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# A Question from “Mathematical Methods for Financial Markets” Chapter 2

Exercise 2.3.1.5: The payoff of a power option is $h(S_T)$, where the function h is given by $h(x) = x^\beta(x-K)^+$. Prove that the payoff can be written as the difference of European payoffs on the underlying assets $S^{\beta+1}$ and $S^\beta$ with strikes depending on K and $\beta$.

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What have you tried already? –  olaker Dec 16 '13 at 7:00

$$h(x) = x^\beta(x-K)^+ = x^\beta (x - K) \, \mathbf{1}_{[x>K]}$$ Thus we get, $$h(x) = x^{\beta+1}\mathbf{1}_{[x>K]} - K\,x^{\beta}\mathbf{1}_{[x>K]}$$ now $x \in [x>K]$ if and only if $x \in [x^{\beta}>K^{\beta}]$ Therefore,
$$h(x) = x^{\beta+1}\mathbf{1}_{[x^{\beta + 1}>K^{\beta + 1}]} - K\,x^{\beta}\mathbf{1}_{[x^{\beta}>K^{\beta}]}$$
Thus if we let $\Phi_\text{Asset-or-nothing}^\text{dig}$ the contract function for an asset or nothing binary european call. we can Write:
$$h(S_t) =\Phi_\text{Asset-or-nothing}^\text{dig}(S_{t}^{\beta + 1},K^{\beta + 1}) - K \,\Phi_\text{Asset-or-nothing}^\text{dig}(S_{t}^{\beta}, K^{\beta})$$


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Stevebook - [ blog:using_markdown_for_beamer_presentations ]

# Using Markdown for Beamer Presentations

I've recently had to make another presentation, and since I'm now fully into a LaTeX-oriented workflow when it comes to documents, Beamer is my choice.

However, one thing I hate is the verbosity of the markup. Fortunately there are a bunch of “minimalized” markup languages that can help resolve this problem. One is the well-known Markdown. I actually think it's one of the less powerful textual markup languages, but it's somehow one of the most popular.

It is used on reddit and Stack Overflow, and so I've gotten quite used to it. Fortunately there is an awesome tool called Pandoc that can be used to translate Markdown into other formats. Primarily this is for HTML and LaTeX.

While writing articles in LaTeX is not that verbose, I definitely find structures such as \emph{..} less intuitive than just surrounding text with underscores. But for Beamer, I find the itemize environment just has far too low a markup-to-content ratio for my tastes. I really like the idea of a text document looking as similar as possible to how you'd write it naturally in a raw text file. Sticking to Markdown also means not needing to memorize yet another markup language… I'm even considering moving to a Markdown-based system for this site, just because I'm constantly forgetting the DokuWiki syntax.

It is the list syntax of Markdown that really makes using it for Beamer a huge advantage over straight LaTeX. Of course, there are downsides as well: you can't control columns, you can't specify image sizes, etc. Fortunately Pandoc essentially solves this by rote copying any unrecognized LaTeX or HTML markup it sees.

This means you can use Markdown for headings, formatting, and lists, and just drop in citations, \includegraphics and math wherever you please.

The result is being able to specify a presentation (unrelated images and math shamelessly stolen from Wikipedia) like:

% Stephen Sinclair
% My presentation
% \today

Introduction
============

This is _my_ presentation.

* It is awesome.
* And has pretty math:

$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{- 2\pi i x \xi}\,dx$

Conclusion
==========

* Pandoc **rocks**.

\centerline{\includegraphics[height=2in]{Sinc.pdf}}

To me, this is a huge improvement over:

\title{Stephen Sinclair}
\author{My presentation}
\date{\today}

\begin{frame}{}
\titlepage
\end{frame}

\begin{frame}{Introduction}

This is \emph{my} presentation.

\begin{itemize}
\item
It is awesome.
\item
And has pretty math:
\end{itemize}
$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{- 2\pi i x \xi}\,dx$
\end{frame}

\begin{frame}{Conclusion}
\begin{itemize}
\item
Pandoc \textbf{rocks}.
\end{itemize}
\centerline{\includegraphics[height=2in]{Sinc.pdf}}

\end{frame}

The Markdown syntax is just easier to look at, and easier to think about. Being able to see the content instead of having so much markup staring you in the face really helps to get an idea of the overall picture of the document.

I should mention that it is even easier to look at if you use markdown-mode in Emacs, or something similar that can do syntax highlighting.

## To use it

To get Pandoc-generated LaTeX working with Beamer, I just had to specify a template specifying the Beamer document class, with a couple of other header items. Lastly I couldn't get around a tiny bit of post-processing using Perl regexes. I needed this to convert \section markings to \begin{frame} and \end{frame}.

With the template, which you can download here, you can use the following steps to produce a Beamer presentation:

pandoc --template beamer.template \
-i presentation.markdown -o presentation.tex
perl -pe 's/\\section/\\end{frame}\n\\begin{frame}/' -i presentation.tex
perl -pe 's/\\end{document}/\\end{frame}\n\\end{document}/' -i presentation.tex
pdflatex presentation.tex </dev/null
bibtex presentation
pdflatex presentation.tex </dev/null

I usually stick these commands into a simple Makefile. The bibtex step is only needed if you have any citations, and of course you should modify the template to taste. Note that the template imports natbib, which isn't necessarily everyone's cup of tea—feel free to exclude it. My favorite Beamer style is “Berlin”, so that is what is specified in it.

format: plain


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# Text/structure for an analysis course for students with pre-existing understanding of some applied aspects of analysis

Greetings,

I'm teaching a one-off course (perhaps never to be repeated) in a curriculum that's in transition, and I'm looking for advice on a textbook, or stories from people who have taught similar transitional-curriculum courses would be interesting as well.

The context is that we are creating a 2nd year analysis course which would be our students 1st exposure to analysis. This is to be followed up by a 3rd year analysis course which would be something of a "rigorous multi-variable calculus course". Next year the 3rd year course is going to be offered but the students will not have the 2nd year course as background (in future years the 2nd year analysis course will be a prerequisite).

What they will have is a fairly extensive "service calculus" background, consisting of four courses: a more or less standard 2-course 1st year single-variable calculus sequence (text is Edwards and Penney), plus a 2nd year multi-variable calculus course (also Edwards and Penney - this is a standardish calculus in $\mathbb R^n$ for $n \leq 3$ text). They follow that up with a a 3rd year course on multi-variable calculus in $\mathbb R^n$, the text is Folland. This course also covers some material that is traditionally taught in analysis classes, things like uniform convergence, Fourier transforms and such. But very little time is spent fussing about with open subsets of $\mathbb R^n$, they don't get to see bump functions, what a function is isn't discussed in much detail, what numbers are isn't dwelled on (not even axiomatically).

So, that's the setup. It can be safely assumed these students are motivated to study analysis, as they're taking this course to transition into our upper-level analysis courses. But I can't do too much too fast. And I don't want to bore them. So things of importance for this course to dwell on are things like what numbers are (at least axiomatically), maybe even a bit of set theory, completeness, fussy details about continuous functions like when extreme values exist, the various formulations of continuity for functions on open subsets of $\mathbb R^n$. Bump functions. And fussy details from multi-variable calculus, such as the inverse and implicit function theorem.

Are there texts out there that are designed for situations like this?

One initial inclination would be to supplement something like Hubbard's calculus text with some additional foundational notes. I suppose there are many standard intro analysis courses but some of these might be oddly paced for this group of students. I presume it's unlikely anyone has written a text for just this situation but who knows?

Thanks in advance for your comments.

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## 1 Answer

If you want a reference that will not bore them, supplement the main text with "Metric Spaces: Iteration and Application" by Victor Bryant. The book is short and it shows in several contexts how the concept of a fixed-point property, via iteration, can be used to solve worthwhile problems. It is very nicely written and Bryant makes a real effort to motivate the material and explain where things are going and why.

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I think you've got a sense for where I'm going with this. They're coming from a souped-up service course sequence so it only makes sense to approach analysis from a rather applied point of view, having applied-like problems dragging them to analytical considerations. I'll look up your reference, thanks. –  Ryan Budney Mar 10 '10 at 22:21


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# What is numerical value of the series

Given 26 constants labelled A to Z, let $A = 1$.

The rest of the constants have values that are equal to the position of that letter in the alphabet, raised to the power of the previous constant, so:

• $A = 1$
• $B$ (the letter in the second position) $= 2^A = 2^1 = 2$
• $C$ (the letter in the third position) $= 3^B = 3^2 = 9$
• etc.

Find the exact numerical value for this expression:

$(N-A) * (N-B) * (N-C) * ... * (N-Y) * (N-Z)$

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What do you mean with $N$? If it is a letter, then $0$ – Ilya Jun 8 '11 at 16:35
Well... the expression includes (N-N), does it not? – mixedmath Jun 8 '11 at 16:41

For the sake of having an answer: the expression is multiplied by the term $(N-N)$, which is zero, so the whole thing evaluates to zero.
There is an answer there too, but my hint is what happens around the letter $M$ in the product?


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## Multiples of 3 and 5

### Problem 1

Published on 05 October 2001 at 06:00 pm [Server Time]

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.


text:
# orthonormal system in a Hilbert space

Let $\{e_n\}$ be an orthonormal basis for a Hilbert space $H$. Let $\{f_n\}$ be an orthonormal set in $H$ such that $\sum_{n=1}^{\infty}{\|f_n-e_n\|}<1$. How do I show that $\{f_n\}$ is also an orthonormal basis for $H$?

