-1666,-1333,-1000,-666,-333,0,333,666,1000,1333,1666,2000,2333,2666,3000,3333,3666,4000,4333,4666,5000] value: 0.0 stops (0)
Still Capture Mode(0x5013):(readwrite) (type=0x4) Enumeration [1,2,32785,32787,32788] value: Power Wind (2)
Burst Number(0x5018):(readwrite) (type=0x4) Range [1 - 49, step 1] value: 1
Focus Metering Mode(0x501c):(readwrite) (type=0x4) Enumeration [2,32784,32785] value: Closest Subject (32785)
White Balance Preset Number(0xd01f):(readwrite) (type=0x2) Range [0 - 1, step 1] value: 0
White Balance Preset Value 0(0xd025):(read only) (type=0x6) 33685926
White Balance Preset Value 1(0xd026):(read only) (type=0x6) 33685926
Sharpening(0xd02a):(readwrite) (type=0x2) Range [0 - 6, step 1] value: Auto (0)
Tone Compensation(0xd02b):(readwrite) (type=0x2) Range [0 - 6, step 1] value: Auto (0)
Color Model(0xd02c):(readwrite) (type=0x2) Range [0 - 2, step 1] value: sRGB (0)
Reset Menu Bank(0xd045):(readwrite) (type=0x2) Range [0 - 1, step 1] value: 0
Auto ISO(0xd054):(readwrite) (type=0x2) Range [0 - 1, step 1] value: On (1)
Exposure Step(0xd056):(readwrite) (type=0x2) Range [0 - 2, step 1] value: 1/3 (0)
Exposure Lock(0xd05e):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Off (0)
Focus Lock(0xd05f):(readwrite) (type=0x2) Range [0 - 5, step 1] value: AE/AF Lock (0)
Auto Meter Off Time(0xd062):(readwrite) (type=0x2) Range [0 - 3, step 1] value: 6 seconds (1)
Self Timer Delay(0xd063):(readwrite) (type=0x2) Range [0 - 3, step 1] value: 10 seconds (2)
LCD Off Time(0xd064):(readwrite) (type=0x2) Range [0 - 4, step 1] value: 20 seconds (1)
Long Exposure Noise Reduction(0xd06b):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Off (0)
File Number Sequencing(0xd06c):(readwrite) (type=0x2) Range [0 - 2, step 1] value: Off (0)
NIKON Auto Bracketing Set(0xd07c):(readwrite) (type=0x2) Range [0 - 2, step 1] value: 0
No CF Card Release(0xd08a):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Off (1)
Image Comment String(0xd090):(readwrite) (type=0xffff) '                                    '
Image Comment Enable(0xd091):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Off (0)
Image Rotation(0xd092):(readwrite) (type=0x2) Range [0 - 1, step 1] value: On (0)
Auto Exposure Bracket Count(0xd0c3):(read only) (type=0x2) Range [1 - 3, step 1] value: 1
White Balance Bracket Step(0xd0c4):(readwrite) (type=0x2) Range [0 - 2, step 1] value: 0
Lens Sort(0xd0e1):(read only) (type=0x2) Range [0 - 1, step 1] value: 1
Min. Focal Length(0xd0e3):(read only) (type=0x6) 35 mm (3500)
Max. Focal Length(0xd0e4):(read only) (type=0x6) 70 mm (7000)
Max. Aperture at Min. Focal Length(0xd0e5):(read only) (type=0x4) f/3.3 (330)
Max. Aperture at Max. Focal Length(0xd0e6):(read only) (type=0x4) f/4.5 (450)
Nikon Exposure Time(0xd100):(read only) (type=0x6) Enumeration [66036,65936,65856,65786,65736,65696,65661,65636,65616,65596,65586,65576,65566] value: 65596
