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# is no3 soluble

soluble. Le nitrate est beaucoup utilisé dans les engrais inorganiques et les explosifs, comme agent de conservation des aliments et comme substance chimique brute dans divers procédés industriels. Lv 7. 2. (full name, no spaces, all lowercase) Learn with flashcards, games, and more — for free. Sign in. Start studying Solublity Rules. Some uses in organic synthesis have been reported for example the nitration of aromatic compounds and selective oxidation of sulfides to sulfoxides. What is the balanced equation for hydrogen phosphate ion (HPO42-) acting as a Bronsted base in a reaction with water? 3)All binary compounds of the halogens (other than F) with metals are soluble, except those of Ag, Hg(I), and Pb. It is soluble in water. docphi03 . Utkarsh Calcium Nitrate (100% Water Soluble Fertilizer) Net Content: Clear: Utkarsh Calcium Nitrate - Ca(NO3)2 (100% Water Soluble Fertilizer)(Foliar Spray Irrigation) quantity. Rule: NO3- , C2H3O2- . Question = Is NO3- polar or nonpolar ? Polar "In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Similarly, what type of compound is Al no3 3? There is not any universal rule to predict whether an ionic compound will be soluble in water or not . Ag2SO4 = insoluble , NaNO3 =soluble. Is CuNo3 insoluble or soluble in water? Answer. So, yes. Toxic oxides of nitrogen are produced in fires involving this material. Barium nitrate | Ba(NO3)2 or BaN2O6 | CID 24798 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological ... pubchem.ncbi.nlm.nih.gov. No, the correct way of putting it is $$\mathrm{Almost~all~of~the~\mathbf{inorganic}~nitrate~salts~are~soluble~in~water. Alkali metal salts are always soluble in water . But there are certain facts that may be useful . CuSO4 is soluble... forms a clear, bright blue solution. Prolonged exposure to fire or heat may result in an explosion. This means that calcium nitrate is a chemical compound formed when calcium (Ca) bonds with the nitrate ion (NO3). *Fertigation is a method of fertiliser application in which fertiliser is incorporated within the irrigation water by the drip system Solubility in water, acetone, ethanol, . Due to this, it is easily soluble in water at a rate of 73.9 g/100ml at 20°C. It is also soluble in acetone, acetic acid and glycerol but practically insoluble in ethanol and ethyl acetate. Which of the following is/are soluble in aqueous ammonia, but not in cold or hot water (choose all that apply) PbI2 AgCl AgNO3 PbCl2 Pb(NO3)2. 0 0. Sodium nitrate is the chemical compound with the formula Na N O 3.This alkali metal nitrate salt is also known as Chile saltpeter (large deposits of which were historically mined in Chile) to distinguish it from ordinary saltpeter, potassium nitrate.The mineral form is also known as nitratine, nitratite or soda niter.. ou un ester (nitrate d'éthyle, nitrate d'amyle, nitrate de cellulose, etc.) Be the first to answer this question. Co(NO3)2 ( Cobalt(II) nitrate ) is Soluble I'll tell you the Soluble or Insoluble bond list below. Polar molecules must contain polar bonds due to a difference in electronegativity between the bonded atoms. phosphates of alkali ions (Li+,Na+,K+,Rb+,Cs+,Fr+) and NH4+ are soluble . Some bright examples are (R) & (S)-miconazole nitrates, isoconazole nitrate and econazol nitrate.Econazol nitrate (Other names: Spectazole, EN) is the most common organic nitrate … Some acids, such as HCl, are strong electrolytes. 33 M K2SO4 the answer in mol/L. Chromium(III) nitrate compounds are of a limited importance commercially, finding some applications in the dyeing industry. CoCl2= soluble CaCl2 = soluble. 0 0. 1, 2, and 3. How to solve: Is Mg(OH)2 soluble or insoluble? The alloy of copper (Cu) and nobelium (No) CuNo3 has probably never been produced since it is very difficult to produce and work with the radioactive element No. so calcium nitrate is soluble. Aluminum nitrate is a solid compound according to the Standard Temperature and Pressure. The resulting aquatic solutions are acidic while aluminum nitrate does not dissolve well in alcohols. (Y or N, do not name exceptions) Compounds containing these ions are soluble. Anonymous. }$$ The families of organic nitrate salts are typically nitrates of azoles and imidazoles. Ag+ and NO3- is not just going to combine to give you solid silver nitrate because it is totally soluble in water, once any solid forms, it'll just dissolve and form the. 4) All sulfates are soluble, except those of barium, strontium, calcium, lead, silver, and mercury (I). Write the formulas for the ions that interact with water as shown in the models when… Most common is the dark violet hydrated solid, but an anhydrous green form is also known. the following are the alllllwayyss solubles: 1) alkali metals (group 1a) 2)amomonia (nh4) 3)nitrate(no3) 4)acetic (c2h3o2) these are soluble with exceptions. all nitrates are soluble . If you want to quickly find the word you want to search, use Ctrl + F, then type the word you want to search. 3. It is used in Be the first to answer! . So it is aqueous (aq) because all the compounds are soluble on both sides of the reaction then there is no reaction. LiI. Register to get answer . As products, sodium nitrate is predicted to be soluble (rules 1 and 2) and will be dissociated. They are . 1)cl, br, i -----are soluble except if the other element is...silver,mrecury,or lead. NaClO3 can be more soluble than KNO3 at different temperatures, but it is not seen that KNO3 is more soluble than NaClO3. Add to cart. So yes Pb(NO3)2 is soluble. BaI 2. soluble. 0 0 1. It varieties a comfortable stability simply by right here equilibrium reaction: H20 --> H+ + OH- This phenomenon is termed autoionization. Soluble or Insoluble? Is Mg3(PO4)2 soluble? soluble - soluble (more than 1g per 100g of water) low - low solubility (0.01g to 1g per 100g of water) insoluble - insoluble (less than 0.01g per 100g of water) not exist - do not exist in the aqueous environment . To find more Chromium(III) nitrate information like chemical properties, structure, melting point, boiling point, density, molecular formula, molecular weight, physical properties and toxicity information. AgCl = insoluble , Co( NO3)2 = soluble. Do these ions have exceptions? Pb(NO3)2 is soluble in water. All nitrates are soluble in water. Mainly because of cation/anion radii ratio and is no3 soluble ions ’ packing efficiency will dissociated... If large quantities are involved in a reaction with water, Ca ( NO3 ) is... Ca ) bonds with the nitrate ion ( NO3 ) 2 is soluble in water NH4+! Solutions are acidic while aluminum nitrate does not dissolve well in alcohols certain facts that may be useful can more! Toxic oxides of nitrogen are produced in fires involving this material phosphates alkali... Nitrate d'amyle, nitrate de cellulose, etc. except if the other is...!!!!!!!!!!!!!... Acetates, and more with flashcards, games, and more with flashcards games! Finding if things are soluble KNO3 and NaClO3 have the same solubility at approximately 95.! Amounts of water learn vocabulary, terms, and more with flashcards, games, and other study tools cl! 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# Third-Order Texture Filtering using Linear Interpolation