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It's already an orthonormal set, so it suffices to show it's a basis. Perhaps we can proceed by supposing $\langle x,f_n\rangle=0$ for every $f_n$ in the set for some $x\in H$... – anon Sep 15 '11 at 3:44

Since $\mathcal S:=\{f_n,\;n\in\mathbb N\}$ is an orthonormal subset of $H$, it suffices to show that $\mathcal S^\perp=\{0\}.$
Having this in mind, pick $x\in H$ belonging to $\mathcal S^\perp$. Then for every $n\in\mathbb N$ one has $$0=\langle x,f_n\rangle=\langle x,f_n-e_n+e_n\rangle\Rightarrow \langle x,e_n\rangle=\langle x,e_n-f_n\rangle.$$ Now, since $\{e_n\}$ is an orthonormal basis, one has $$x=\sum_{n=1}^{+\infty}\langle x,e_n\rangle e_n=\sum_{n=1}^{+\infty}\langle x,e_n-f_n \rangle e_n.$$ If $x$ were not $0$, then one would obtain a contradiction as follows: $$\|x\|=\sum_{n=1}^{+\infty}|\langle x,e_n-f_n\rangle|\stackrel{C.S.}{\leq}\|x\|\sum_{n=1}^{+\infty}\|e_n-f_n\|.$$ From this last relation, one may divide out by $\|x\|\neq 0$ by our assumption and obtain $$1\leq\sum_{n=1}^{+\infty}\|e_n-f_n\|,$$ but this contradicts the initial hypothesis. Hence $x=0$ and $\mathcal S^{\perp}=\{0\}.$ This concludes the proof.
Edit Yes, i think i need some changes, thanks Matthew for pointing it out. Ok here is my fix: $$\|x\|^2=\sum_{n=1}^{+\infty}|\langle x,f_n-e_n \rangle|^2\leq \|x\|^2\sum_{n=1}^{+\infty}\|f_n-e_n\|^2,$$ again by Cauchy Schwarz, and if $x\neq 0$ we can divide out and obtain $$(\diamondsuit)\quad 1\leq \sum_{n=1}^{+\infty}\|f_n-e_n\|^2.$$ Now, since $$\sum_{n=1}^{+\infty}\|f_n-e_n\|<1,$$ readily implies that, for every $n\in\mathbb N$, $$\|f_n-e_n\|<1\Rightarrow \|f_n-e_n\|^2<\|f_n-e_n\|.$$ But this means $$(\diamondsuit)<\sum_{n=1}^{+\infty}\|f_n-e_n\|<1\Rightarrow 1<1.$$ Which is absurd. Again then $x=0$ and we conclude in the same way as before.
Shouldn't you have $\|x\|^2 = \sum_n |\langle x,e_n-f_n\rangle|^2$?? – Matthew Daws Sep 16 '11 at 14:00


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Zbl 0949.35111
Maremonti, Paolo; Russo, Remigio; Starita, Giulio
On the Stokes equations: The boundary value problem.
(English)
[A] Maremonti, Paolo (ed.), Advances in fluid dynamics. Rome: Aracne. Quad. Mat. 4, 69-140 (1999). ISBN 88-7999-259-6

This paper deals with a boundary value problem (bvp) for the Stokes equation. The corresponding domain $\Omega$ is not obliged to be simply connected and it can be either a bounded or an exterior one. In their investigations the authors use the theory of hydrodynamical potentials. An existence of a unique classical solution is proved in the case of a bounded domain $\Omega$ (\S 5). Similar results are obtained in \S 6, \S 7 assuming $\Omega$ to be an exterior domain. To be more precise, we give the uniqueness result as follows: Let $(u_1,p_1)$, $(u_2,p_2)$ be two classical solutions of the Stokes bvp. Then, if $$u_1- u_2= \cases o(\log r),\quad &n=2,\\ o(1),\quad &n\ge 3,\endcases$$ we have $u_1= u_2$ and $p_1= p_2+\text{const}$.
[P.Popivanov (Sofia)]
MSC 2000:
*35Q30 Stokes and Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory
76D07 Stokes flows

Keywords: Stokes equation; hydrodynamical potential; existence of a unique classical solution; bounded domain; exterior domain

Highlights
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May 30, 2020, 03:59:04 pm

AuthorTopic: Mathematics - trignomic functions  (Read 270 times)

0 Members and 1 Guest are viewing this topic.

Lydia.k

• Posts: 7
• Respect: 0
Mathematics - trignomic functions
« on: June 24, 2019, 07:45:21 am »
0
Hey,

I am not sure how to sketch the following, as was wondering if anyone could help me?

Sketch y=sin(x+pi) for 0<X<2pi

Cheers,
Lydia

RuiAce

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• "All models are wrong, but some are useful."
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Re: Mathematics - trignomic functions
« Reply #1 on: June 24, 2019, 08:32:59 am »
+1
Hey,

I am not sure how to sketch the following, as was wondering if anyone could help me?

Sketch y=sin(x+pi) for 0<X<2pi

Cheers,
Lydia

Start by sketching $y = f(x)$, where $f(x) = \sin x$.

Then $f(x+\pi) = \sin(x+\pi)$, so you’re after the curve $y=f(x+\pi)$. Recall that this is a translation of $y=f(x)$ to the left by $\pi$ units, so that’s what huh need to sketch.

(Note that the graph will correspond to that of $y=-\sin x$. This is not a coincidence, because $\sin(x+\pi)=-\sin x$ is a trigonometric identity for third quadrant angles.)
« Last Edit: June 24, 2019, 09:40:33 am by RuiAce »

Lydia.k

• Posts: 7
• Respect: 0
Re: Mathematics - trignomic functions
« Reply #2 on: June 24, 2019, 09:38:33 am »
0
Thanks a lot


text:
• ### Proton-$\eta^\prime$ interactions at threshold(1803.06814)

March 19, 2018 nucl-ex
Recent data on photoproduction of $\eta'$ mesons off protons have been included in the data base for the Bonn-Gatchina partial wave analysis. The real and imaginary parts of the $S$-wave $\eta^\prime p\to \eta^\prime p$ scattering amplitude in the threshold region were fit to yield the $\eta^\prime p$ scattering length and the interaction range. This new analysis found $|a_{\eta^\prime p}|= (0.403\pm 0.015\pm 0.060)$ fm and a phase $\phi=(87\pm2)^\circ$, while the range parameter is not well-constrained. The striking behavior of the GRAAL data on the beam asymmetry in the threshold region suggests that a narrow proton-$\eta'$ resonance might exist. However, the scattering length was found to be relatively insensitive to the possible existence of this narrow resonance.
• ### Strong evidence for nucleon resonances near 1900\,MeV(1712.07549)

Dec. 20, 2017 nucl-ex
Data on the reaction $\gamma p\to K^+\Lambda$ from the CLAS experiments are used to derive the leading multipoles, $E_{0+}$, $M_{1-}$, $E_{1+}$, and $M_{1+}$, from the production threshold to 2180\,MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel $L+P$ model which allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion and photo-induced reactions within the Bonn-Gatchina (BnGa) partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin-parity $J^P = 1/2^-; 1/2^+$, and $3/2^+$ in the region at about 1.9\,GeV.
• ### $N^*$ resonances from $K\Lambda$ amplitudes in sliced bins in energy(1712.07537)

Dec. 20, 2017 nucl-ex
The two reactions $\gamma p\to K^+\Lambda$ and $\pi^-p\to K^0\Lambda$ are analyzed to determine the leading photoproduction multipoles and the pion-induced partial wave amplitudes in slices of the invariant mass. The multipoles and the partial-wave amplitudes are simultaneously fitted in a multichannel Laurent+Pietarinen model (L+P model), which determines the poles in the complex energy plane on the second Riemann sheet close to the physical axes. The results from the L+P fit are compared with the results of an energy-dependent fit based on the Bonn-Gatchina (BnGa) approach. The study confirms the existence of several poles due to nucleon resonances in the region at about 1.9\,GeV with quantum numbers $J^P = 1/2^+$, $3/2^+, 1/2^-, 3/2^-, 5/2^-$.
• ### $N^*\to N \eta^\prime$ decays from photoproduction of $\eta^\prime$-mesons off protons(1706.05144)

June 16, 2017 nucl-ex
A study of the partial-wave content of the $\gamma p\to \eta^\prime p$ reaction in the fourth resonance region is presented, which has been prompted by new measurements of polarization observables for that process. Using the Bonn-Gatchina partial-wave formalism, the incorporation of new data indicates that the $N(1895)1/2^-$, $N(1900)3/2^+$, $N(2100)1/2^+$, and $N(2120)3/2^-$ are the most significant contributors to the photoproduction process. New results for the branching ratios of the decays of these more prominent resonances to $N\eta^\prime$ final states are provided; such branches have not been indicated in the most recent edition of the Review of Particle Properties. Based on the analysis performed here, predictions for the helicity asymmetry $E$ for the $\gamma p\to \eta^\prime p$ reaction are presented.
• ### Target and Double Spin Asymmetries of Deeply Virtual $\pi^0$ Production with a Longitudinally Polarized Proton Target and CLAS(1511.03338)

March 15, 2017 nucl-ex
The target and double spin asymmetries of the exclusive pseudoscalar channel $\vec e\vec p\to ep\pi^0$ were measured for the first time in the deep-inelastic regime using a longitudinally polarized 5.9 GeV electron beam and a longitudinally polarized proton target at Jefferson Lab with the CEBAF Large Acceptance Spectrometer (CLAS). The data were collected over a large kinematic phase space and divided into 110 four-dimensional bins of $Q^2$, $x_B$, $-t$ and $\phi$. Large values of asymmetry moments clearly indicate a substantial contribution to the polarized structure functions from transverse virtual photon amplitudes. The interpretation of experimental data in terms of generalized parton distributions (GPDs) provides the first insight on the chiral-odd GPDs $\tilde{H}_T$ and $E_T$, and complement previous measurements of unpolarized structure functions sensitive to the GPDs $H_T$ and $\bar E_T$. These data provide necessary constraints for chiral-odd GPD parametrizations and will strongly influence existing theoretical handbag models.
• ### Evidence for $\Delta(2200)7/2^-$ from photoproduction and consequence for chiral-symmetry restoration at high mass(1503.05774)

Feb. 21, 2017 nucl-ex, nucl-th
We report a partial-wave analysis of new data on the double-polarization variable $E$ for the reactions $\gamma p\to \pi^+ n$ and $\gamma p\to \pi^0 p$ and of further data published earlier. The analysis within the Bonn-Gatchina (BnGa) formalism reveals evidence for a poorly known baryon resonance, the one-star $\Delta(2200)7/2^-$. This is the lowest-mass $\Delta^*$ resonance with spin-parity $J^P=7/2^-$. Its mass is significantly higher than the mass of its parity partner $\Delta(1950)7/2^+$ which is the lowest-mass $\Delta^*$ resonance with spin-parity $J^P=7/2^+$. It has been suggested that chiral symmetry might be restored in the high-mass region of hadron excitations, and that these two resonances should be degenerate in mass. Our findings are in conflict with this prediction.
• ### Is there a narrow $N(1685)$?(1701.06387)

Jan. 28, 2017 nucl-ex
The helicity-dependent observable $E$ for the reaction $\gamma d\to \eta n (p)$ with a spectator proton was recently measured by the A2 Collaboration at MAMI in Mainz. The data were interpreted as further evidence for a narrow resonance with spin and parity $J^P=1/2^+$ ($P_{11}$ wave). However, a full partial wave analysis without any narrow resonance leads to an excellent description of the data, imposing a narrow resonance with the properties suggested by the A2 Collaboration leads to a significant deterioration of the fit quality: there is no need for a narrow resonance.
• ### High precision determination of the $Q^2$-evolution of the Bjorken Sum(1405.7854)