AC Power(0xd101):(read only) (type=0x2) Range [0 - 1, step 1] value: Yes (1)
Maximum Shots(0xd103):(read only) (type=0x2) Range [0 - 49, step 1] value: 4
AF Locked(0xd104):(read only) (type=0x2) Range [0 - 1, step 1] value: No (0)
AE Locked(0xd105):(read only) (type=0x2) Range [0 - 1, step 1] value: No (0)
FV Locked(0xd106):(read only) (type=0x2) Range [0 - 1, step 1] value: No (0)
Active AF Sensor(0xd108):(readwrite) (type=0x2) Range [0 - 4, step 1] value: Centre (0)
Flexible Program(0xd109):(readwrite) (type=0x1) Range [-30 - 30, step 2] value: 0
Exposure Meter(0xd10a):(read only) (type=0x1) Range [-128 - 127, step 1] value: -6.7 stops (-81)
Recording Media(0xd10b):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Card (0)
CCD Serial Number(0xd10d):(read only) (type=0xffff) '            20058684'
Camera Orientation(0xd10e):(read only) (type=0x2) Range [0 - 2, step 1] value: 0' (0)
External Flash Attached(0xd120):(read only) (type=0x2) Range [0 - 1, step 1] value: No (0)
External Flash Status(0xd121):(read only) (type=0x2) Range [0 - 1, step 1] value: No (0)
External Flash Sort(0xd122):(read only) (type=0x2) Range [0 - 1, step 1] value: 0
External Flash Compensation(0xd124):(read only) (type=0x1) Range [-18 - 18, step 1] value: 0 (0)
External Flash Mode(0xd125):(read only) (type=0x2) Range [0 - 7, step 1] value: 0
Flash Exposure Compensation(0xd126):(readwrite) (type=0x1) Range [-18 - 6, step 2] value: 0.0 stops (0)
Optimize Image(0xd140):(readwrite) (type=0x2) Range [0 - 7, step 1] value: Normal (0)
Saturation(0xd142):(readwrite) (type=0x2) Range [0 - 2, step 1] value: Normal (0)
AF Beep Mode(0xd160):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Off (1)
Autofocus Mode(0xd161):(readwrite) (type=0x2) Range [0 - 2, step 1] value: AF-A (2)
AF Assist Lamp(0xd163):(readwrite) (type=0x2) Range [0 - 1, step 1] value: On (0)
Auto ISO P/A/DVP Setting(0xd164):(readwrite) (type=0x2) Range [0 - 7, step 1] value: 1/30 (2)
Image Review(0xd165):(readwrite) (type=0x2) Range [0 - 1, step 1] value: On (0)
AF Area Illumination(0xd166):(readwrite) (type=0x2) Range [0 - 2, step 1] value: Auto (0)
Flash Mode(0xd167):(readwrite) (type=0x2) Range [0 - 1, step 1] value: iTTL (0)
ISO Auto(0xd16a):(readwrite) (type=0x2) Range [0 - 1, step 1] value: 0
Remote Timeout(0xd16b):(readwrite) (type=0x2) Range [0 - 3, step 1] value: 1 min (0)
Flash Mode Manual Power(0xd16d):(readwrite) (type=0x2) Range [0 - 4, step 1] value: Full (0)
CSM Menu(0xd180):(readwrite) (type=0x2) Range [0 - 1, step 1] value: Yes (1)
Bracketing Frames and Steps(0xd190):(readwrite) (type=0x2) Range [0 - 12, step 2] value: 12
Exposure Display Status(0xd1b0):(read only) (type=0x2) Range [0 - 4, step 1] value: No (0)
Flash Open(0xd1c0):(read only) (type=0x2) Range [0 - 1, step 1] value: Yes (1)
Flash Charged(0xd1c1):(read only) (type=0x2) Range [0 - 1, step 1] value: Yes (1)

