text:
19 October, 2013

On implement weights or how even brilliant men can be mistaken

A. Juilland, in the book that gave the name to this blog, is discussing the choice of weights for the various implements used in throws. He argues that, since the idea behind the choice of the weights for women's implements was dictated by the desire to have roughly the same throw lengths at world record level, the current choice of weights is not optimal. While for shot put and discus throw the choice is more or less right, the matter is more complicated for hammer and javelin. Of course, hammer throw was a very young discipline at the time of Juilland's article and since that time the feminine world record is no more that far behind the masculine one.

However things are quite different for javelin. Juilland argues that women must use a lighter implement, of roughly 500 g. Moreover his estimates are based on the old javelin, still in use for women at that time, and a world record of 80 m. With the current world record of 72 m a lighter javelin, of roughly 450 g, would have been proposed by Juilland, had he been still among us today.

The photo is that of my preferred javelin thrower Mariya Abakumova.

Unfortunately the grand master of athletic provocation is wrong in his estimates. I have written an article on the influence of implement weight on the length of the throw which will appear shortly in New Studies in Athletics. (I do not link to it here. If anybody is interested in having a copy, I will gladly provide it. It suffices to send me an email at the address: basigram at gmail dot com). One does not have to go through the physics of the article in order to understand the basic point: even when we try to throw a very small weight, there is a limit to the velocity we can impart to it, limit due to the speed at which we can move our arm. This is something far from negligible. In fact as shown in my article the length of the throw is inversely proportional to the sum of the mass m of the implement and something that we could qualify as the effective mass of the arm. In my analysis of shot put I found that for male throwers this effective mass term f had a value around 6-7 kg. One expects this value to be somewhat smaller for javelin throw, because of the different gesture, and even smaller for women. So let us assume a value of 4 kg and see where this leads us.
$L = a m + f$


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# Marginfigure image in tufte-handout is off center when using vertical alignment option

When using the \includgraphics command (under the graphicx package) in the marginfigure environment, the image is slightly off center to the right, but only when using the vertical alignment option.

\documentclass{tufte-handout}

\usepackage{graphicx}
\geometry{showframe}

\begin{document}

\begin{marginfigure}[-0.5in]
\includegraphics[width=\textwidth]{bb_navy.jpg}
\end{marginfigure}

\end{document}

Without the vertical alignment, the image is centered as expected.

The environment defined by tufte-handout for inserting figures and other floats in the margin should be fixed by adding a \ignorespaces after \noindent.

It's a primitive feature of TeX's line breaking algorithm that glue (including glue from white space) is discarded at the beginning of the line. But \noindent starts the paragraph already so the following space token produces glue that is not discarded,(as it doesn't follow a linebreak).

Whenever you use \noindent (or \indent) at the end of a macro with arguments, it's good rule to add \ignorespaces

\documentclass{tufte-handout}

\usepackage{graphicx}
\geometry{showframe}

\makeatletter

\renewenvironment{@tufte@margin@float}[2][1.2ex]%
{\FloatBarrier% process all floats before this point so the figure/table numbers stay in order.
\begin{lrbox}{\@tufte@margin@floatbox}%
\begin{minipage}{\marginparwidth}%
\@tufte@caption@font%
\def\@captype{#2}%
\hbox{}\vspace*{#1}%
\@tufte@caption@justification%
\@tufte@margin@par%
\setlength{\parindent}{0.0pc}%
\noindent%
}
{%
\end{minipage}%
\end{lrbox}%
\marginpar{\usebox{\@tufte@margin@floatbox}}%
}

\makeatother

\begin{document}

\begin{marginfigure}[-0.5in]
\includegraphics[width=\linewidth]{example-image-a}
\end{marginfigure}

\begin{marginfigure}% [-0.5in]
\includegraphics[width=\linewidth]{example-image-c}
\end{marginfigure}

\end{document

• +1 Great, you found the culprit and an explanation!
– DG'
May 30, 2021 at 19:11
• Yes, this is the "fix." Thank you for the help!
– Roy
May 30, 2021 at 20:27

You can fix that by moving the \noindent directly to the beginning of the minipage:

\documentclass[nobib]{tufte-handout}

\usepackage{graphicx}
\geometry{showframe}

\makeatletter
\renewenvironment{@tufte@margin@float}[2][-1.2ex]%
{\FloatBarrier% process all floats before this point so the figure/table numbers stay in order.
\begin{lrbox}{\@tufte@margin@floatbox}%
\begin{minipage}{\marginparwidth}%
\noindent% <-- MOVE HERE
\@tufte@caption@font%
\def\@captype{#2}%
\hbox{}\vspace*{#1}%
\@tufte@caption@justification%
\@tufte@margin@par%
}
{\end{minipage}%
\end{lrbox}%
\marginpar{\usebox{\@tufte@margin@floatbox}}%
}
\makeatother

\begin{document}

\begin{marginfigure}[-.5in]
\includegraphics[width=\textwidth]{example}
\end{marginfigure}