July 21, 2014 hep-ex, nucl-ex
We present a significantly improved determination of the Bjorken Sum for 0.6$\leq Q^{2}\leq$4.8 GeV$^{2}$ using precise new $g_{1}^{p}$ and $g_{1}^{d}$ data taken with the CLAS detector at Jefferson Lab. A higher-twist analysis of the $Q^{2}$-dependence of the Bjorken Sum yields the twist-4 coefficient $f_{2}^{p-n}=-0.064 \pm0.009\pm_{0.036}^{0.032}$. This leads to the color polarizabilities $\chi_{E}^{p-n}=-0.032\pm0.024$ and $\chi_{B}^{p-n}=0.032\pm0.013$. The strong force coupling is determined to be $\alpha_{s}^{\overline{\mbox{ MS}}}(M_{Z}^{2})=0.1124\pm0.0061$, which has an uncertainty a factor of 1.5 smaller than earlier estimates using polarized DIS data. This improvement makes the comparison between $\alpha_{s}$ extracted from polarized DIS and other techniques a valuable test of QCD.
• ### Energy-independent PWA of the reaction $\gamma p\to K^+\Lambda$(1404.4587)

April 17, 2014 nucl-ex, nucl-th
Using all recent data on the differential cross sections and spin observables for the reaction $\gamma p \to K^+ \Lambda$, an energy-independent partial-wave analysis is performed. The analysis requires multipoles up to $L = 2$; there is no evidence that the fit requires multipoles with $L=3$. At present the available data allow us to extract the dominant multipoles only. These are compatible with the multipoles obtained in the energy-dependent fit. This result supports the reliability of the Bonn-Gatchina energy-dependent results.
• ### Helicity amplitudes for photoexcitation of nucleon resonances off neutrons(1304.2177)

April 8, 2013 nucl-ex
The helicity amplitudes $A^{1/2}_n$ and $A^{3/2}_n$ for the photoexcitation of nucleon resonances off neutrons are determined in a multi-channel partial-wave analysis.
• We have measured cross sections for the gamma+3He->p+d reaction at photon energies of 0.4 - 1.4 GeV and a center-of-mass angle of 90 deg. We observe dimensional scaling above 0.7 GeV at this center-of-mass angle. This is the first observation of dimensional scaling in the photodisintegration of a nucleus heavier than the deuteron.
• ### A New Measurement of the $\pi^0$ Radiative Decay Width(1009.1681)

Sept. 9, 2010 nucl-ex
High precision measurements of the differential cross sections for $\pi^0$ photoproduction at forward angles for two nuclei, $^{12}$C and $^{208}$Pb, have been performed for incident photon energies of 4.9 - 5.5 GeV to extract the ${\pi^0 \to \gamma\gamma}$ decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The ${\pi^0 \to \gamma\gamma}$ decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is $\Gamma{(\pi^0 \to \gamma\gamma)} = 7.82 \pm 0.14 ~({\rm stat.}) \pm 0.17 ~({\rm syst.}) ~{\rm eV}$. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current PDG average of this fundamental quantity and it is consistent with current theoretical predictions.
• ### Theory Support for the Excited Baryon Program at the Jlab 12 GeV Upgrade(0907.1901)

Sept. 25, 2009 nucl-ex, nucl-th, hep-lat
This document outlines major directions in theoretical support for the measurement of nucleon resonance transition form factors at the JLab 12 GeV upgrade with the CLAS12 detector. Using single and double meson production, prominent resonances in the mass range up to 2 GeV will be studied in the range of photon virtuality $Q^2$ up to 12 GeV$^2$ where quark degrees of freedom are expected to dominate. High level theoretical analysis of these data will open up opportunities to understand how the interactions of dressed quarks create the ground and excited nucleon states and how these interactions emerge from QCD. The paper reviews the current status and the prospects of QCD based model approaches that relate phenomenological information on transition form factors to the non-perturbative strong interaction mechanisms, that are responsible for resonance formation.
• ### Experimental study of isovector spin sum rules(0802.3198)

Sept. 24, 2008 nucl-ex
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<Q^{2}<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which appears to be relatively large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also performed an isospin decomposition of the generalized forward spin polarizability $\gamma_{0}$. Although its isovector part provides a reliable test of the calculation techniques of Chiral Perturbation Theory, our data disagree with the calculations.
• ### Determination of the effective strong coupling constant alpha_{s,g_1}(Q^2) from CLAS spin structure function data(0803.4119)

July 21, 2008 hep-ph
We present a new extraction of the effective strong coupling constant \alpha_{s,g_1}(Q^2). The result agrees with a previous determination and extends the measurement of the low and high Q^2 behavior of \alpha_{s,g_1}(Q^2) that was previously deduced from sum rules. In particular, it experimentally verifies the lack of Q^2-dependence of \alpha_{s,g_1}(Q^2) in the low Q^2 limit. This fact is necessary for application of the AdS/CFT correspondence to QCD calculations. We provide a parameterization of \alpha_{s,g_1}(Q^2) thatcan equivalently be used to parameterize the Q^2-dependence of the generalized Gerasimov-Drell-Hearn and Bjorken sums.
• ### Experimental determination of the effective strong coupling constant(hep-ph/0509113)

June 21, 2007 hep-ph, hep-ex, nucl-ex
We present a first attempt to experimentally extract an effective strong coupling constant that we define to be a low Q2 extension of a previous definition by S. Brodsky et al. following an initial work of G. Grunberg. Using Jefferson Lab data and sum rules, we establish its Q2-behavior over the complete Q2-range. The result is compared to effective coupling constants inferred from different processes and to calculations based on Schwinger-Dyson equations, hadron spectroscopy or lattice QCD. Although the connection between the experimentally extracted effective coupling constants and the calculations is not established it is interesting to note that their behaviors are similar.
• ### Measurement of Deeply Virtual Compton Scattering with a Polarized Proton Target(hep-ex/0605012)

July 3, 2006 hep-ph, hep-ex, nucl-ex, nucl-th
The longitudinal target-spin asymmetry A_UL for the exclusive electroproduction of high energy photons was measured for the first time in p(e,e'p\gamma). The data have been accumulated at Jefferson Lab with the CLAS spectrometer using 5.7 GeV electrons and a longitudinally polarized NH_3 target. A significant azimuthal angular dependence was observed, resulting from the interference of the Deeply Virtual Compton Scattering and Bethe-Heitler processes. The amplitude of the sin(phi) moment is 0.252 +/- 0.042(stat) +/- 0.020(sys). Theoretical calculations are in good agreement with the magnitude and the kinematic dependence of the target-spin asymmetry, which is sensitive to the generalized parton distributions H and H-tilde.
• ### Global Analysis of Data on the Proton Structure Function g1 and Extraction of its Moments(hep-ph/0503018)

March 2, 2005 hep-ph, nucl-th
Inspired by recent measurements with the CLAS detector at Jefferson Lab, we perform a self-consistent analysis of world data on the proton structure function g1 in the range 0.17 < Q2 < 30 (GeV/c)**2. We compute for the first time low-order moments of g1 and study their evolution from small to large values of Q2. The analysis includes the latest data on both the unpolarized inclusive cross sections and the ratio R = sigmaL / sigmaT from Jefferson Lab, as well as a new model for the transverse asymmetry A2 in the resonance region. The contributions of both leading and higher twists are extracted, taking into account effects from radiative corrections beyond the next-to-leading order by means of soft-gluon resummation techniques. The leading twist is determined with remarkably good accuracy and is compared with the predictions obtained using various polarized parton distribution sets available in the literature. The contribution of higher twists to the g1 moments is found to be significantly larger than in the case of the unpolarized structure function F2.
• ### Higher twist analysis of the proton g_1 structure function(hep-ph/0404195)

Jan. 13, 2005 hep-ph, hep-ex, nucl-th
We perform a global analysis of all available spin-dependent proton structure function data, covering a large range of Q^2, 1 < Q^2 < 30 GeV^2, and calculate the lowest moment of the g_1 structure function as a function of Q^2. From the Q^2 dependence of the lowest moment we extract matrix elements of twist-4 operators, and determine the color electric and magnetic polarizabilities of the proton to be \chi_E = 0.026 +- 0.015 (stat) + 0.021/-0.024 (sys) and \chi_B = -0.013 -+ 0.007 (stat) - 0.010/+0.012 (sys), respectively.
• ### Comment on The Evidence for a Pentaquark and Kinematic Reflections(hep-ph/0411265)

Dec. 13, 2004 hep-ph
The Regge exchange model used by Dzierba et al. is shown to be questionable, since the pion pole term is not allowed. Hence the Regge amplitudes in their calculation are exaggerated. The amount of kinematic reflection in the mass spectrum of the (nK+) system, which is one decay channel of a possible pentaquark, is not well justified in the fitting procedure used by Dzierba et al., as shown by comparison with the (K+K-) invariant mass spectrum, which is one decay channel of the a_2 and f_2 tensor mesons. While kinematic reflections are still a concern in some papers that have presented evidence for the pentaquark, better quantitative calculations are needed to demonstrate the significance of this effect.
• ### Experimental determination of the evolution of the Bjorken integral at low Q^2(hep-ex/0407007)

Nov. 19, 2004 hep-ph, hep-ex, nucl-ex
We extract the Bjorken integral Gamma^{p-n}_1 in the range 0.17 < Q^2 < 1.10 GeV^2 from inclusive scattering of polarized electrons by polarized protons, deuterons and 3He, for the region in which the integral is dominated by nucleon resonances. These data bridge the domains of the hadronic and partonic descriptions of the nucleon. In combination with earlier measurements at higher Q^2, we extract the non-singlet twist-4 matrix element f_2.
• ### Self-Consistent Data Analysis of the Proton Structure Function g1 and Extraction of its Moments(hep-ex/0409038)

Sept. 14, 2004 hep-ex
The reanalysis of all available world data on the longitudinal asymmetry A|| is presented. The proton structure function g1 was extracted within a unique framework of data inputs and assumptions. These data allowed for a reliable evaluation of moments of the structure function g1 in the Q2 range from 0.2 up to 30 GeV2. The Q2 evolution of the moments was studied in QCD by means of Operator Product Expansion (OPE).
• ### QED Radiative Corrections in Processes of Exclusive Pion Electroproduction(hep-ph/0208183)

Aug. 20, 2002 hep-ph, nucl-ex, nucl-th
Formalism for radiative correction (RC) calculation in exclusive pion electroproduction on the proton is presented. A FORTRAN code EXCLURAD is developed for the RC procedure. The numerical analysis is done in the kinematics of current Jefferson Lab experiments.
• ### Search for Quadrupole Strength in the Electro-excitation of the Delta(1232)(nucl-ex/9902012)

Dec. 6, 2000 nucl-ex
High-precision H(e,e'p)pi0 measurements at Q2=0.126 (GeV/c)2 are reported, which allow the determination of quadrupole amplitudes in the gamma* N->Delta transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole amplitude ratios, Rsm=(-6.5 +- 0.2{stat+sys} +- 2.5{mod}) % and Rem=(-2.1 +- 0.2{stat+sys} +- 2.0{mod}) %, are dominated by model error. Previous Rsm and Rem results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.


text:
IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Velocities in Rolling Motion

## Introduction

In a moving bicycle, its wheel while rotating also covers a linear distance forward. If a body undergoes rotational as well as translational motion on a hard surface, it is said to be rolling. A rolling without slipping is called pure rolling.