Additional software used:  ruby (via rvm) and scheduling of photo snapping was done via crontab.

## Picking Up Pears

We have two pear trees on the property. Two very large pear trees. An arborist, who recently visited, pegged the age of each tree at between fifty and seventy years old. In talking with one of our neighbors this spring, it was mentioned that much of the land through this sliver of St. Paul, was once part of an orchard at the beginning of the twentieth century. Depending upon how you look at it, our trees could have been planted toward the end of the orchard’s formal existence, or these trees (the pears and the old apple trees) are from happenstance seedlings.

Last year, we had just moved in at the beginning of August. I am not recalling that we had as many pears (or apples for that matter) as we have this year. It might be a combination of a couple things – (1) we fenced in much of the yard for the hounds; (2) we have four stacks of expensive pollinators at the back of the property – honeybees.

With the fence in place, fallen fruit is not being eaten by the herd of whitetail deer that live in the forest that covers this part of St. Paul. This means that we maybe seeing a more accurate account of the volume of fruit from the trees. Secondly, we have the honeybees. This spring, just prior to my epic Yukon road trip, the pear trees were in bloom. The trees were buzzing with honeybee activity.

Whatever the mainspring of the volume of pears is, it is kind of irrelevant at this point in the season. We have a lot of pears. We have cleaned up the yard four times, and I suspect we will be picking up pears at least once more before the snow flies.

So, I picked up the pears, again. This time, I did what I like to do with videoing things: recorded it, and then sped it up. Enjoy. The variety of pear, at least those that I am picking up, as far as I can tell, are Seckel pears.

## Rouge Vif d’Etampes (Fancy Pumpkins)

The last week leading into this weekend and then through this weekend, weather-wise, has been on the extreme-side of pleasant.  I would call this goldilocks weather. It has been not too cold and not too hot.  Cool in the evenings and into the nights and cool in the mornings with just the right amount of sun and warmth with partly cloudiness throughout the day.

It’s good sitting-around-weather.  Good outdoor-project-tinkering-weather. Great reading-a-book-while-sipping-lemonaid-weather.

Minnesota Public Radio’s chief meteorologist, Paul Huttner, remarked both on-air and on his Updraft Blog that…

It doesn’t get any better than this folks. This may be the best weekend of summer. Lazy high pressure drifting east brings a return southerly flow and gradual warming trend.  Plenty of sun and highs in the 80? Cue the brass band, beach-goers and lemonade stands.

But with the cool mornings and equally cool nights, I can’t help but think that fall is just over the horizon.  The kind of tinge to the air that reminds you that the amount of time you have worn shorts this summer is greater than the amount of time remaining to wear shorts this summer.  Driving home from Zumbrota this afternoon, we saw a truck hauling ears of corn – it’s getting to be harvest time – maybe hauling to a farmer’s corn crib to dry out for winter cattle feed, or maybe to a wet-mill.

Here at the house with our small garden, we are growing a bit of corn.  It is an heirloom bi-color sweet corn.  The ears are small, and the stalks are short.  We might just end up feeding partially developed ears of corn to the chickens.  We have also had mixed success with peas and beans.  The first patch of peas was small – we ended up with a only a single bowl.  The garlic that we grew was small, but has been very tasty.  Dill, thyme and basil have all been abundant and flavorful.  The few varieties of tomatoes that we grew this season, like Burpee’s Northern Exposure, have been doing well.  I am starting to not mind tomatoes in salads, but I am likely being spoiled with the slow nature that our tomato production operates under.  Instead of forcing the tomatoes to grow and instead of picking them too early, we can pick them when we want and more on their own schedule.

But, of all the things we planted, the one that has left me gobsmacked, is the Rouge Vif d’Etampes.  It’s basically a fancy pumpkin of French origin.  According to our garden plans, we planted five mounds – with roughly a few seeds to each mound.  In the U.S., it appears these pumpkins are often colloquially known as Cinderella pumpkins.

As I mentioned, previously, these Cinderella pumpkins are growing with the vigor and perceived determination of Audrey II from Little Shop of Horrors, just without having to resort to bringing bodies to the pumpkins.  At last count, there were 18 to 20 pumpkins, in various stages, growing in the garden.