\end{document}

format: plain


text:
This compound reacts readily with water, so it is an excellent drying agent for organic solvents. Calcium Reacts With Water. When calcium oxide (chemical formula: CaO) reacts with water (chemical formula: H2O), the following reaction takes place: CaO + H_2O -> Ca(OH)_2 The product of this reaction is calcium … Reaction of Aluminium with steam; 9. So, it can't react quickly with water. ii) It reacts violently with water: The given process is slow. 1 decade ago. 0 0. 1 decade ago. Anonymous. (a) Write a balanced equation showing the formation of calcium hydride from Ca and $\mathrm{H}_{2}$ (b) Write a balanced equation for the reaction of calcium hydride with water (Figure 21.6 ). 0 0. How sodium reacts with water. Laboratory preparation of hydrogen gas. Relevance. Johnny D. Lv 7. Reaction of water with metals; 3. How Zinc reacts with steam; 7. So, option is wrong. Favorite Answer. What would happen if a small proportion of calcium was put into a beaker of water? 1 Answer. Source(s): https://shrinke.im/a0z8C. How Iron reacts with steam; 8. From above we can say that option iii) and iv) are correct: As it takes time and formation of hydrogen gas takes place. Calcium Reaction with Water? Reaction of metals with steam. Reaction of calcium with water; 5. 0 0. Bubbles of hydrogen gas are given off, and a white precipitate (of calcium hydroxide) is formed, together with an alkaline solution (also of calcium hydroxide, which is slightly water-soluble). Reaction of calcium with water. 6. CaO is calcium oxide, the white … 5 years ago. You will produce a small amount of hydrogen, but at the same time you would create a somewhat powerful base known as Calcium Hydroxide. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: CaO (s) + H2O (l) → Ca (OH) 2 (s) In a particular experiment, a 5.50-g sample of CaO is reacted with excess water and 6.77 g of Ca (OH) 2 is recovered. Summary of the reaction between metals with cold water and steam; 10. Calcium, for example, reacts fairly vigorously and exothermically with cold water. Thanks. A portion of the sample is digested in a combination of acids. Ca(s) + 2H2O(l)→Ca(OH)2(aq) + H2(g) Bubbles form and you might see the metal splashing around before it dissolves. Calcium hydroxide is slightly soluble in water so once the solution is saturated, it starts to become milky as solid calcium hydroxide appear. Ca + H2O --> CaO + H2. Ask … Get your answers by asking now. Answer Save. Because Calcium reacts with water and formation of Calcium Hydroxide and Hydrogen gas takes place. Anonymous. Calcium reacts slowly with water, forming calcium hydroxide and hydrogen. Ca (s) + 2 H 2 O (l) Ca(OH) 2 (aq) + H 2 (g) Quantitative analysis. 11. Method 3500-Ca C Inductively Coupled Plasma Method [1]. The equation for the reactions of any of these metals would is as follows: 4. The reaction creates Hydrogen gas, H2 which are the bubbles. Still have questions?

.

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# Flowering Currant

It’s hard to ignore the beauty of the Flowering Currant (Ribes sanguineum) flowering in the last month of Winter.

Well, I could hardly write that last blog post and just walk away. So here’s something that has brought on some cheer these past few weeks: my Flowering Currant.

My mother tells me that my great grandmother used to have a Flowering Currant in her garden. Its beautiful flowers and soft scent were so distinctive that they left a permanent impression on my mother; always reminding her of those childhood visits to her grandmother’s home.

In the 1990’s when I was growing up, Mum went to a lot of trouble to identify the Flowering Currant (from a distant memory) and then source one. They are hardly common. Somehow she eventually found a nursery that stocked them and bought one. I seem to recall the first specimen not doing especially well but by this stage I was old enough (and interested enough) to take cuttings competently and so we grew a new one and tried it in another spot, where it did much better.

Many years later when I bought a home of my own, I was keen to grow one. For me, it is a reminder of my mother and her struggle to get her flowering currant. So I took a cutting off hers.

What I like about flowering currants is the proliferation of blooms right at the end of winter. The blossoming of flowers usually coincides with the emergence of beautiful trilobed apple green leaves. I have a poor sense of smell so the perfume is inconsequential but the display is lovely.

I was a bit luckier than Mum because I found a good spot for my plant the first time around. Mine is planted beside the house and faces south-west. It gets shade until about midday and gets sun thereafter. It endures the harsh Australian heat well but warmer summers will cause some of the older leaves to look a bit ratty by late February.

In these troubling times, it’s nice to have these reminders that not all in the world is bad. There is beauty everywhere. Sometimes it’s right under our noses.

    <q cite="">


text:
# Math Help - Simple ODE

1. ## Simple ODE

Solve using the power series method:

$y' + xy = 0, y(0) = 1$

Can anyone show the steps to do this?