A straightfoward implementation of bi- or tricubic texture filtering requires lots of texture lookups. As texture lookups are slow on current graphics hardware, reducing their number greatly improves the performance of high-order filtering kernels. In contrast, linear interpolation is relatively cheap as it is supported by the hardware. This fact has been exploited by Sigg and Hadwiger (2005) to make cubic interpolation much faster by performing a series of linear texture lookups. In this article, an in-depth explanation of their technique is given, starting with some general information on linear interpolation and approximation using cubic B-splines.

At first, we will focus on the one dimensional case. Suppose we have two data points $f_i$ and $f_{i+1}$ and we want to interpolate the values between these points. Using linear interpolation, this results in the following equation:

$f(t) = w_0(t) f_i + w_1(t) f_{i+1} = (1-t) f_i + t f_{i+1}$,

where $0 \le t \le 1$. The functions $w_0(t)=1-t$ and $w_1(t)=t$ determine the filtering weight for each point. The values are interpolated such that $f(t)$ is $f_i$ at $t=0$ and $f_{i+1}$ at $t=1$. The following images show the liner basis functions (left) and the result of interpolating some points (right):

The formula is automatically evaluated on the GPU if linear filtering is activated in OpenGL and, for example, texture is used in the fragment shader to fetch a texel from texture memory.