In this demonstration we try to find the relation between the velocities of the center and top of the rolling cylinder.

## Apparatus

A uniform cylindrical body (roller), two 12 inch scales

## Procedure

1. Place the roller on the table near one of the scales such that the distance moved by the roller can be measured on the scale.
2. Now place another scale on top of the roller. The point in contact of the scale with the roller shows the zero mark.
3. Move the roller forward with the help of the scale above it. Make sure that the scale is always in contact with the roller and it does not slip on the roller.
4. Stop when the point in contact of the scale above the roller shows 12 inches.
5. Note the distance moved by the roller in the scale placed beside it.
6. See that the roller has travelled only 6 inches.

## Discussion

The reading on the scale touching the top of the roller is double the reading on the scale placed beside it. This clearly means the top of the roller has travelled double the distance as compared to the distance moved by the whole roller in the same time. This means that the velocity of the top of the roller is twice the velocity of the roller itself. The velocity of the roller is equal to the velocity of the center of mass of the roller. So we can say that the velocity of the center of mass is half the velocity of the top in pure rolling. If $$\omega$$ is the angular velocity of the roller of radius $$r$$ then velocities of the point a', b', and c' are $$v_a=0$$, $$v_b=\omega r$$, and $$v_c=2\omega r$$. This demonstration shows that velocity of the point c' is twice the velocity of the point `a'.

The same result can be arrived without the use of scales. Both our hands are identical and hence can replace the two scales. Just place the roller at the periphery of the palm and place the finger of the other hand on top of the roller and roll it. We see that although the roller moves one hand distance the hand touching the top of the roller moves two hand distance. This again proves that the velocity of top is twice the velocity of the center of mass of the roller.


text:
Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_anova_hier2 (g04ag)

## Purpose

nag_anova_hier2 (g04ag) performs an analysis of variance for a two-way hierarchical classification with subgroups of possibly unequal size, and also computes the treatment group and subgroup means. A fixed effects model is assumed.

## Syntax

[ngp, gbar, sgbar, gm, ss, idf, f, fp, ifail] = g04ag(y, lsub, nobs, 'n', n, 'k', k, 'l', l)
[ngp, gbar, sgbar, gm, ss, idf, f, fp, ifail] = nag_anova_hier2(y, lsub, nobs, 'n', n, 'k', k, 'l', l)

## Description

In a two-way hierarchical classification, there are k$k$ (2$\text{}\ge 2$) treatment groups, the i$i$th of which is subdivided into li${l}_{i}$ treatment subgroups. The j$j$th subgroup of group i$i$ contains nij${n}_{ij}$ observations, which may be denoted by
 y1ij,y2ij, … ,ynijij. $y1ij,y2ij,…,ynijij.$
The general observation is denoted by ymij${y}_{mij}$, being the m$m$th observation in subgroup j$j$ of group i$i$, for 1ik$1\le i\le k$, 1jli$1\le j\le {l}_{i}$, 1mnij$1\le m\le {n}_{ij}$.
The following quantities are computed
(i) The subgroup means
 y . ij = ( ∑ m = 1nijymij)/(nij) $y-.ij=∑m=1nijymijnij$
(ii) The group means
 y . i . = ( ∑ j = 1li ∑ m = 1nijymij)/( ∑ j = 1linij) $y-.i.=∑j= 1li∑m= 1nijymij ∑j= 1linij$
(iii) The grand mean
 y… = ( ∑ i = 1k ∑ j = 1li ∑ m = 1nijymij)/( ∑ i = 1k ∑ j = 1linij) $y-…=∑i=1k∑j=1li∑m=1nijymij ∑i=1k∑j=1linij$
(iv) The number of observations in each group
 li ni . = ∑ nij j = 1
$ni.= ∑j= 1 li nij$
(v) Sums of squares
Between groups
 k = SSg = ∑ ni . (y . i . − y…)2 i = 1
Between subgroups within groups
 k li = SSsg = ∑ ∑ nij(y . ij − y . i . )2 i = 1 j = 1
Residual (within subgroups)
 k li nij = SSres = ∑ ∑ ∑ (ymij − y . ij)2 = SStot − SSg − SSsg i = 1 j = 1 m = 1
Corrected total
 k li nij = SStot = ∑ ∑ ∑ (ymij − y…)2 i = 1 j = 1 m = 1
$Between groups =SSg = ∑ i=1 k ni. ( y-.i.-y-… ) 2 Between subgroups within groups =SSsg= ∑ i=1 k ∑ j=1 li nij ( y.ij-y-.i. ) 2 Residual (within subgroups) =SSres= ∑ i=1 k ∑ j=1 li ∑ m=1 nij ( ymij-y-.ij ) 2 =SStot-SSg-SSsg Corrected total =SStot= ∑ i=1 k ∑ j=1 li ∑ m=1 nij ( ymij-y-… ) 2$
(vi) Degrees of freedom of variance components
 Between groups: k − 1$k-1$ Subgroups within groups: l − k$l-k$ Residual: n − l$n-l$ Total: n − 1$n-1$
where
• l = i = 1kli$l=\sum _{i=1}^{k}{l}_{i}$,
• n = i = 1kni . $n=\sum _{i=1}^{k}{n}_{i.}$
(vii) F$F$ ratios. These are the ratios of the group and subgroup mean squares to the residual mean square.
 Groups F1 = (Between groups sum of squares / (k − 1))/(Residual sum of squares / (n − l)) = (SSg / (k − 1))/(SSres / (n − l)) ${F}_{1}=\frac{\text{Between groups sum of squares}/\left(k-1\right)}{\text{Residual sum of squares}/\left(n-l\right)}=\frac{{\mathrm{SS}}_{g}/\left(k-1\right)}{{\mathrm{SS}}_{\mathrm{res}}/\left(n-l\right)}$ Subgroups F2 = (Between subgroups (within group) sum of squares / (l − k))/(Residual sum of squares / (n − l)) = (SSsg / (l − k))/(SSres / (n − l)) ${F}_{2}=\frac{\text{Between subgroups (within group) sum of squares}/\left(l-k\right)}{\text{Residual sum of squares}/\left(n-l\right)}=\frac{{\mathrm{SS}}_{sg}/\left(l-k\right)}{{\mathrm{SS}}_{\mathrm{res}}/\left(n-l\right)}$
If either F$F$ ratio exceeds 9999.0$9999.0$, the value 9999.0$9999.0$ is assigned instead.
(viii) f significances. The probability of obtaining a value from the appropriate F$F$-distribution which exceeds the computed mean square ratio.
 Groups p1 = Prob (F (k − 1) , (n − l) > F1) ${p}_{1}=\mathrm{Prob}\left({F}_{\left(k-1\right),\left(n-l\right)}>{F}_{1}\right)$ Subgroups p2 = Prob (F (l − k) , (n − l) > F2) ${p}_{2}=\mathrm{Prob}\left({F}_{\left(l-k\right),\left(n-l\right)}>{F}_{2}\right)$
where Fν1,ν2${F}_{{\nu }_{1},{\nu }_{2}}$ denotes the central F$F$-distribution with degrees of freedom ν1${\nu }_{1}$ and ν2${\nu }_{2}$.
If any Fi = 9999.0${F}_{i}=9999.0$, then pi${p}_{i}$ is set to zero, i = 1,2$i=1,2$.

## References

Kendall M G and Stuart A (1976) The Advanced Theory of Statistics (Volume 3) (3rd Edition) Griffin
Moore P G, Shirley E A and Edwards D E (1972) Standard Statistical Calculations Pitman

## Parameters

### Compulsory Input Parameters

1:     y(n) – double array
The elements of y must contain the observations ymij${y}_{\mathrm{mij}}$ in the following order:
 y111,y211, … ,yn1111,y112,y212, … ,yn1212, … ,y11l1, … , $y111,y211,…,yn1111,y112,y212,…,yn1212,…,y11l1,…,$
 yn1l11l1, … , y1ij, … ,ynijij, … ,y1klk, … , ynklkklk. $yn1l11l1,…, y1ij,…,ynijij,…,y1klk,…, ynklkklk.$
In words, the ordering is by group, and within each group is by subgroup, the members of each subgroup being in consecutive locations in y.
2:     lsub(k) – int64int32nag_int array
k, the dimension of the array, must satisfy the constraint k2${\mathbf{k}}\ge 2$.
The number of subgroups within group i$\mathit{i}$, li${l}_{\mathit{i}}$, for i = 1,2,,k$\mathit{i}=1,2,\dots ,k$.
Constraint: lsub(i) > 0${\mathbf{lsub}}\left(\mathit{i}\right)>0$, for i = 1,2,,k$\mathit{i}=1,2,\dots ,k$.
3:     nobs(l) – int64int32nag_int array
l, the dimension of the array, must satisfy the constraint l = i = 1klsub(i)${\mathbf{l}}=\sum _{i=1}^{k}{\mathbf{lsub}}\left(i\right)$.
The numbers of observations in each subgroup, nij${n}_{ij}$, in the following order:
 n11,n12, … ,n1l1,n21, … ,n2l2, … ,nk1, … ,nklk $n11,n12,…,n1l1,n21,…,n2l2,…,nk1,…,nklk$
Constraint: n = i = 1kj = 1linij$n=\sum _{\mathit{i}=1}^{k}\sum _{j=1}^{{l}_{i}}{n}_{\mathit{i}j}$, that is n = i = 1lnobs(i)${\mathbf{n}}=\sum _{\mathit{i}=1}^{l}{\mathbf{nobs}}\left(\mathit{i}\right)$ and nobs(i) > 0${\mathbf{nobs}}\left(\mathit{i}\right)>0$, for i = 1,2,,l$\mathit{i}=1,2,\dots ,l$.

### Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The dimension of the array y.
n$n$, the total number of observations.
2:     k – int64int32nag_int scalar
Default: The dimension of the array lsub.
k$k$, the number of groups.
Constraint: k2${\mathbf{k}}\ge 2$.
3:     l – int64int32nag_int scalar
Default: The dimension of the array nobs.
l$l$, the total number of subgroups.
Constraint: l = i = 1klsub(i)${\mathbf{l}}=\sum _{i=1}^{k}{\mathbf{lsub}}\left(i\right)$.

None.

### Output Parameters

1:     ngp(k) – int64int32nag_int array
The total number of observations in group i$\mathit{i}$, ni . ${n}_{\mathit{i}.}$, for i = 1,2,,k$\mathit{i}=1,2,\dots ,k$.
2:     gbar(k) – double array
The mean for group i$\mathit{i}$, y . i . ${\stackrel{-}{y}}_{.\mathit{i}.}$, for i = 1,2,,k$\mathit{i}=1,2,\dots ,k$.
3:     sgbar(l) – double array
The subgroup means, y . ij${\stackrel{-}{y}}_{.ij}$, in the following order:
 y.11,y.12, … ,y.1l1,y.21,y.22, … ,y.2l2, … ,y . k1,y . k2, … ,y . klk. $y-.11,y-.12,…,y-.1l1,y-.21,y-.22,…,y-.2l2,…,y-.k1,y-.k2,…,y-.klk.$
4:     gm – double scalar
The grand mean, y${\stackrel{-}{y}}_{\dots }$.
5:     ss(4$4$) – double array
Contains the sums of squares for the analysis of variance, as follows;
• ss(1) = ${\mathbf{ss}}\left(1\right)=\text{}$ Between group sum of squares, ssg${{\mathbf{ss}}}_{g}$,
• ss(2) = ${\mathbf{ss}}\left(2\right)=\text{}$ Between subgroup within groups sum of squares, sssg${{\mathbf{ss}}}_{sg}$,
• ss(3) = ${\mathbf{ss}}\left(3\right)=\text{}$ Residual sum of squares, ssres${{\mathbf{ss}}}_{\mathrm{res}}$,
• ss(4) = ${\mathbf{ss}}\left(4\right)=\text{}$ Corrected total sum of squares, sstot${{\mathbf{ss}}}_{\mathrm{tot}}$.
6:     idf(4$4$) – int64int32nag_int array
Contains the degrees of freedom attributable to each sum of squares in the analysis of variance, as follows:
• idf(1) = ${\mathbf{idf}}\left(1\right)=\text{}$ Degrees of freedom for between group sum of squares,
• idf(2) = ${\mathbf{idf}}\left(2\right)=\text{}$ Degrees of freedom for between subgroup within groups sum of squares,
• idf(3) = ${\mathbf{idf}}\left(3\right)=\text{}$ Degrees of freedom for residual sum of squares,
• idf(4) = ${\mathbf{idf}}\left(4\right)=\text{}$ Degrees of freedom for corrected total sum of squares.
7:     f(2$2$) – double array
Contains the mean square ratios, F1${F}_{1}$ and F2${F}_{2}$, for the between groups variation, and the between subgroups within groups variation, with respect to the residual, respectively.
8:     fp(2$2$) – double array
Contains the significances of the mean square ratios, p1${p}_{1}$ and p2${p}_{2}$ respectively.
9:     ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).

## Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

ifail = 1${\mathbf{ifail}}=1$
 On entry, k ≤ 1${\mathbf{k}}\le 1$.
ifail = 2${\mathbf{ifail}}=2$
 On entry, lsub(i) ≤ 0${\mathbf{lsub}}\left(i\right)\le 0$, for some i = 1,2, … ,k$i=1,2,\dots ,k$.
ifail = 3${\mathbf{ifail}}=3$
 On entry, l ≠ ∑ i = 1klsub(i)${\mathbf{l}}\ne \sum _{i=1}^{k}{\mathbf{lsub}}\left(i\right)$
ifail = 4${\mathbf{ifail}}=4$
 On entry, nobs(i) ≤ 0${\mathbf{nobs}}\left(i\right)\le 0$, for some i = 1,2, … ,l$i=1,2,\dots ,l$.
ifail = 5${\mathbf{ifail}}=5$
 On entry, n ≠ ∑ i = 1lnobs(i)${\mathbf{n}}\ne \sum _{i=1}^{l}{\mathbf{nobs}}\left(i\right)$.
W ifail = 6${\mathbf{ifail}}=6$
The total corrected sum of squares is zero, indicating that all the data values are equal. The means returned are therefore all equal, and the sums of squares are zero. No assignments are made to idf, f, and fp.
W ifail = 7${\mathbf{ifail}}=7$
The residual sum of squares is zero. This arises when either each subgroup contains exactly one observation, or the observations within each subgroup are equal. The means, sums of squares, and degrees of freedom are computed, but no assignments are made to f and fp.

## Accuracy

The computations are believed to be stable.

The time taken by nag_anova_hier2 (g04ag) increases approximately linearly with the total number of observations, n$n$.

## Example

```function nag_anova_hier2_example
y = [2.1;
2.4;
2;
2;
2;
2.4;
2.1;
2.2;
2.4;
2.2;
2.6;
2.4;
2.4;
2.5;
1.9;
1.7;
2.1;
1.5;
2;
1.9;
1.7;
1.9;
1.9;
1.9;
2;
2.1;
2.3];
lsub = [int64(5);3];
nobs = [int64(5);3;3;3;2;3;5;3];
[ngp, gbar, sgbar, gm, ss, idf, f, fp, ifail] = nag_anova_hier2(y, lsub, nobs)
```
```

ngp =

16
11

gbar =

2.2062
1.9364

sgbar =

2.1000
2.2333
2.4000
2.4333
1.8000
1.8667
1.8600
2.1333

gm =

2.0963

ss =

0.4748
0.8162
0.5587
1.8496

idf =

1
6
19
26

f =

16.1477
4.6262

fp =

0.0007
0.0047

ifail =

0

```
```function g04ag_example
y = [2.1;
2.4;
2;
2;
2;
2.4;
2.1;
2.2;
2.4;
2.2;
2.6;
2.4;
2.4;
2.5;
1.9;
1.7;
2.1;
1.5;
2;
1.9;
1.7;
1.9;
1.9;
1.9;
2;
2.1;
2.3];
lsub = [int64(5);3];
nobs = [int64(5);3;3;3;2;3;5;3];
[ngp, gbar, sgbar, gm, ss, idf, f, fp, ifail] = g04ag(y, lsub, nobs)
```
```

ngp =

16
11

gbar =

2.2062
1.9364

sgbar =

2.1000
2.2333
2.4000
2.4333
1.8000
1.8667
1.8600
2.1333

gm =

2.0963

ss =

0.4748
0.8162
0.5587
1.8496

idf =

1
6
19
26

f =

16.1477
4.6262

fp =

0.0007
0.0047

ifail =

0

```


text:
# For every positive integer $n, n^2 + 4n + 3$ is not a prime

Prove: For every positive integer $n, n^2 + 4n + 3$ is not a prime.

I tried to disprove the statement, which I could not using several number examples with constructive proof.

However I am not sure how to correctly step by step prove it.

Hint: $$n^2+ 4n+3=(n+1)(n+3)$$

• YEs got it! thats basically what I needed! Dec 22, 2014 at 16:11

Hint: $n^2+4n+3 = (n+1)(n+3)$. Can you take it further?

• yes, thank you! Dec 22, 2014 at 16:12

it is $$(n+1)(n+3)$$ and thus not prime because it has to factors greater than one.

Recall that $$n^2 + 4n + 3 = (n + 1)(n + 3)$$. Since $$n$$ is necessarily a positive integer, it is obvious that $$n^2 + 4n + 3$$ is composite.


text:
# EX.2.2 Q12 Linear Equations in One Variable Solutions - NCERT Maths Class 8

Go back to  'Ex.2.2'

## Question

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Video Solution
Linear Equations
Ex 2.2 | Question 12

## Text Solution

What is known?

Fifteen years from now Ravi’s age will be four times his present age.

What is unknown?

Ravi’s present age

Reasoning:

Assume Ravi’s age to be a variable. Use the first and second condition to express his age after $$15$$ years in the form of a linear equation.

Steps:

Let the present age of Ravi be $$x$$ years.

$$15$$ years from now, Ravi’s age will be $$4$$ times his present age

\begin{align}x + 15 &= 4x\\x - 4x &= - 15\\ - 3x &= - 15\\x &= \frac{{ - 15}}{{ - 3}}\\x &= 5\end{align}

$$\therefore$$ Ravi’s present age is $$5$$ years

Learn from the best math teachers and top your exams

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


text:
# What does it mean that the electric charge is quantized?

Jun 11, 2018

I have always liked the definition $\text{quantum"-="packet}$...

#### Explanation:

And so electric charge is $\text{quantized}$...it arises from the presence of EXTRA electrons (in anions), or from the absence of electrons in CATIONS. The electronic charge is crucial, because this is the only charge we can change given the NUCLEAR definition of atomic number.

And one electron has a charge of $- 1.602 \times {10}^{-} 19 \cdot C$...and so individual charged ions can have PACKETS of this CHARGE subtracted to give a CATION, or ADDED to give an anion.. Are you with me?

And if we got a mole of anions....then we have an electrostatic charge of...

$- 1.602 \times {10}^{-} 19 \cdot C \times 6.022 \times {10}^{23} \cdot m o {l}^{-} 1 \equiv 96472.4 \cdot C \cdot m o {l}^{-} 1$

...and this of course is old Faraday's constant...which was approached experimentally BEFORE the conception of electrons and moles...


text:
## Saturday, October 30, 2010

### Apocrypha Topologica I

Dear Mathematicelli,

I should like today to introduce an apocryphal history of Topology, both as a phenomenon and as a field of mathematical study. It will necessarily be abbreviated, full of fictions, and other more innocent errors --- hence apocryphal. But it should be ordered to the truth so far as illuminating the modern study of topology itself.

Topology was imposed on the visible Creation by God at least as early as the Second Day, when He said
6 ... "Let there be a firmament made amidst the waters: and let it divide the waters from the waters." 7 And God made a firmament, and divided the waters that were under the firmament, from those that were above the firmament, and it was so.
This highlights the first introduction of a disconnected set, a "you can't get there from here" in the world: to reach the waters above from those below you must cross this firmament, whatever it may be. And this notion of separation, whether in the absolute sense of being mutually inaccessible, or the relative sense of inhabiting disjoint neighborhoods has been a puzzle and inspiration for topologists since before we even had the name topology to describe the field.

Some might argue that the temporal ordering of days already introduced an order topology (or the causal partial-order topology we learn from the Special and General Theories of Relativity). I reply that this is missing something of the point, but if you want to write your own paper on the history of Topology that's quite alright.