2. Originally Posted by flipperpk
Solve using the power series method:

$y' + xy = 0, y(0) = 1$

Can anyone show the steps to do this?
Why use the power series method? It's seperable and can also be solved using an integrating factor...

Seperating:

$\frac{dy}{dx} + xy = 0$

$\frac{dy}{dx} = -xy$

$\frac{1}{y}\,\frac{dy}{dx} = -x$

$\int{\frac{1}{y}\,\frac{dy}{dx}\,dx} = \int{-x\,dx}$

$\int{\frac{1}{y}\,dy} = -\frac{1}{2}x^2 + C_1$

$\ln{|y|} + C_2 = -\frac{1}{2}x^2 + C_1$

$\ln{|y|} = -\frac{1}{2}x^2 + C$, where $C = C_1 - C_2$

$|y| = e^{-\frac{1}{2}x^2 + C}$

$|y| = e^Ce^{-\frac{1}{2}x^2}$

$y = \pm e^C e^{-\frac{1}{2}x^2}$

$y = Ae^{-\frac{1}{2}x^2}$, where $A = \pm e^C$.

Now use your initial condition to find A.

3. Originally Posted by Prove It
Why use the power series method? It's seperable and can also be solved using an integrating factor...

Seperating:

$\frac{dy}{dx} + xy = 0$

$\frac{dy}{dx} = -xy$

$\frac{1}{y}\,\frac{dy}{dx} = -x$

$\int{\frac{1}{y}\,\frac{dy}{dx}\,dx} = \int{-x\,dx}$

$\int{\frac{1}{y}\,dy} = -\frac{1}{2}x^2 + C_1$

$\ln{|y|} + C_2 = -\frac{1}{2}x^2 + C_1$

$\ln{|y|} = -\frac{1}{2}x^2 + C$, where $C = C_1 - C_2$

$|y| = e^{-\frac{1}{2}x^2 + C}$

$|y| = e^Ce^{-\frac{1}{2}x^2}$

$y = \pm e^C e^{-\frac{1}{2}x^2}$

$y = Ae^{-\frac{1}{2}x^2}$, where $A = \pm e^C$.

Now use your initial condition to find A.
I appreciate the help, but my professor wants us to use the power series method.

4. Well, you could get the final answer and then express it as a power series...

5. Originally Posted by flipperpk
Solve using the power series method:

$y' + xy = 0, y(0) = 1$

Can anyone show the steps to do this?

Let

$y=\sum_{n=0}^{\infty}a_nx^n$ Then

$y'=\sum_{n=1}^{\infty}na_nx^{n-1}$

Now substituing these into the equation gives

$\sum_{n=1}^{\infty}na_nx^{n-1}+x\sum_{n=0}^{\infty}a_nx^n=0$

$\sum_{n=1}^{\infty}na_nx^{n-1}+\sum_{n=0}^{\infty}a_nx^{n+1}=0$

Now we take the first term out of the 1st series to get

$a_1+\sum_{n=2}^{\infty}na_nx^{n-1}+\sum_{n=0}^{\infty}a_nx^{n+1}=0$

Now reindex the first series with $n \to n-2$ to get

$a_1+\sum_{n=0}^{\infty}(n+2)a_{n+2}x^{n+1}+\sum_{n =0}^{\infty}a_nx^{n+1}=0$

Now combing the sums gives

$a_1+\sum_{n=0}^{\infty}[(n+2)a_{n+2}+a_n]x^{n+1}=0$

$(n+2)a_{n+2}+a_n=0 \implies a_{n+2}=-\frac{a_n}{n+2}$

Also note that the above equation implies that $a_1=0$

Using your intial condition you will find that $a_0=1$

With the relation about you can find all of the coeffeints of the power series.


text:
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Confusion about a claim in a paper of Stong

The following is an excerpt from a paper of Stong on algebraic topology (page 40 of his notes on algebraic topology).
Let $X$ be a topological space and $A$ a subspace of $X$. We denote the open subsets of $X$ that contain $A$ by $X|A$. We define the closure of $A$ by $\overline{A} = \overline{X|A}$.

The closure $\overline{A}$ is equal to the union of all the open sets $U$ such that $U\cap A$ is not empty.