If we want to use cubic filtering, we have to use the following formula:

$f(t) = w_0(t) f_{i-1} + w_1(t) f_i + w_2(t) f_{i+1} + w_3(t) f_{i+2}$,

where $w_j(t)$ are now third-order polynomials. We will choose weightings based on uniform cubic B-splines, so the weighting functions become

$w_0(t) = \frac{1}{6} (-t^3 + 3t^2 - t + 1) \\ w_1(t) = \frac{1}{6} (3t^3 - 6t^2 + 4) \\ w_2(t) = \frac{1}{6} (-3t^3 + 3t^2 + 3t + 1) \\ w_3(t) = \frac{1}{6} t^3$.

Although four points $f_{i-1} ... f_{i+2}$ are used, the function constructs only points between $f_i$ and $f_{i+1}$ for $0 \le t \le 1$. This range is called a segment of the curve. However, rather than interpolating the points $f_{i}$ and $f_{i+1}$ as above, $f(t)$ only approximates the values now. That means that at $t=0$ and $t=1$, $f(t)$ does not pass through the data points $f_i$ and $f_{i+1}$. Nevertheless, the resulting function is geometrically continuous, as the approximated value at $t=1$ of a segment is the same as the approximated value at $t=0$ of the next segment. This is shown on the following image on the right (left: cubic B-spline basis functions). Note that the curve does not pass through the blue dots and that the first and last segment is missing.

As we can see from the equation for cubic interpolation, four texture lookups are necessary. This becomes even worse in two and three dimensions, where 16 and 64 lookups are required, respectively. As mentioned in the introduction, it is possible to replace a cubic interpolation by a sequence of linear interpolations. As a result, in 1D the 4 lookups can be reduced to 2 linear lookups. The 16 lookups in 2D can be replaced by 4 linear lookups, the 64 lookups in 3D by 8. In general, $4^n$ lookups are replaced by $2^n$ linear lookups.

Now, let’s focus on how the optimization works. Actually, it is pretty simple: just write the cubic interpolation as the sum of two linear interpolations:

$f(t) = \underbrace{w_0(t) f_{i-1} + w_1(t) f_i}_{\text{First linear interpolation}} + \underbrace{w_2(t) f_{i+1} + w_3(t) f_{i+2}}_{\text{Second linear interpolation}}$.

For this purpose, let’s first find a notation for the operation that the graphics card executes when performing a linear texture lookup:

$f(t) = (1-t) f_i + t f_{i+1} = f_{i+t}$.

That shows that when we want to interpolate between two texels, we just extract a constant from texture memory at $f_{i+t}$. However, that is not sufficient if we want to write weighted sums $a f_{i} + b f_{i+1}$ with two weights $a$ and $b$ as linear interpolation. So, we have to scale $a$ and $b$, resulting in the new variables $a'$ and $b'$ with $a'+b'=1$:

$a' = \frac{a}{a+b} \\ b' = \frac{b}{a+b}$.

Then, we write the sum as follows:

$(a+b) (a' f_{i} + b' f_{i+1}) = (a+b) ((1-b') f_{i} + b' f_{i+1})$.

Notice that this looks exactly like an ordinary linear interpolation, scaled by the factor $a+b$. Using the above notation, the weighted sum becomes

$a f_{i} + b f_{i+1} = (a+b) f_{i+\frac{b}{a+b}}$.

There is a small restriction: it only works if $0 \le \frac{b}{a+b} \le 1$. Fortunately, that is satisfied when using cubic B-splines.

Finally, third-order texture filtering is obtained by the following two linear interpolations:

$f(t) = (w_0(t) + w_1(t)) f_{i-1+\frac{w_1(t)}{w_0(t) + w_1(t)}} \\ ~~~~~~ + (w_2(t) + w_3(t)) f_{i+1+\frac{w_3(t)}{w_2(t) + w_3(t)}}$.

In conclusion, this post has presented an efficient technique for third-order texture filtering in 1D based on hardware-accelerated linear interpolation. In the next post, this will be extended to two and three dimensions, where the performance gain is much more significant.