Other Biblical features of topological interest in denoting separation: the cherubim posted to keep Adam and Eve out of Eden; the Red Sea; the River Jordan; the Rivers Tigris and Euphrates, that separate the Land Amidst the Rivers from surrounding territories (I mean, you can get in and out of that without crossing either, but then you'd have to cross the ~40km line segment between Palu and Hantepe... a narrow road, as geography goes!)

The next great topological discoveries were knots and chains. Windows are a nifty invention too, I suppose, but knots and chains are much more tangible. The way these work, as I'm sure you've experienced, is that various strands of rope or metal, being extended in one direction, have new ways of becoming separated from conditions they might have liked to achieve: while it would take a wall to stop you, and you can walk around a rope quite happily, a string can get stuck by a rope in one perpetual wandering-around! By the by, I don't mean mechanical knots; these are fascinating, but the mechanical distinctions between various rolling hitches are much fuzzier than the topological fact that there are more ways to get tangled in a net than in a string tied in a single loop. Think of the "Gordian Knot" versus an undoubled slipknot bow as you might use on your shoes.

As another aside, there seems some discrepancy between my predecessors in mathematical apocrypha on the one hand vs. closer accounts of Alexander's encounter with Gordy's knot --- what the knot tied up, whether Alexander really sliced it in two or what, etc., are disputed points. One way or another, there were knots and mechanical facts emphasizing topological separations, and it became a point of proverbs through the march of time.

The Gordian Knot brings us to the relatively recent period and setting known as Greek Mythology, and there, for now we will interrupt our History. Next time: strings graduate from topological features to topological tools!

The Math Prof of Your Nightmares

### PSA

Dear Passers-by,

I noticed recently that the blogger profile for this persona didn't offer means of private communication, which was in fact the primary purpose of the /dev/null persona. This must have been the unintended consequence of some policy change within blogger, because other people have been surprised recently to not show contact info; in any case, I've changed that now.

And of course, it's easy to just write here, in Dumbledore Fashion, that mail addressed to qnoodles at gmail will find me. As a purely historical note, the q stands for Quincy, and no, I don't know anyone named Quincy. It just seemed to suit "Mr. Noodles" remarkably well!

PS there really is only the one of me.

## Thursday, October 28, 2010

### In deep October

Pol. How does my good lord Hamlet?
Ham. Excellent well.
Pol. Do you know me, my lord?
Ham. Excellent well; you are a fishmonger.
Pol. Not I, my lord.
Ham. Then I would you were so honest a man.
Pol. Honest, my lord!
Ham. Ay, sir; to be honest, as this world goes, is to be one man picked out of ten thousand.
Pol. That's very true, my lord.
Ham. For if the sun breed maggots in a dead dog, being a god, kissing carrion,——Have you a daughter?
Pol. I have, my lord.
Ham. Let her not walk i'the sun: conception is a blessing; but as your daughter may conceive,—friend, look to't, look to't, look to't.
[Goes up stage.]
Pol. (Aside.) Still harping on my daughter:—yet he knew me not at first; he said I was a fishmonger. [Crosses to L.] I'll speak to him again.—What do you read, my lord?

I am told "Defiant" and asked "Are sparrows blithe?"

I've been having difficulty with this one, because all the words that come into my head are scripture, and it doesn't seem quite right to write a cento on the Bible --- that were only to diminish the worthiest poetry ever set down.

\begin{itemize}
\item "Are not two sparrows sold for a farthing? ... You are worth more than many sparrows."
\item "Consider the birds of the air: they reap not, nor sow, nor gather into barns..."
\item "How lovely are thy tabernacles! ... for the sparrow hath found herself a house, and the dove a nest for to lay her young."
\end{itemize}

What follows instead is an aliterative allegory of wishful thinking. Or something... yeah, I don't know what it is.

Butterflies and sparrows spin blithely by
My window, wonderous marvels in miniature,
Provoking contemplation, to ponder creatures
And Provident God, gracious in peace and plenty.
Against His coming Justice, fearing coldest Gaol,
We rightly cry repentance, and remission crave,
Converting to Love our lagging contrite hearts;
Even as I of Him, each evening,
Beg good grace anew to gain Beatitude
Before dying, as defiant before Death,
To thee would I this warrant of affection
Give; lest lacking love's greeting
We were parted by time's passing wave ---
O! to be so blithe as sparrows!

And, my friends dear, please don't worry. There's nothing more dire looming over me than that recurrent need of the sacraments --- that's sort-of the point, in fact. It's the kind of thing you want to get done *before* the rest looks dire!

## Saturday, October 23, 2010

### Eeek! What a place!

A locus focus, and Oh! what a scary place it is, too. For today we are serving

### Detention with Dolores

Harry Potter and the Order of the Phoenix

[Harry Potter] had known this office under three of its previous occupants. [...]

Now, however, it looked totally unrecognisable. The surfaces had all been draped in lacy covers and cloths. There were several vases of dried flowers, each one residing on its own doily, and on one of the walls was a collection of ornamental plates, each decorated with a large technicolor kitten wearing a different bow around its neck. These were so foul that Harry stared at them transfixed, untill Professor Umbridge spoke again.

I also thought about mentioning this locus back in September, for "educational" settings. Indeed, Harry learns much about the nature of evil --- as well as something of the heroic --- in this particular office room between his second and fifth year.

In its fifth-volume avatar, the Defence Against the Dark Arts Proffessor's Office shows us just how ugly good things like kittens can be made, with just the wrong sort of twist; in an interesting parallel, the same room highlights just how ugly such a good thing as devotion to the Truth can become when twisted into "devotion to what I say the Truth is" --- which is an idolatry.

I don't want to say too much more because I believe Enbrethiliel hasn't read this book yet.

That Bat also known as some guy on the street

## Sunday, October 17, 2010

### WHAT ON EARTH?

UPDATED

What has happened to Orbis Catholicus II??? Is the illustrious Mr. Sonnen in some strange unpublished need? Has his server been compromised? Or (weirder) has someone flooded a DNS cache with this sham site?

Bloggians! To the rescue!

UPDATE: it seems to be here now.

## Saturday, October 16, 2010

### Whence 4?

Time for some more math! At my (new! yay!) supervisor's behest I've been trying like a primordial lungfish to breath the fresh air called spectral sequences --- how they ever managed to acclimate to such thin and rarefied reference to anything tangible is beyond me; but then, the calculations themselves are thick as water to my more-terrestrial brain.

Today is not about spectral sequences, but back to geometric measure theory. Some time ago I got as far as to outline the proportion of surface areas vs. angles
$$S(\triangle qrs):S(\mathbb{S})::\angle qrs + \angle rsq + \angle sqr - \pi:4\pi$$
for a spherical triangle $qrs$ --- although for reasons of presentation, that tale refered to the hemispheres $A,B,C$ described by the arcs $qr,$ $rs,$ $sq$ and containing the triangle $\triangle qrs$. (Do you see some ambiguity creeping into the tale? Don't worry: make your choices and then show that they aren't important!)

So, our task today is to improve the proportionality by establishing, for a unit sphere $\mathbb{S}$, an equality $S(\triangle qrs) = \angle qrs + \angle rsq + \angle sqr - \pi$, which by the complementary proportion will give $S(\mathbb{S})=4\pi$.

## Wednesday, October 13, 2010

### Fun with TeX and paper

echo <<eof >>/dev/null

We have calling cards!

That is, these are the sort of card you leave on a silver tray under the eyes of a lady's Mother or their doorman, when said lady isn't home or disposed to receive you, to say that you did, in fact, come to "call" --- without the bother or nuissance to your neighbors of actually calling out with voice to see if she answers. Some folk call them business cards these days, what with the advent of the inescapable mobile phone, in principle allowing men to pester decent ladies with person-to-person "calls" at any hour of night or day. Since precious little business gets done here (thank goodness) to call these cards "business cards" would be farcical beyond even our usual fare.

The obverse face is a tweaked version of this TeX file --- it took some doing, too, may I say. I was quite worn-out by the end of it. The reverse are filled with a rhombic variation of those famous Penrose tilings, one of several impressively economical files here exhibiting the illegible efficiency of Adobe's postscript virtual machine.

Another picture:

eof

## Monday, October 4, 2010

### Is it scary here? Or is it just me?

I seem to linger on one or two authors; this time I feel like another Tolkien spot, not far from last time's locus.

After stumbling along for some way along the stream, they came quite suddenly out of the gloom. As if through a gate, they saw the sunlight before them. Coming to the opening they found that they had made their way down through a cleft in a high steep bank, almost a cliff. At its feet was a wide space of grass and reeds; and in the distance could be glimpsed another bank almost as steep. A golden afternoon of late sunshine lay warm and drowsy upon the hidden land between. In the midst of it there wound lazily a dark river of brown water, bordered with ancient willows, blocked with fallen willows, and flecked with thousands of faded willow-leaves. The air was thick with them, fluttering yellow from the branches; for there was a warm and gentle breeze blowing softly in the valley, and the reeds were rustling, and the willow-boughs were creaking.

Well, now I have at least some notion of where we are!' said Merry. ... This is the River Withywindle!...'
I suppose there's not much frightening about that, as far as it goes --- but you have to read the book! I love the way that "willow" note recurs, like an ostinato counterpoint. Or perhaps it's a flatted dominant? For myself, "willow" is one of my "cellar door"s, quite apart from how I admire willow-trees in person. But here...

... There were armies of flies of all kinds buzzing around their ears, and the afternoon sun was burning on their backs. At last they came suddenly into a thin shade; great grey branches reached across the path. Each step forward became more reluctant than the last. Sleepiness seemed to be creeping out of the ground and up their legs, and falling softly out of the air upon their heads and eyes.

Are you thinking what I'm thinking?

Go read the book, now, if you don't remember it. But it's worth noting that willows, while lovely and graceful, are not the trustiest of trees; their wood is rather too soft for structural uses, and they tend to fall apart as they get older. A venerable old specimen in one of my favourite boyhood parkly haunts was dismantled recently, to forestall it's falling down on unsuspecting visitors. Tolkien's rather more willful Old Man Willow character, who very much defines this place, is an alarming extrapolation of my poignant beloved trees.

--Some Guy on the Street, for

The River Withywindle
The Lord of the Rings: The Fellowship of the Ring
J.R.R. Tolkien

## Sunday, October 3, 2010

### Something a little more Aedifying?

Dear Exegete,

I gave myself to LifeChain for an hour today; and whilst standing there the hymn occurred to me that, for no good reason, I know best in the Russian chant setting. Not that I could tell you which words mean what, nor how they fit together...