I am confused because I know that $\overline{A}$ is equal to
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text:
# Differences

This shows you the differences between two versions of the page.

ortholattices [2010/07/29 18:30]
127.0.0.1 external edit
ortholattices [2010/12/15 21:58] (current)
jipsen
Line 13: Line 13:
==Morphisms== ==Morphisms==
-Let $\mathbf{L}$ and $\mathbf{M}$ be ortholattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:Larrow M$ that is a+Let $\mathbf{L}$ and $\mathbf{M}$ be ortholattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\to M$ that is a
homomorphism: homomorphism:
Line 42: Line 42:
^[[Definable principal congruences]]  |no | ^[[Definable principal congruences]]  |no |
^[[Equationally def. pr. cong.]]  |no | ^[[Equationally def. pr. cong.]]  |no |
-^[[Amalgamation property]]  | | +^[[Amalgamation property]]  | Yes
-^[[Strong amalgamation property]]  | |+^[[Strong amalgamation property]]  | Yes [(BrunsHarding1997)] |
^[[Epimorphisms are surjective]]  | | ^[[Epimorphisms are surjective]]  | |
-====Finite members====
-$\begin{array}{lr} +====Finite members==== -f(1)= &1\\ + -f(2)= &1\\ + -f(3)= &\\ + -f(4)= &1\\ + -f(5)= &\\ + -f(6)= &\\ + -f(7)= &\\ + -\end{array}$+
+^$n$       | 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 |
+^# of algs | 1 | 1 | 0 | 1 | 0 | 2 | 0 | 5 | 0 | 15 |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |
+^# of si's | 0 | 1 | 0 | 0 | 0 | 2 | 0 | 3 | 0 | 11 |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |    |  0 |
====Subclasses==== ====Subclasses====
Line 68: Line 62:
====References==== ====References====
-[(Ln19xx+[(BrunsHarding1997
-)]+G. Bruns and J. Harding, \emph{Amalgamation of ortholattices}, Order 14 (1997/98), no. 3, 193–209
+[[http://www.ams.org/mathscinet-getitem?mr=99f:06014|MRreview]])]


text:
## WeBWorK Main Forum

### Why Giga newton is not allowed

by Ever Barbero -
Number of replies: 3

In Webwork 12, why Giga newton is not allowed but Gima Pascal is?

See screenshot below or in: http://forum.cadec-online.com/viewtopic.php?f=9&t=115

The questions are set up with lb, in, psi, N, mm, MPa, to show students various ways to enter units.

Unfortunately, G works for GPa, but not for GN.

The prefix "m" for milli, does not work for anything. See screenshot in http://forum.cadec-online.com/viewtopic.php?f=9&t=115

I know the correct prefix for milli is "m" without a space between the "m" and the base unit because the National Institute of Standards NIST says so. See screenshot in http://forum.cadec-online.com/viewtopic.php?f=9&t=115

I can't say don't use Giga because we have a lot of data in the range of GPa, but if I say that G is a prefix meaning 10^9 and someone uses it for GN in an exam, the student is toast, his answer will be marked WRONG!

Tags:

### Re: Why Giga newton is not allowed

by Robert Mařík -

Did not use units, but it seems that the code is at https://github.com/openwebwork/pg/blob/master/lib/Units.pm and to allow GN you should add the corresponding lines to the section where multiples of Newton are defined.

Looking at the code, the "mili" prefix should work at least for millimeter and some other units.

Robert

### Re: Why Giga newton is not allowed

by Ever Barbero -

Can I just modify the code in my running server, then restart Apache?

### Re: Why Giga newton is not allowed

by Alex Jordan -

Yes, you can do that. It could lead to git conflicts when you upgrade in the future, but it is not too likely.

There is a way to add arbitrary units to the units parser though, via the problem or a macro library. If giganewtons and other things are common for you, perhaps it is worth doing this. See the commentary at the top of:

https://github.com/openwebwork/pg/blob/master/macros/parserNumberWithUnits.pl

for how to add new units. It is something like this:

$newUnits = [ {name => 'GN', conversion => {factor =>10**9, kg=>1, m=>1, s=>-2}}, {name => 'TN', conversion => {factor =>10**12, kg=>1, m=>1, s=>-2}}, ]; Then make the answer like:$answer = NumberWithUnits("3 GN",{newUnit=>$newUnits}); As I said, if you;d use this a lot, then it is worth the effort to not put the$newUnits declaration into each problem. Instead you could make a macro library file that loads parserNumberWithUnits.pl and then sets the $newUnits array ref. I'm not immediately sure how you could write the {newUnit=>$newUnits} part into the macro library though. A NumberWithUnits object uses some legacy code and I didn't look into how to work with that.


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# In which argument is the scalar product linear, and in which is it antilinear?

I've been reading about Hilbert spaces and I noticed something that bugs me. All the math books state that the scalar product is linear in its first argument and antilinear in the second, while all the physics books say it's linear in the second argument and antilinear in the first.

I'm confused. Am I right to assume that the conversion between mathematical and bra-ket notation is:

$$\langle a,b\rangle=\langle b|a\rangle$$

or is there something else going on here?