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American Institute of Mathematical Sciences

December  2011, 1(4): 437-468. doi: 10.3934/mcrf.2011.1.437

Pathwise Taylor expansions for Itô random fields

 1 Département de Mathématiques, Université de Bretagne-Occidentale, CS 93837, F-29238 Brest cedex 3, France 2 Universität Greifswald Institut für Mathematik und Informatik, Walther-Rathenau-Straβe 47, 17487 Greifswald, Germany 3 Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States

Received  August 2010 Revised  June 2011 Published  November 2011

In this paper we study the pathwise stochastic Taylor expansion, in the sense of our previous work [3], for a class of Itô-type random fields in which the diffusion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an "self-exciting" type particularly contains the fully nonlinear stochastic PDEs of curvature driven diffusion, as well as certain stochastic Hamilton-Jacobi-Bellman equations. We introduce the new notion of "$n$-fold" derivatives of a random field, as a fundamental device to cope with the special self-exciting nature. Unlike our previous work [3], our new expansion can be defined around any random time-space point (τ,ξ), where the temporal component τ does not even have to be a stopping time. Moreover, the exceptional null set is independent of the choice of the random point (τ,ξ). As an application, we show how this new form of pathwise Taylor expansion could lead to a different treatment of the stochastic characteristics for a class of fully nonlinear SPDEs whose diffusion term involves both the solution and its gradient, and hence lead to a definition of the stochastic viscosity solution for such SPDEs, which is new in the literature, and potentially of essential importance in stochastic control theory.
Citation: Rainer Buckdahn, Ingo Bulla, Jin Ma. Pathwise Taylor expansions for Itô random fields. Mathematical Control and Related Fields, 2011, 1 (4) : 437-468. doi: 10.3934/mcrf.2011.1.437
References:
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# Solution for equation of 2,3,4, degree

1. Mar 26, 2014

### Jhenrique

I noticed that is always possible to find the roots of polynomials of kind:
$A\lambda^2 + B$
$A\lambda^3 + B$
$A\lambda^4 + B$
$A\lambda^5 + B$

So I thought to transform the quadratic, the cubic, the quartic and the quintic function in the forms above, look:

$ax^3+bx^2+cx+d=0$

$(x=\lambda+u+v)$

$a(\lambda+u+v)^3+b(\lambda+u+v)^2+c(\lambda+u+v)+d=0$

$\\a \left ( \begin{matrix} \lambda^3 & +3\lambda^2u & +3\lambda u^2 & +u^3\\ +3\lambda^2v & +6\lambda u v & +3u^2 v & \\ +3\lambda v^2 & +3uv^2 & & \\ +v^3 & & & \\ \end{matrix} \right ) + b \left ( \begin{matrix} \lambda^2 & +2\lambda u & +u^2\\ +2\lambda v & +2 u v & \\ +v^2 & & \end{matrix} \right ) + c (\lambda + u + v) + d = 0$

$a\lambda^3+(3a(u+v)+b)\lambda^2+(3a(u+v)^2 + 2b(u+v) + c)\lambda + (a(u+v)^3 + b(u+v)^2 + c(u+v) + d) = 0$

So, comparing the equations:

$A\lambda^3 + B = a\lambda^3+(3a(u+v)+b)\lambda^2+(3a(u+v)^2 + 2b(u+v) + c)\lambda + (a(u+v)^3 + b(u+v)^2 + c(u+v) + d) = 0$

implies that:
$\begin{cases} A=a\\ 0=(3a(u+v)+b)\\ 0=(3a(u+v)^2 + 2b(u+v) + c)\\ B=(a(u+v)^3 + b(u+v)^2 + c(u+v) + d)\\ \end{cases}$

So,
$A\lambda^3 + B = 0\;\;\;\Rightarrow\;\;\;\;\lambda = \sqrt[3]{\frac{-B}{A}} \;\;\;\Rightarrow\;\;\;\; x-u-v = \sqrt[3]{\frac{-B}{A}} \;\;\;\Rightarrow\;\;\;\; x = \sqrt[3]{\frac{-B}{A}} + (u+v)\;\;\;\Rightarrow\;\;\;\; x = \sqrt[3]{\frac{-(a(u+v)^3 + b(u+v)^2 + c(u+v) + d)}{a}} + (u+v)$

Happens that
$0=3a(u+v)+b\;\;\;\Rightarrow\;\;\;\;u+v = \frac{-b}{3a}$

Conclusion:
$$x=\sqrt[3]{\frac{d}{a}-\frac{2b^3}{3^3a^3}-\frac{bc}{3a^2}}-\frac{b}{3a}$$

This ideia is correct?

2. Mar 26, 2014

### micromass

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Line

(Redirected from Lines)
Figure 1. A line is the intersection of a 4D bivector with the 3D subspace where $$w = 1$$.