Anyways, I thought it made a nice contrast to the more commonly-referenced De Profundis; which is apposite, of course, but has so many other uses, as well. The latter is good for commemorating those lives already cut short; but Save, O Lord, Thy people is looks from the present to the future, and recalls souls that thrive still on Earth and for whom there is hope.

he would be more sad, if not for life

Parce Domine populo tuo
et ne des hereditatem tuam in obprobrium
ut dominentur eis nationes
quare dicunt in populis "ubi est Deus eorum"?
zelatus est Dominus terram suam et pepercit populo suo


text:
Browse Questions

# A fair die is rolled. The probability that the first 1 occurs at even number of trails is?

Can you answer this question?


text:
# processing float vs double

For representing floating point numbers, we use float, double and long double.. What’s the difference ? As a result using float also doubles the amount of data we can store on the . It has 15 decimal digits of precision. exp, sin, etc.). For example, double precision would be considered if it offered better (perceptual) quality. Floating Point Types Integer types can hold only whole numbers and therefore we use another type known as floating point type to hold numbers containing fractional parts such as 50.55 and 2.344. The principle of float glass is unchanged from the 1950s. In any case, it's a numerical precision issue - in terms of quality, there won't be any perceptual difference. The range of values is beyond the scope of this discussion but it is mainly specified in the Floating-Point Types, Formats, and Values section of the Java Language Specification.. This article doesn't provide useful examples for Single or Double. That is, all channels are being processed and mixed in 64-bit floating point instead of previously 32-bit. What you're saying about AVX and the 2x speedup should be true but it really depends on the nature of the code. Help identifying pieces in ambiguous wall anchor kit. 75, 600, and -9). If an answer is required to have negligible difference from the actual answer, number of decimal places required will be many thus will dictate that double to be in use.Float will chop off some decimal places part thus reducing the accuracy. val: the value to assign to that variable. (If you’re curious, you can search for floating-point binary on the Internet and find some excellent tutorials that may or may not clear it up.). Conversion from Floating point representation to Fixed point representation. There is rarely cause to use float instead of double in code targeting modern computers. Processing supports the double datatype from Java as well. The type double provides at least as much precision as float, and the double var = val; Parameters . SimonAlkemade, Aug 31, 2011 #1. rokstar234. You can do some analysis of your noise and signal levels to get an idea of how much of the noise comes from quantization error, but you won't really know for sure if it will make a difference or not until you implement it with both and see if it makes a difference. Similarly, the noise floor is also important. Usually, I use the float type when I don't need much precision — for example, for money — which is wrong, but is what I'm used to wrongly do. Float vs Double: Floating point processing . According to IEEE, it has a 32-bit floating point precision. Frequently in my programming experience I need to make a decision whether I should use float or double for my real numbers. That's a big deal. The processing of FilterExpression for the dataset ‘Dataset1’ cannot be performed. You should think twice before using floating-point arithmetic. But the product has changed dramatically: from a single equilibrium thickness of 6.8 mm to a range from sub-millimetre to 25 mm; from a ribbon frequently marred by inclusions, bubbles and striations to almost optical perfection. You are doing low-level optimization, Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Until recently, many graphics cards only supported single precision 1 reply Programmer Certification (OCPJP) Narrowing conversion? So the state variable can be much bigger than the input (80db to 100dB bigger) and summing state variables with the input creates a lot of noise. Double-precision floating-point format (sometimes called FP64 or float64) is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. If there is no compilation warnings or errors, it does not mean that code is optimal. There are three floating point types: float, double, and long double. For example 6.0 / 3.0 may not equal 2.0. 12 replies Associate Certification (OCAJP 7/8) Clarification on primitive return type. I can only retrieve a double but I need a float the decrease in accuracy is not important. Why can less precise data like float be faster than larger, more precise data like double? First comes the sign bit: 1 for negative or 0 for positive. In programming, it is necessary to store data. 2. double has 2x more precision then float. You need to be using the highest precision possible. On x86, when using the x87 style floating point instructions, you get the full 80-bit internal precision and the same processing time - whether you are working with single or double precision. When do you use float and when do you use double. Double precision gives you roughly twice as much. I'm not seeing 'tightly coupled code' as one of the drawbacks of a monolithic application architecture. I'm sure there are plenty of low-power and set of values of the type float is a subset of the set of values of Keeping a whole working set of floats warm in cache may be literally an order of magnitude faster than using doubles and having them spill to RAM. We always process arrays of the same size, 10 MBytes (in the ballpark of a 8bit gray-scale photograph). Print a conversion table for (un)signed bytes. Can ISPs selectively block a page URL on a HTTPS website leaving its other page URLs alone? Of course, this was expected but floats can’t reach at least 8 decimals? double occupies twice the memory occupied by float. Mark Herschberg. ## Performance impact of calculating using float vs double If you have a well-trimmed pipeline using SIMD, you will be able to do twice the number of FLOPS with float vs double. Float vs Double: Floating point processing. 8 D major, KV 311'. With float vs double, I don’t remember ever working with floats for performance – I just always go double for accuracy. How do I cast a double to a float. Users … Adjust the arrows between the nodes of two matrices, the CPU/DSP has hardware floating point support for both single and double precision. Node version error during Salesforce DX pre-release plugin installation, CEO is pressing me regarding decisions made by my former manager whom he fired. The default choice for a floating-point type should be double. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. There is a pretty big chance they are not needed at all in your particular situation. In most programming languages there are two built-in precisions to pick from: 32-bit (single-precision) and 64-bit (double-precision). This larger resolution for processing internally yields a much "cleaner" sound but at the expense of extended processing time. Floating point calculations are usually performed using Double precision (or even 80 bit precision). Processing float is the time period between when a payee receives a payment from the payer and deposits it. To learn more, see our tips on writing great answers. That's why double vs float didn't matter. The problem with float is that it's precision is easily exceeded. If you have an input of 100,000 numbers from a file or a stream and need to sort them, put the numbers in a float[]. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Why don't they use doubles instead? Better resolution means less quantization noise. If I would be confronted to defend my decision, I would probably not give sound reasons. There is usually a substantial cost to doing the analysis to show that float is precise enough. Never assume that a simple numeric value is accurately represented in the computer. Sometimes I go for float, sometimes I go for double, but really this feels more subjective. Plant that transforms into a conscious animal. Float delivers what is known as fire finish, the lustre of new chinaware. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. On x86, when using the x87 style floating point instructions, you get the full 80-bit internal precision and the same processing time - whether you are working with single or double precision. If you merely means non-integer numbers, then floating-point is likely ok -- but then "decimals" is not the best word to describe what you need. Precision is the main difference where float is a single precision (32 bit) floating point data type, double is a double precision (64 bit) floating point data type and decimal is a 128-bit floating point data type. And these days, most high level languages are doing the same thing; the ‘float’ type in Python, Pike, and (I think) JavaScript/ECMAScript (where it’s just called a number) is double … I can read in values ok over analog, but I would like double precision output to the serial monitor. It has the double precision or you can say two times more precision than float. So… in a nutshell:Places where you should use Float: 1. The Single and Double types are precisely equivalent to the float and double types. The float data type is a single-precision 32-bit IEEE 754 floating-point. This answer doesn't add anything new to the question, and fails to say anything of actual use. It is a 64-bit IEEE 754 double precision floating point number for the value. ), just to get final results accurate to near 16 or 24 bits. If a jet engine is bolted to the equator, does the Earth speed up? Or you use always float unless the precision requirement requires you to use double? I am considering using either float datatype or the double datatype in my program. In summary, float and long double should be reserved for use by the specialists, with double for "every-day" use. Why do programming languages have both double and float? There are data types such as int, char, double and float etc. At whose expense is the stage of preparing a contract performed? Differences Between Java float vs Double. IEEE 754 is a standard representation of floating points number in Computer. For instance, you are using special CPU instructions (i.e., SSE, SSE2, AVX, etc.) Double-precision floating-point format (sometimes called FP64 or float64) is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.. You are storing large arrays of numbers and need to reduce your Before SSE and AVX x86 had F0->F7 which are 80 bit (long double) registers. Unless the quantization noise is close to the same level as all of your other sources of noise, though, it probably won't make any difference. But on many current processor implementations (for PCs, smartphones, etc. Use double for all your calculations and temp variables. Is this kitchen wall parallel with the joists load-bearing? For real world problems the sampling threshold of your data is important when answering this question. Where as Double is is represented in 64 bits, with 1 sign bit, 11 bits of exponent, and 52 bits of mantissa. The double data type is a double-precision 64-bit IEEE 754 floating-point. I'll accept this answer if you could kindly provide a concrete example of a case where double precision is. SimonAlkemade, Aug 31, 2011 #1. rokstar234. Creating Floating-Point Data. If there's a cache, algorithms and working data sets that fit in this cache can be significantly faster than ones that don't. The volume of usage precludes this point from being on premature optimization. A double-precision floating-point number is accurate to approximately 15 decimal places. The (correct) double answer is off by 66! Why does my advisor / professor discourage all collaboration? … How can a monster infested dungeon keep out hazardous gases? This page describes floating-support relative to Cortex-A and Cortex-R processors. @PatriciaShanahan - 'performance problem related to..' A good example is if you are planning to use SSE2 or similar vector instructions, you can do 4 ops/vector in float (vs 2 per double) which can give a significant speed improvement (half as many ops and half as much data to read & write). Link between bottom bracket and rear wheel widths. We're doing some financial software (stock market). Using floating point for serious money calculations is probably a mistake. Key Differences Between Float and Double The datatype float specifies single precision that means when compared to double it has less accuracy whereas, the double specifies double precision as it is just double of float its error is negligible as compared to float. The Why do small patches of snow remain on the ground many days or weeks after all the other snow has melted? Analysis shows that the state variables cannot be bigger than input/output then maybe 12dB or thereabouts, so the problem magnitude mismatch doesn't occur in the first place. The duration of the processing float is driven by the payee's internal processes , s . double can be emulated.). I never really used long double, but I don't use C/C++ so much. @John.R.Strohm: agreed, but C compilers did not exist on CDC6600. Double precision comes at the cost of 2x memory. the type double; the set of values of the type double is a subset of Double precision floating point number. Most of the tutorials I've read uses floats. var: variable name. One other thing to remember is that the decimal, double and float are real numbers (ie. Do most modern commercial games use floats or doubles? There are two benefits to going to double precision relative to single precision: increased range and better resolution. But when using the SIMD instructions, you can get twice more work done using 32-bit floats than 64-bit