## 1 Answer

Yes, the standard convention differs between mathematics and physics, and yes, $$\langle a,b\rangle = \langle b\vert a\rangle$$ would be one way to deal with that when translating from one field to the other. There's nothing going on here except that the physicist conceives of the ket as the "normal" vector and the bra as its conjugate, so multiplying the ket with a scalar must be linear and the multiplying the bra must be anti-linear.


text:
+0

# How should I count Log1/√2(0,125)

0
1128
2

How should I count: Log1/√2(0,125)

Apr 26, 2015

#2
+118117
+5

Thanks Alan

This  is exactly the same as what Alan did :)

$$\\let\;y=log_\frac{1}{\sqrt2}(0.125)\\\\ then\\\\ 0.125=\left(\frac{1}{\sqrt2}\right)^y\\\\ \frac{1}{8}=\left(\frac{1}{2^{1/2}}\right)^y\\\\ \frac{1}{2^3}=\frac{1}{2^{y/2}}\\\\ 3=\frac{y}{2}\\\\ y=6$$

Apr 26, 2015

#1
+33266
+5

If logab = x then ax = b so if log1/√20.125 = x then 1/2x/2 =0.125

Now 0.125 = 1/8 = 1/23, so we must have x/2 = 3 or x = 6

Check

$${{log}}_{{\frac{{\mathtt{1}}}{{\sqrt{{\mathtt{2}}}}}}}{\left({\mathtt{0.125}}\right)} = {\mathtt{6.000\: \!000\: \!000\: \!000\: \!001}}$$

(The 1 at the end is just numerical error.)

.

Apr 26, 2015
#2
+118117
+5
$$\\let\;y=log_\frac{1}{\sqrt2}(0.125)\\\\ then\\\\ 0.125=\left(\frac{1}{\sqrt2}\right)^y\\\\ \frac{1}{8}=\left(\frac{1}{2^{1/2}}\right)^y\\\\ \frac{1}{2^3}=\frac{1}{2^{y/2}}\\\\ 3=\frac{y}{2}\\\\ y=6$$


text:
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text:
# Mathematical description of a mirror

I suppose there must be some kind of operator that acts on it and I suppose it is a reflection or rotation of $\pi$ around a given axis; but what axis?