In the 4D projective geometric algebra $$\mathcal G_{3,0,1}$$, a line $$\mathbf L$$ is a bivector having the general form

$$\mathbf L = v_x \mathbf e_{41} + v_y \mathbf e_{42} + v_z \mathbf e_{43} + m_x \mathbf e_{23} + m_y \mathbf e_{31} + m_z \mathbf e_{12}$$ .

The components $$(v_x, v_y, v_z)$$ correspond to the line's direction, and the components $$(m_x, m_y, m_z)$$ correspond to the line's moment. To possess the geometric property, the components of $$\mathbf L$$ must satisfy the equation

$$v_x m_x + v_y m_y + v_z m_z = 0$$ ,

which means that, when regarded as vectors, the direction and moment of a line are perpendicular.

The bulk of a line is given by its $$m_x$$, $$m_y$$, and $$m_z$$ coordinates, and the weight of a line is given by its $$v_x$$, $$v_y$$, and $$v_z$$ coordinates. A line is unitized when $$v_x^2 + v_y^2 + v_z^2 = 1$$.

When used as an operator in the sandwich product, a unitized line is a specific kind of motor that performs a 180-degree rotation about itself.

Lines at Infinity

Figure 2. A line at infinity consists of all points at infinity in directions perpendicular to the moment $$\mathbf m$$.

If the weight of a line is zero (i.e., its $$v_x$$, $$v_y$$, and $$v_z$$ coordinates are all zero), then the line lies at infinity in all directions perpendicular to its moment $$(m_x, m_y, m_z)$$, regarded as a vector, as shown in Figure 2. Such a line cannot be unitized, but it can be normalized by dividing by its bulk norm.

When the moment $$\mathbf m$$ is regarded as a bivector, a line at infinity can be thought of as all directions $$\mathbf v$$ parallel to the moment, which satisfy $$\mathbf m \wedge \mathbf v = 0$$.

Skew Lines

Figure 3. The line $$\mathbf J$$ connecting skew lines is given by a commutator.

Given two skew $$\mathbf K$$ and $$\mathbf L$$, as shown in Figure 3, a third line $$\mathbf J$$ that contains a point on each of the lines $$\mathbf K$$ and $$\mathbf L$$ is given by the commutator

$$\mathbf J = [\mathbf K, \mathbf L]^{\Large\unicode{x27C7}}_- = (v_yw_z - v_zw_y)\mathbf e_{41} + (v_zw_x - v_xw_z)\mathbf e_{42} + (v_xw_y - v_yw_x)\mathbf e_{43} + (v_yn_z - v_zn_y + m_yw_z - m_zw_y)\mathbf e_{23} + (v_zn_x - v_xn_z + m_zw_x - m_xw_z)\mathbf e_{31} + (v_xn_y - v_yn_x + m_xw_y - m_yw_x)\mathbf e_{12}$$ .

The direction of $$\mathbf J$$ is perpendicular to the directions of $$\mathbf K$$ and $$\mathbf L$$, and it contains the closest points of approach between $$\mathbf K$$ and $$\mathbf L$$.


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text:
# finding value of x for an equation

if we have an equation of form $y=x^{nx+1}$ and if we are given the values of $y$ and $n$ then how can one find $x$? I have reduced the equation to $\log(y)/\log(x)=nx+1$ but can't proceed further. Is there some kind of standard equation? Thanks

-

There is no solution in terms of the standard functions of calculus (powers, roots, logs, exponentials, trig functions, inverse trig functions). There are numerical methods for getting good approximate answers (the best ones rely on Calculus). It may be possible to express solutions in terms of the Lambert-W function, which you might want to look up.

-
thanks Gerry, i tried to find approximate value by differentiating both sides with respect to x . On taking double differentiation to find the value of X , I get X=2/n but i don't think its correct . – pranay Jun 16 '12 at 14:12
If you know about differentiation then you should look up "Newton's Method." $x=2/n$ can't possibly be correct, even as an approximate answer; for one thing, it doesn't involve $y$. – Gerry Myerson Jun 16 '12 at 22:15

A quick search on Google reveals the page http://mathforum.org/library/drmath/view/70483.html, where Doctor Vogler points out that the function $f(X) = x^x$ is not injective, since $$(\frac{1}{2})^{(1/2)} = (\frac{1}{4})^{(1/4)}.$$ However, he points out that it is possible to restrict the domain of the function so that it is injective. Nevertheless, I'm inclined to think that due to this observation, no notation may have been invented specifically for the inverse of this function, unlike other functions such as $f(x) = e^x$ which have inverses like $f^{-1}(x)=ln(x)$.