So, what is so special about these pumpkins?  It is an heirloom variety that was first introduced to the United States from France in 1883 by Burpee.  It is a variety of Cucurbita maxima (this is the same species as butternut or hubbard squashes).  Among its characteristics, it is supposed to have sweet, orange flesh with a strong flavor.  But, I think its most endearing characteristic is its whimsical shape.  Squat like a short-stack of extra wide pancakes, these pumpkins simply stand-out in the garden.

Along with their stand-out nature, the vines being produced seem to have a mind of their own.  Depending upon what source of information you assume is canonical, the spread can be anywhere from 6 to 20 feet; we are seeing a spread just above that upper bound.  And, since we have fencing around the garden, we are seeing the spread in all three dimensions.

But, as with many things in the garden (or, sometimes life), things can quickly turn in a different direction.  With this coming week, we are supposed to have a bit more summer-like weather.  My thoughts on the onset of fall may temporarily be put the side, but they will still be there.  And when fall finally does show up and we get that first frost, I am sure I will write again about these magnificently shaped pumpkins and how they turned out.

## Lawnmowers & Vespidae

Before leaving for Portland, I had been putzing with the lawn tractor and its mower deck.  The mower deck has a Rube-Goldbergian pulley system from taking power from the engine and directing it to the mower blades.  For a while (prior to traveling to Portland), I have been trying to get the right belt for the mower deck.  The mower itself is a Sears.  Its green color is not original, nor is the yellow mower deck.  The belt that was on the machine when my father-in-law was cracked and worn and continually slipped off. Amazon.com has been stellar with their selection of belts.  Props to Amazon for having belts listed by size and not simply the model of the machine they will fit.  I have bought several – different circumferences and different thicknesses.  Except for the last belt I tried, the others keep violently vibrating and slip off of the pulleys.  The last belt was simply too short.

With the far-back garage closed and the not-mowing-mower in said garage, Melissa was not able to get the grass cut while I was in Portland.  The grass also did not get cut the first week back from Portland.  This was more than nerve-racking for Melissa, and she had had enough.  We bought a new self-propelled push mower yesterday.

Melissa is a tomboy.  She likes things with engines – lawnmowers, tractors, fishing boats.  Whenever I would get the lawn tractor out to mow, inevitably, Melissa would wander out and ask if she could take over.

Like a kid with a new toy, I could barely get the few things I was carrying out and into the house; she wanted the new mower unpacked and working.

With the jerrycan of 92 octane gasoline empty after filling the new machine, I headed to a gas station; Melissa buzzed around the front yard with the new mower.

When I returned, she had moved into the backyard.  She had mowed in front of the entrance to the vegetable garden and was now mowing lengthwise in front of the chicken coop.

I had noticed a mole hole near the entrance to the garden several days ago.  I had made a mental note to fill it with dirt, but had since lost the mental note.  Walking to check the expansive Little Shop of Horrors-like squash plant (I have not had to feed it bodies, yet, but the plant is enormous, and, in the hot weather of several weeks ago, it was growing nearly 12″ per day) that had been looking dehydrated earlier in the day, I noticed activity around the mole hole – insects, flying insects, black and yellow flying insects.

A closer inspection revealed wasps.  Depending upon which entomology camp you follow, you call them Vespula alascensis, or you might call them Vespula vulgaris.  Either way, they are wasps.

Melissa had apparently, and unknowingly mowed over the mole hole that now contained the wasps.  Before I inevitably had to put wasp spray into their home, I set up a video camera and videoed them cleaning out the grass clippings that had landed at the entrance.


text:
# How to calculate the bending resistance of a square metal bar?

I have an old bend/twisted wooden door. It has some character to it so I want to keep it and add square metal bars to straighten it. I have provided a sample drawing of the door and where it is twisted. I have drilled a hole in the upper most open part and if I pull with a scale I am able to straighten it with about 20kg (I haven't used a scale yet, but I will)

I intend to put square metal bars on the bent sides (maybe even inside and out) and straighten the wood.