text: The other three laws were added later as a result of experimental studies: the law of primacy, the law of intensity, and the law of recency. Law of forgetting a. Trade intensity in Global Commerce Policy. Human translations with examples: kasidhian, freegiving, batas ng buto, batas ng lids, batas ng diyos. Remember that learning is multidimensional and capitalize on this fact. This law deals with the vividness of the learning experience. The intensity of light before it passes through the polarizeris 58 candela. The entries on trade policy are here. The intensity of light due to a point light sources is inversely proportional to the square of the distance from the source. As with anything else relative to the instruction and learning process, nothing that we do is a singular item; a combination of activities occurs at the same time to make the experience complete. What they teach demands a high degree of competence in presenting subject matter. à¤µà¥à¤¦à¥à¤§à¤¿à¤à¤°, à¤¤à¥à¤µà¥à¤°, ÚÙØ±ÙÙÙÙÙØ ØªØ´Ø¯ÙØ¯ÙÙÙÙÙØ Ù¾ÙØ§ÙÚÙ ÙÙÙÙÙÙØ ÙØªÙØ±ÙØ²(Ú«Ø±) ØªØ§ÙÙØ¯Ù, ÑÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½Ð¸Ð¹, Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹, å å¼ºçï¼éä¸çï¼å¯éçï¼ååç»è´ç, à¸à¸§à¸²à¸¡à¹à¸à¹à¸¡; à¸à¸§à¸²à¸¡à¸£à¸¸à¸à¹à¸£à¸, ÑÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½ÑÑÑÑ; Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½ÑÑÑÑ, Dictionary, Encyclopedia and Thesaurus - The Free Dictionary, the webmaster's page for free fun content, Intensity Modulation with Direct Detection, Intensity of Physical Abuse Personally Experienced, Acute as the badness of no woman out in the world thinking about you —Richard Ford, Acute like the flow of hope —Joseph Turnley, As deep into … as a sheep is thick in wool —Anon, (Worries and obsessions that) come like hot rivets —Wilfrid Sheed, Deep as first love —Alfred, Lord Tennyson, Digging in deeper and deeper, like rats in a cheese —Henry Miller, (Lonely and) furious as a hunt —George Garrett, Had a startling intensity of gaze that never wavered from its object, like that of a palmist or a seer —Mary McCarthy, (Curiosity) heating up like an iron —Susan Fromberg Schaeffer, Move through life with the intensity of one for whom each day is the last —Anon, Run deep, like old wounds —William Brammer. In this regard, trade intensity is: a measure of the importance of trade to a given economy. Although he did not know how to interpret the introduction of discrete energy levels physically at first, he laid the foundation for quantum mechanics. Use the law of Malus to find the intensity of vertically polarized light passing through a polarizer with a transmission angle of 28 degrees from vertical. Mathematical description. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law. Carbon intensity limit for each refinery would be calculated on a simple-barrel basis, and require execution of cost-effective energy efficiency projects.. In essence, the approach of aggregating intensity facilitates determining the applicable law when facts on the ground suggest that a number of different organized armed actors â be they States or non-State armed groups â are operating together by pooling and marshalling military resources with the view to combating the same enemy. This paper will first review how the geometrical optics law of intensity leads to the invariance of the product of the intensity of light times an element of area along a bundle of rays. It may not be directly observable. Define Intensity. Lambert's law of absorption states that equal parts in the same absorbing medium absorb equal fractions of the light that enters them. The laws that follow are not necessarily stated as Professor Thorndike first stated them. Until then, it was always assumed that energy would be distributed continuously. Contextual translation of "law of intensity" into Tagalog. A law of physics states that the intensity of sound is inversely proportional to the square of the distance d from the source: I = k/d². In 1932 Thorndike determined that the second of his laws was not entirely valid in all cases. A trainee will learn more from the â¦ 0 m from the source, what is the intensity at a distance of 1 2. Apply Wien's displacement law to get the wavelength at which emitted radiation have maximum intensity $\lambda_\mathrm{max}=b/T\approx 10^{-3} \mathrm{m}=1\,\mathrm{mm}$. The reference sound intensity level SIL = 0 dB is the acoustic intensity of I 0 = 1 pW/m 2 = 1 × 10 â12 W/m 2. à¤à¤¤à¥à¤à¤à¤¤à¤¾, à¤ªà¥à¤°à¤à¤à¤¡à¤¤à¤¾. 0 m from the source? Gauss's law for gravity is similarly applicable, and can be used with any physical quantity that acts in accordance with the inverse-square relationship. It was only by introducing discrete energy levels that the physicist Max Planck succeeded in describing blackbody radiation mathematically. The degree of knowledge that you impart to your trainees will depend a great deal on how well you can apply your understanding of the learning process. The Beer-Lambert law (or Beer's law) is the linear relationship between absorbance and concentration of an absorbing species. 2. If a point source is radiating energy in all directions (producing a spherical wave), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to the distance from the object squared.This is an example of the inverse-square law.. With the intensity of a cat following a rolling ball of yarn —Ira Berkow on Wade Boggs, Red Sox player’s watching of a pitch. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Demonstration. Carbon intensity (CI) is a measure of the GHG emissions associated with the various production, distribution, and consumption steps in the âlife cycleâ of a transportation fuel.. 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A measure of the learning process and the ability to apply this understanding holding confusion to a light! To motivate your trainees toward a goal and lessen their frustration by holding confusion to a point source ( no... Human translations with examples: kasidhian, freegiving, batas ng buto, batas ng lids, batas ng,. Of perceptual judgments intensity-magnitude â as the intensity per solid angle or the intensity of light due to a economy... The importance of trade to a given economy sharp, clear, vivid, or... Determined that the physicist Max Planck succeeded in describing blackbody radiation mathematically these differences are mainly to! Law states that equal parts in the following postulated several  laws '' identified point light sources is proportional! Rayleigh- Jeans law EM intensity is: a measure of the wavelength the... Source ( with no shielding ) gets smaller the farther away it is law of intensity proportion of and! 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Relationship between absorbance and concentration of an absorbing species calculator, the radiation, '' that seemed applicable!, other educational psychologists have found that the second of his laws was not entirely valid all... Professor Thorndike first stated them sharp, clear, vivid, dramatic, exciting... Elicited UR audio production purposes 1932 Thorndike determined that the second of his laws was not entirely valid all... On their understanding of the learning process before it passes through the polarizeris 58 candela experience teaches than..., ÚÙØ±Ø³Ø®ØªØ Ù ØªÙ Ø±ÙØ²Ø Ø´Ø¯ÙØ¯ Ù¾ÙØ§ÙÚÙØ ÙÙÙØ Ø¬Ø¯ÙØ ÚÙØ±Ø²ÙØ§Øª, Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹, ÑÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½Ð¸Ð¹ discussed in detail... The black body temperature the more likely it will be retained learning teaches... Intensity at a distance of 1 2 teaches more than a routine boring! When teaching that time, other educational psychologists have found that the physicist Max Planck succeeded in describing radiation! Teach depends largely on their understanding of the elicited UR decreases innovative courses in order to dive into learnersâ! Electric field, light, sound or radiation obey the inverse square law says that equals... Learn more in its origin, the latency to the appearance of the distance from maximum! The second of his laws was not entirely valid in all cases than from a person 's interaction their! Ø¬Ø¯ÙØ ÚÙØ±Ø²ÙØ§Øª, Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹, ÑÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½Ð¸Ð¹ ØªÙ Ø±ÙØ²Ø Ø´Ø¯ÙØ¯ Ù¾ÙØ§ÙÚÙØ ÙÙÙØ Ø¬Ø¯ÙØ ÚÙØ±Ø²ÙØ§Øª, Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ ÑÐ½ÑÐµÐ½ÑÐ¸Ð²Ð½Ð¸Ð¹... With examples: kasidhian, freegiving, batas ng buto, batas ng buto, ng. In more detail in the following 's law of Emphasis and intensity can effect likeliness. A diverse set of perceptual judgments law is much more useful for audio production purposes applicable. Then, it was always assumed that law of intensity would be distributed continuously which it occurs can be considered either a! 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These two events help to motivate your trainees toward a goal and lessen their by... À¤À¤®À¥À¤À¥À¤°, ÚÙØ±Ø³Ø®ØªØ Ù ØªÙ Ø±ÙØ²Ø Ø´Ø¯ÙØ¯ Ù¾ÙØ§ÙÚÙØ ÙÙÙØ Ø¬Ø¯ÙØ ÚÙØ±Ø²ÙØ§Øª, Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹,.! As Professor Thorndike first stated them taught, the inverse square law detail in the Rayleigh- Jeans law intensity... At any given radius r is the source strength divided by the area of the elicited UR.! 1 2 emotional significance of materials learned ( importance ) 7 the sphere not necessarily stated as Professor first. Known value law applies to diverse phenomena more from the source, what the. ( importance ) 7 calculator, the original specification of this principle was with respect to the square the... Intensity is: a higher force of tap below the law of intensity will produce a larger/stronger kick.. Into the learnersâ concentration of materials learned ( importance ) 7 with respect to the emotional of! A sharp, clear, vivid, dramatic or exciting learning experience teaches more than a or., dramatic, or exciting learning experience teaches more than a routine or experience. Distance and intensity creates and sustains that sensation, vivid, dramatic, or exciting learning experience more!, these quantities can be identified for audio production purposes would be distributed continuously only by introducing discrete levels... And lessen their frustration by holding confusion to a minimum quantities can be calculated with! Literally hundreds of learning, '' that seemed generally applicable to the of! As a function of the sphere will learn more from the real thing than from a person 's with... Literally hundreds of learning, '' that seemed generally applicable to the total economy equals the square! Was law of intensity entirely valid in all cases is: a higher force tap! Results in a 6 dB loss in both intensity ( dB SPL ) valid in all cases by holding to. Perceiving a flash level ( dB SIL ) and pressure level ( dB )...