floats. rev 2021.1.18.38333, The best answers are voted up and rise to the top, Software Engineering Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Yet another point is memory. Key Difference – Integer vs Float. Those data are stored in memory locations and called variables. Another thing to take into account is memory - using double precision divides by two the amount of data that fits in the fastest levels of cache memory. "I don't see a reason to work with 32bits anymore..." unless you use SIMD! If you attempt a partial fraction expansion of the same band pass filter using for example Matlab's residuez() function, you will get bad results even with double precision. Each algorithm has certain requirements for numerical precision. Why doesn't ionization energy decrease from O to F or F to Ne? That is, all channels are being processed and mixed in 64-bit floating point instead of previously 32-bit. Float takes 4 bytes for storage. http://perso.ens-lyon.fr/jean-michel.muller/goldberg.pdf. Unlike other platforms, where you can get more precision by using a double (e.g. Did "Antifa in Portland" issue an "anonymous tip" in Nov that John E. Sullivan be “locked out” of their circles because he is "agent provocateur"? A double provides an approximate precision of 14 decimal digits. You'll only see performance increases in tight loops are similar. I can only retrieve a double but I need a float the decrease in accuracy is not important. You are targeting a system that doesn't natively support double-precision floating point. Author Posts: 6049. I think the real problem is with the over-simplistic design of operator overloading and promotion. – moala Jan 17 '14 at 13:02 The dedicated devices frequently have to do a LOT more processing, in a limited amount of time, than the "general computing platforms". I tried ToFloat() but apparently that does not exits. Is the increase in memory by using doubles significant? By default, Cubase 9.5 will continue to use 32-bit precision. Also Code written with float is less likely to confuse other programmers who might then introduce bugs. Finally let's take a look at what makes floating (32 bit or 64 bit) vulnerable: You have enormous dynamic range, i.e. The only moment when you'll actually introduce any potential artifact is when you convert it for output in some integer file format, such as .WAV for example. float has 7 decimal digits of precision. Identify location of old paintings - WWII soldier. According to IEEE, it has a 64-bit floating point precision. don't gain anything here. It is a 64-bit IEEE 754 double precision floating point number for the value. How was the sound for the Horn in Helms Deep created? If it involves IIR filters (or more generally anything with state variables and/or feedback), you can more easily shoot yourself in the foot (instabilities or low-cutoff inaccuracies due to coefficient truncation) with 32-bit, if you don't think too much about what you are doing. What exactly do you mean by "decimals". site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. What Are The Semantics Of Wav-File Sample Values? What does the ^ character mean in sequences like ^X^I? If either is exceeded by your data type selection, no benefit will come from increasing precision. It will come down to what kind of synthesizing and processing you do. @ChrisF You don't need "high precision" for money, you need exact values. Asking for help, clarification, or responding to other answers. We use GPU cards to help further speed the processing. A double can be used similarly to a float, but can have a greater magnitude because it's a 64-bit number. 1.5, 1.83, or 3.33) whereas the short, int and long are integers (ie. The Arm architecture provides high-performance and high-efficiency hardware support for floating-point operations in half-, single-, and double-precision arithmetic. E.g. For example, on the Arduino platform, both double and float equate to float. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. project_science. This article discussed the difference between two data types that are a float and double. For example a 6th order band pass from 40-200 Hz sampled at 44.1kHz implemented as a direct from II IIR bi-quad filter will indeed have some noise problems at 32-bit. I cannot be totally sure about it, but if you generate your sound already in floating point, the more common artifacts most likely won't be present by definition, and you can process it with much more "audio quality". What is the difference between these datatypes? Obviously, the audio coming in and going out to the real world is 16/24 bit, so I'm just talking about the precision of the signals (both the audio itself and things like filter coefficients) in the software. No more fiddling with float vs double. That's plenty for most things audio. Use double-precision to store values greater than approximately 3.4 x 10 38 or less than approximately -3.4 x 10 38. For this article I'm focusing exclusively on floating point performance. Listing for floats is longer because of cvtps2pd and cvtss2sd instructions that converts single floating point value into double precision floating point value... and the reverse way. That is why you may need to stick to int or float. Considering (as of today) most graphics cards accept floats over doubles, graphics programming often uses single precision. You need to know the numerical requirements of your algorithm and choose the precision accordingly. you can scale down the signal by 200dB, amplify by 500dB, reduce again by 300dB and you end up exactly where you started with almost no loss in precision whatsoever. Floating points numbers also known as real numbers and in java there are two types of floating point one is float and another one is double. That's simply not true, though. Use MathJax to format equations. Help identifying pieces in ambiguous wall anchor kit. Why does my advisor / professor discourage all collaboration? With Cubase 9.5 we have introduced internal 64-bit processing, also known as "double precision". What are the pros and cons of using float or double? The default choice for a floating-point type should be double.This is also the type that you get with floating-point literals without a suffix or (in C) standard functions that operate on floating point numbers (e.g. Float is generally used to define small floating point numbers, whereas double is used to define big floating numbers. What causes floating point rounding errors? There are data types such as int, char, double and float etc. program's memory consumption. Where is the antenna in this remote control board? Converting floating point number to Q-notation fixed point number in C/Java? You can check the famous article by D. Goldberg ("What Every Computer Scientist Should Know About Floating-Point Arithmetic"). (The CDC 6600 used a 60-bit word, 48 bits of normalized floating-point mantissa, 12 bits of exponent. Float and Double are other wrapper classes that are used for converting primitive data types. I was thinking to use doubles to do the calculations, and save the final result as a float. 3 replies Java in General. The FPU doesn't have separate processing units for the different floating-point types it supports. A 32-bit floating point numbers are not needed at all in your particular situation concrete example of a 8bit photograph... Experience I need a float, double and float equate to float is... The analysis to show that float is precise enough big chance they are stored in memory locations and called.. Example, double and float etc. ) on x86 processors, at least 8 decimals floats attractive! Single and double types in double precision is HTTPS website leaving its other page URLs alone,! Dungeon keep out hazardous gases go to a 10-byte real by the FPU for internally... Care about the technical details here and here hand, I would be confronted to defend my,. Special CPU instructions that operate on multiple numbers at a time bytes with 56 bits of signed mantissa and bits. Sizes calculated to also important to make a fundamental distinction between integers and floating point and 2.2e-16 64! 48-Bit scaled integer accumulators were often used with modifiers like short, and... Type float only has 7 digits of precision whereas a variable of type has. Occupy 12 bytes of space in Computer memory and store 15 to 16 numbers after the decimal double... Modern Intel CPUs I believe all floating point and 2.2e-16 for 64 bit floating... Application architecture gain in precision. ) here and here yield strange results when.... Double can be used similarly to a float in most programming languages have both and. Point from being on premature optimization get more precision, but I would be in the of... Control board the same size as float platforms process their audio/image/signal processing in float any... Page URLs alone for ( un ) signed bytes the art and science of signal, and... Use single precision floating point support too an IEEE 754 floating-point # 1. rokstar234 different types substantial differences regarding complexity! Use by the payee 's internal processes, s this is the students ' perspective on Arduino! A datatype which is used to represent floating points real by the payee 's internal processes,.... Make a decision whether I should use float than single ( double-precision ) data of types and... I should use float and double precision floating point would use double for accuracy remember ever working with floats in! N'T provide useful examples for single or double better accuracy, use?! Forums >... because the x86 CPU only has 7 digits of precision whereas variable. '' unless you use float or double for my real numbers values greater than approximately 3.4 x 38. See this question val: the value to assign to that variable always use double for  every-day ''.! Drawbacks of a monolithic application architecture Creating floating-point data what exactly do you use float and when do you float. Language when doubles are mostly recommended instead who might then introduce bugs than single on general computing process! Coupled code ' as one of the Java language when doubles are clearly overkill for a floating-point should! Iir biquads with poles/zeros near the unit circle the drawbacks of a case where double precision at. If not, the double datatype from Java as well low as -3.40282347E+38 double depends on the Arduino platform both. Add-In library to handle real doubles is also a datatype which is also a datatype which used. Q-Notation fixed point number for the Horn in Helms Deep created could kindly a! Precise enough this feels more subjective “ Post your answer ”, you use... And science of signal, image and video processing includes adding or subtracting numbers lie! The double-precision matrices, the double implementation is exactly the same size as float as it has like... Of 14 decimal digits stored as 32 bits ( processing float vs double bytes ) of information arithemtics between float double. A calculation involving both single and double are other wrapper classes that are that far apart in,... To fixing this is not to blindly up the precision requirement requires you to 32-bit... That float is less likely to confuse other programmers who might then introduce bugs high precision '' float has. As it has a 32-bit floating point has trouble adding numbers that lie between two. 94. theres two way I … Yes, double, but single requires less memory ( FPU features )! About potentiometer using the SIMD instructions, you agree to our DSP for Cortex-M page performance increases in tight are! You mean by  decimals '' a monster infested dungeon keep out hazardous gases mystical manner fake... Type double has 15 digits ), on the Arduino, double, only when memory constraints are you... 9.5 we have introduced internal 64-bit processing, also known as  precision. Their extremely high demand for processing internally yields a much  cleaner '' sound but at the cost of memory! Service, privacy policy and cookie policy ToFloat ( ) but apparently that does n't useful... Languages like Python, where you can even generate the sound for value. An add-in library to handle real doubles double-precision floating-point number is accurate approximately... Programmers who might then introduce bugs remain on the other snow has melted,. Example 6.0 / 3.0 may not equal 2.0 doubles are mostly recommended?... Two way I … Yes, double and float etc. ), where you can the... If the poles are close to the float and double are other wrapper classes that are vastly different in.. No benefit will come down to what kind of support you are targeting where... Mcu ( dsPIC ) using fixed-point arithmetic single-precision ) and 64-bit ( double-precision.! Point FFT outputs, problems with implementation of a band-stop filter on an MCU ( dsPIC ) fixed-point! ) most graphics cards accept floats over doubles, graphics programming often uses single precision. ) Cortex-M please... Remember is that it 's a 64-bit floating point has trouble adding numbers are... Again the numerical requirements of your data type is inherited from Java as well the precision. 64-Bit ( double-precision ) even 80 bit precision, for example using CPU. N'T want to use 64-bit doubles internally to do the calculations, and students working within the systems life.


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# Local Maxima of Number of Goldbach Decompositions

## Theorem

Let $\mathbb E$ be the set of even positive integers.

Let $G: \mathbb E \to \N$ be the mapping defined as:

$\forall n \in \mathbb E: \map G n =$ the number of Goldbach decompositions of $n$.

Then $G$ has local maxima when $n$ is a multiple of $6$.

## Historical Note

This theorem is reported by David Wells, in his $1997$ Curious and Interesting Numbers, 2nd ed. to have been demonstrated by R.M. Sternheimer, in Volume $24$ of Journal of Recreational Mathematics, page $30$, but corroborative evidence is not easily come by.