My question is what is the formula that I can use to calculate the size of the metal bar? For example I see there is a square profile bar 40x40x3mm that I will be able to buy and attach. So, is this going to be enough for the long side 2m and for the short side 1m? I can also order this square profile bar to be slightly bent and attach it so the two bends - the one of the wood and the one of the metal counter each other. But I am not really willing to go that way. I think its way too complicated.

Edit:

1. I think a visible rectangle bar on one or both faces will be stronger and more simple to attach, so I will go with that.
2. No bend is acceptable - I want it straight.
3. So the next question following the comment is how much of a bend do I need for what type of bar for each of the sides - short(1m) and long (2m)?
• If you don't go with the counter-bend, the reinforced door will still bend outwards, just less so. In which case you need to decide how much of a bend is acceptable and edit that into your question. Also, is your idea to attach this bar to one of the faces of the door (so that it's sticking out and visible on one side)? Or do you intend to actually get a U-shape and "wrap" the end of the door with the bar (which will probably require filing down the door a bit so that it still closes. – Wasabi Sep 26 '18 at 19:35
• Please check the edit I placed in the original question – kdobrev Sep 26 '18 at 20:09

If you estimate force needed to straighten the door applied at the corner is 20kg, it would be equivalent to the reaction of a uniformly loaded beam (your square bar) at one end.

So lets design the bar and for simplicity only the top bar, we can do the side later if we need to.

Lets say the door stays out of door jamb 2cm at the corner. So now we have all the data to design a bar or strap that has a deflection, built in bend, of 1/2 times 2cm =1cm and the 2 end reactions of 20kg, which for a 1m long strap mean omega is 40kg/m.

Deflection in a simply supported strap:

$$\delta = \frac {5 }{384 } \frac {\omega L^3}{EI}$$ This means $$0.01 = 5/384 \times40\times 1^3/(200GPa\times I)$$ $$2GPa\times I = 5/384\times 40$$

This Gives the second moment, "I" of your strap and from there you can select the section of the bar that gives you optimal looks and required strength. Again this bar need to have a camber of 1cm built into it, so that after you attach it the door will be pressed into straight line.

• Thank you for this answer, although I did not understand it. I was trying to make sense reading en.m.wikipedia.org/wiki/Deflection_(engineering) but there I see your formula with L^4. Also I did not see the elasticity of my chosen bar 40x40x3mm. Also should I take into account to put just half of the force because I will be using two bars - vertical and horizontal. – kdobrev Sep 27 '18 at 11:01
• Thank you for this answer, although I did not understand it. I was trying to make sense reading en.m.wikipedia.org/wiki/Deflection_(engineering) but there I see your formula with L^4. Also I do not sundestand what is I. I suppose 2GPa is the elasticity of my chosen bar 40x40x3mm. Also should I take into account to put just half of the force because I will be using two bars - vertical and horizontal. – kdobrev Sep 27 '18 at 11:12
• @kdobrev no, you need to install a strap on top 1 meter long and calculate its dimension from the I. The power is 3 when you apply the total omega and 4 when you use omega/m.. if you install another one on the side vertically because of its length, it will contribute very little. – kamran Sep 27 '18 at 15:05
• I am honestly lost. I don't understand how only one strap will fix 2 curvatures. And since the I is some integral that I cannot compute I will provide a link with the possible materials I could use and please somebody pick one up for me, translate.google.com/… – kdobrev Sep 27 '18 at 18:42
• @Kamran is right. The Modulus of elasticity is going to be negligible for the size of angle iron chosen by virtue of its shape. Steel is incredibly strong so you really need to think about applied deformations to wood as "creep" due to moisture content. Think about adding a moisturiser to the door so that restoration is achieved faster with less damage. – Rhodie Jan 20 '19 at 3:37


text:
# How to define an action space when an agent can take multiple sub-actions in a step?