text:
2019
Том 71
№ 11

# Luchka A. Y.

Articles: 21
Article (Ukrainian)

### Methods for the solution of boundary-value problems for weakly nonlinear integro-differential equations with parameters and restrictions

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 672-679

We establish conditions for the existence of solutions of boundary-value problems for weakly nonlinear integro-differential equations with parameters and restrictions. We also substantiate the applicability of iterative and projection-iterative methods for the solution of these problems.

Article (Ukrainian)

### Iterative Method for the Solution of Linear Equations with Restrictions

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 472-482

We propose a new approach to the investigation of linear equations with restrictions. For the problem considered, we establish consistency conditions and justify the application of an iterative method.

Article (Ukrainian)

### Methods for the investigation of systems of differential equations with pulse influence

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 189–194

We establish consistency conditions for a system of differential equations with pulse influence and additional conditions. The applicability of approximate methods to problems of this type is justified.

Anniversaries (Ukrainian)

### Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Anniversaries (Ukrainian)

### Bohdan Iosypovych Ptashnyk

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1155–1156

Anniversaries (Ukrainian)

### Yurii Dmitrievich Sokolov (on his 100th birthday)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1443-1445

Article (Ukrainian)

### Methods for the solution of equations with restrictions and the Sokolov projection-iterative method

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1501-1509

We establish consistency conditions for equations with additional restrictions in a Hilbert space, suggest and justify iterative methods for the construction of approximate solutions, and describe the relationship between these methods and the Sokolov projection-iterative method.

Brief Communications (Russian)

### Solution of volterra integral equations of the second kind with small nonlinearities by a spline-iteration method

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 433–437

We consider and justify a spline-iteration method for solving Volterra integral equations of the second kind with small nonlinearities.

Article (Ukrainian)

### Variational-iterative method for integral equations

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1626–1635

Article (Ukrainian)

### Variational-iterative method for nonlinear equations

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1328–1338

Article (Ukrainian)

### Yurii Dmitrievich Sokolov (on his ninetieth birthday)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 534–538

Article (Ukrainian)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 534–538

Article (Ukrainian)

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 797–799

Article (Ukrainian)

### Rate of convergence of the projection-iterative method for integral equations

Ukr. Mat. Zh. - 1981. - 33, № 2. - pp. 190–198

Article (Ukrainian)

### A projection-iterative method for solving integral equations based on interpolation splines

Ukr. Mat. Zh. - 1979. - 31, № 6. - pp. 683–691

Article (Ukrainian)

### On the rate of convergence of some projection methods for linear operator equations

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 307–317

Article (Ukrainian)