I'm attempting to design an action space in OpenAI's gym and hitting the following roadblock. I've looked at this post which is closely related but subtly different.

The environment I'm writing needs to allow an agent to make between $$1$$ and $$n$$ sub-actions in each step. Leaving it up to the agent to decide how many sub-actions it wants to take. So, something like (sub-action-category, sub-action-id, action) where the agent can specify between $$1$$ and $$n$$ such tuples.

It doesn't seem possible to define a Box space without specifying bounds on the shape which is what I need here. I'm trying to avoid defining an action space where each sub-action is explicitly enumerated by the environment like (action) tuple with n entries for each sub-action.

Are there any other spaces I could use to dynamically scale the space?

• Is the last element of the tuple (sub-action-category, sub-action-id, action) a discrete or continuous value? What is its dimension? gym offers the class MultiDiscrete for a similar use case. You could also write your own action type if you wanted to, but imo the straightest way to deal with this is to have actions to be instances of some suitably defined Python class you can document etc. and deal with the details of the execution to the Environment subclass. – Miquel Ramirez Feb 19 at 9:51


text:
Exports an H2OModel to HDFS.

h2o.exportHDFS(object, path, force = FALSE)

## Arguments

object an H2OModel class object. The path to write the model to. Must include the driectory and filename. logical, indicates how to deal with files that already exist.


text:
## Book Store

Currently only available for.
CBSE Gujarat Board Haryana Board

## Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

• 2g/3

• g/2

• 5g/6

• g

B.

g/2

For the mass m,
mg-T = ma

As we know, a = Rα    ... (i)
So, mg-T = mRα
T x R = mR2α ...... (ii)
From Eqs. (i) and (ii), we get
a = g/2
Hence, the acceleration of the mass of a body fall is g/2.

For the mass m,
mg-T = ma

As we know, a = Rα    ... (i)
So, mg-T = mRα
T x R = mR2α ...... (ii)
From Eqs. (i) and (ii), we get
a = g/2
Hence, the acceleration of the mass of a body fall is g/2.

455 Views

State Galileo’s law of motion.

Galileo’s law of motion states that, a body continues to move in the same direction with constant speed, if no force is acting on the body.
1332 Views

When the branches of an apple tree are shaken, the apples fall down. Why?

The apple fall from an apple tree when it shaken because of inertia of rest. Apple is in a state of rest and when the tree is suddenly shaken, apples still tends to remain in it's same state of rest whereas branches move.

So, the apples fall down.
1475 Views

Define inertia.

The property by virtue of which the body cannot change its state of rest or uniform motion in a straight line, unless an external force is acting on the body is called as Inertia.
1316 Views

What is Aristotle’s law of motion?

Aristotle’s law of motion states that an external force is required to keep the body in motion.
2445 Views

Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false.
1233 Views


text:
# Differing axioms for Stiefel-Whitney class

In Milnor and Stasheff, it is taken as part of the first axiom that all Stiefel-Whitney classes of a bundle vanish in dimensions greater than the rank of the bundle. However, in other sources this is omitted. The wikipedia article makes it seem like this is actually a result of the axioms. Is there a simple proof of this (the axioms I am using are those listed here http://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class#Axioms)?

-

## 1 Answer

It is certainly both of constructions of the Stiefel-Whitney classes that I know. The construction via the Thom Isomorphism and the Steenrod operations clearly must vanish seeing as the Thom class of the bundle will be in a dimension that is killed by the Steenrod Operation because of instability.

For the construction via universal bundles you look at the universal rank $k$-bundle $\gamma_k$, it has $w_n(\gamma_k)=0$ simply by looking at the cohomology of $BO(k)$, there isn't a polynomial generator in that dimension. The above observation coupled with naturality should give the result, but i don't know if that should count as following from the axioms.

I can flesh this out a bit later if you like.

-
Thanks for the answer! I am wondering though if there is a more direct proof from the axioms (instead of going through a construction and proving uniqueness). –  Eric O. Korman Jan 9 '11 at 23:36
I understand completely. Hopefully, someone will come by with an answer. –  Sean Tilson Jan 10 '11 at 2:41
Also, it should be pointed out that it could be a mistake in the wikipedia entry... –  Sean Tilson Jan 10 '11 at 2:42


text:
IntMath Home » Forum home » Functions and Graphs » How to obtain 0.84?

How to obtain 0.84? [Solved!]

My question

In Example 1 on the page, how do you obtain 0.84? Please show calculation for common mortals. Thank you.

Relevant page

3. Graphs of y = a sin(bx + c) and y = a cos(bx + c)

What I've done so far

Read other examples, tried substituting

X

In Example 1 on the page, how do you obtain 0.84? Please show calculation for common mortals. Thank you.
Relevant page

3. Graphs of y = a sin(bx + c) and y = a cos(bx + c)

What I've done so far

Read other examples, tried substituting

Re: How to obtain 0.84?

Hello L. Aureli

The 0.84 comes from substituting x = 0 into y = sin(2x + 1), that is y = sin(0+1) = sin 1.

Using calculator, sin 1 = 0.84 (you must be in radians.)

Hope that makes sense.

Regards

X

Hello L. Aureli

The 0.84 comes from substituting x = 0 into y = sin(2x + 1), that is y = sin(0+1) = sin 1.

Using calculator, sin 1 = 0.84 (you must be in radians.)

Hope that makes sense.

Regards

Re: How to obtain 0.84?

Doh - I was in degrees and couldn't get 0.84.

Thanks a lot.

X

Doh - I was in degrees and couldn't get 0.84.

Thanks a lot.


text:
I'm given a hexadecimal number in string form with a leading "0x" that may contain 1-8 digits, but I need to pad the number with zeros so that it always has 8 digits (10 characters including the "0x").

For example:

• "0x123" should become "0x00000123".
• "0xABCD12" should become "0x00ABCD12".
• "0x12345678" should be unchanged.

I am guaranteed to never see more than 8 digits, so this case does not need to be handled.

Right now, I have this coded as:

padded = '0x' + '0' * (10 - len(mystring)) + mystring[2:]

It works, but feels ugly and unpythonic. Any suggestions for a cleaner method?

Perhaps you're looking for the .zfill method on strings. From the docs:

Help on built-in function zfill:

zfill(...)
S.zfill(width) -> string

Pad a numeric string S with zeros on the left, to fill a field
of the specified width.  The string S is never truncated.

Your code can be written as:

def padhexa(s):
return '0x' + s[2:].zfill(8)

• This is exactly what I was looking for. Thanks! – Sohcahtoa82 Oct 23 '14 at 17:42

I would suggest interpreting the input as a number, then using standard number-formatting routines.

padded = str.format('0x{:08X}', int(mystring, 16))

The string → int → string round trip may seem silly, but it is also beneficial in that it provides validation of the input string.

I'd use something like this:

def format_word(word, prefix=None, size=None):
if prefix is None:
prefix = '0x'
if size is None:
size = 2
if not isinstance(word, int):
word = int(word, 16)
if word > 2**(8 * size) - 1:
raise ValueError('word too great')
prefix=prefix,
word=word,

Using None as defaults and assigning true defaults later makes it easier to wrap the function.

def format_word(word, prefix=None, size=None):
if prefix is None:
prefix = '0x'
if size is None:
size = 2

If word isn't already a int try to convert it. It'll choke if it's not a str, bytes, or bytearray. We need the type check because int(word, 16) would choke if word was already an int.

if not isinstance(word, int):
word = int(word, 16)

Check that the word isn't going break the formatting.

if word > 2**(8 * size) - 1:
raise ValueError('word too great')

Finally, format the word, using keywords to decouple the string to the argument order.

return '{prefix}{word:0{padding}X}'.format(
prefix=prefix,
word=word,
`