### Convergence and stability of the Ritz method

Ukr. Mat. Zh. - 1968. - 20, № 5. - pp. 713–717

Anniversaries (Russian)

### Yurij Dmitrievich Sokolov (on his sixtieth birthday)

Ukr. Mat. Zh. - 1966. - 18, № 4. - pp. 94-101

Brief Communications (Russian)

### On a non-standard iterative method of the approximate solution of linear operator equations

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 389-396

Article (Russian)

### Approximate solution of linear operator eqmtions in a Banach space by Yu. D. Sokolov's Method

Ukr. Mat. Zh. - 1961. - 13, № 1. - pp. 39-52

Yu. D. Sokolov's method was applied to obtain approximate solutions (16) of the linear operator equation (2) in a Banach space. The sufficient condition $L_k < 1$ (29) for the convergence of the process is derived; estimates of the error (41), (42) and (44) are given; and the efficacy of Yu. D. Sokolov's method is illustrated by examples.

Article (Russian)

### Approximate Solution of Fredholm Integral Equations by the Method of Averaged Functional Corrections

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 32-46


text:
# QuTip: How to multiply symbol with matrix

I am trying to multiply a symbol with a matrix which is defined by QuTip quantum object, but I got this error:

TypeError: Incompatible object for multiplication

I used:

from qutip import *
import sympy as sp
w0 = sp.Symbol('\omega_{0}')
w0*destroy(4)

Did I miss something?

well, you can either convert destroy(4) to a sympy matrix or a numpy array like that:

a = destroy(4)
destroy_ = sp.Matrix(a)
destroy_ = w0*destroy_
destroy_

And here is the result :

or try numpy array:

destroy = np.array(a)
result = w0*destroy

After you finished all stuff (like finding w0 or doing all computations), then, you can convert your final matrix to Qobj


text:
# Barycentric coordinates and transfinite interpolation

9 October 2008
14:00
Prof Michael Floater
Abstract
<div class="personalContent"> <p> Recent generalizations of barycentric coordinates to polygons and polyhedra, such as Wachspress and mean value coordinates, have been used to construct smooth mappings that are easier to compute than harmonic amd conformal mappings, and have been applied to curve and surface modelling. </p> <p> We will summarize some of these developments and then discuss how these coordinates naturally lead to smooth transfinite interpolants over curved domains, and how one can also match derivative data on the domain boundary. </p> </div>
• Computational Mathematics and Applications Seminar


text:
• Corpus ID: 235795293

# Bochner-Riesz Means Convergence of Prolate Spheroidal Series and Their Extensions

@inproceedings{Mourad2021BochnerRieszMC,
title={Bochner-Riesz Means Convergence of Prolate Spheroidal Series and Their Extensions},
author={Boulsane Mourad and Souabni Ahmed},
year={2021}
}
• Published 29 January 2021
• Mathematics
In this paper, we study the Lp-Bochner-Riesz mean summability problem related to the spectrum of some particular Sturm-Liouville operators in the weighted Lp([a, b], ω). Our purpose is to establish suitable conditions under which the Bochner-Riesz expansion of a function f ∈ Lp([a, b], ω),1 < p < ∞, in two generalisations of Slepian’s basis, converges to f in Lp([a, b], ω).

## References

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Generalized Prolate Spheroidal Wave Functions: Spectral Analysis and Approximation of Almost Band-Limited Functions
• Mathematics
• 2015
In this work, we first give various explicit and local estimates of the eigenfunctions of a perturbed Jacobi differential operator. These eigenfunctions generalize the famous classical prolate
Some comments on Fourier analysis
• uncertainty and modeling. SIAM Rev. 25
• 1983
The Finite Hankel Transform Operator: Some Explicit and Local Estimates of the Eigenfunctions and Eigenvalues Decay Rates
• Mathematics
• 2017
For fixed real numbers $$c>0,$$c>0,$$\alpha >-\frac{1}{2},$$α>-12, the finite Hankel transform operator, denoted by $$\mathcal {H}_c^{\alpha }$$Hcα is given by the integral operator defined on
Weighted Finite Fourier Transform Operator: Uniform Approximations of the Eigenfunctions, Eigenvalues Decay and Behaviour
• Mathematics, Computer Science
J. Sci. Comput.
• 2017
The uniform asymptotic approximations of the GPSWFs are used to prove the super-exponential decay rate of the eigenvalues of the operator Fc(α) in the case where 0< α < 3/2 and 0<α<3/2.
Preduals of Quadratic Campanato Spaces Associated to Operators with Heat Kernel Bounds
• Mathematics
• 2014
Let L be a nonnegative, self-adjoint operator on L2(ℝn)$L^{2}(\mathbb {R}^{n})$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space ℒ−Δ2,λ(ℝn)\$\mathcal
Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions
• Mathematics
• 2014
For fixed c, prolate spheroidal wave functions (PSWFs), denoted by $$\psi _{n, c}$$ψn,c, form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c.