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thanks Andrew for the information – pranay Jun 16 '12 at 14:15

To solve an equation like this you need the generalized Lambert's function.

First of all apply natural log on both sides:

$(nx+1)\ln x=\ln y$

Now rewrite $x$ as:

$(ne^{\ln x}+1)\ln x=\ln y$

So we can rewrite the equation in the form:

$e^{\ln x}\ln x+\frac 1n \ln x=\frac 1n \ln y$

Then apply the generalized Lambert function (you can read about that here http://arxiv.org/pdf/1408.3999v1.pdf):

$\ln x=W_{\frac 1n}(\frac 1n \ln y)$

$$x=e^{W_{\frac 1n}(\frac 1n \ln y)}$$

-


text:
# Navigating YouTrack Issues

I used to use YouTrack to track all issues. Some times I need to open an issue in YouTrack by number. This usually happens if team-mate says me a number or if I see only a issue id without a link. My solution is to crate a small .bat file placed in the system path.

Source of my TW.bat:
explorer
http://www.jetbrains.net/tracker/issue/TW-%1

Now to open an issue I do the following:
- press WIN + R
- type tw <space> <issue number>
- press ENTER

For me this work as fast as possible.


text:
Home Excel-VBA: Get numeric value from alphanumeric

# Excel-VBA: Get numeric value from alphanumeric

user7348
1#
user7348 Published in September 19, 2018, 9:09 am

I have a column (Column A) which has alphanumeric text and I want to read it and write it back to another column (Column C). The code is;

Sub getnumber()

'Define Variable
Dim anicode As Variant
Dim n As Long
Dim lastrowdata As Long

'Data Location
Sheets("Sheet1").Activate
lastrowdata = range("A2").end(xlDown).Row - 1

'Redefine Array
ReDim anicode(lastrowdata)

For n = 1 To lastrowdata
anicode(n) = Sheets("Sheet1").Cells(1 + n, 1)
Next n

'Altering Data
For n = 1 To lastrowdata
If IsNumeric(anicode(n)) Then
anicode(n) = NumericOnly
Else
End If
Next n

'Write Data
For n = 1 To lastrowdata
Sheets("Sheet1").Cells(1 + n, 3) = anicode(n)
Next n

End Sub

I am stuck at the Altering Data part where I want to get value from the text only. I only new in VBA and only know IsNumeric function currently. In the column A, the data is alphanumeric and is random, where it might have dash (-) or space ( ) or even jumble up with alphabet such as S2 or X4. There is possibility that the data is only numeric (since the data is long ~8k and will be growing).

As examples; in Column A, I have

R1-Adapa S2
R3-Omis 14
R4-189

and in Column C, I would like to have the numeric only

R1-002
R2-002
R3-014
R4-189

Appreciate if any possible function or any opinion regarding my problems or on my code. Thanks stackoverflow.com

• What if in A column we have Adapa S11 or R1-Adapa S2500? – Michał Turczyn Apr 17 at 5:18
• @MichałTurczyn for Adapa S11 will give result 011. The data only has max of 3 digits. Though, if it has above 3, it will be 2500. yet, I am sure that the value is up till 3 digits only. – Mohamad Faisal Apr 17 at 5:25


text:
# News

Hackers donate 90% of profit to charity 2019/06/13

Bob Goudriaan successor of Marc Gauw 2017/10/12

# Project Mail::Box final report

[Mark Overmeer, MARKOV Solutions, 4 January 2004]

## Introduction

Early 2002, foundation Stichting NLnet offered Mark Overmeer a grant to improve the development and user support for the Mail::Box software he had developed. The project started in May 2002, and was extended into a follow-up in January 2003. In December 2003, NLnet's involvement ends with this project final paper.

Mail::Box is an Open Source software library for the Perl programming language. It is designed to help (mainly system administrators) implement automatic e-mail processing. For instance, it can be used to create automatic replies on incoming e-mail, do spam and virus filtering, and implement web-based e-mail clients. The software is released under GPL.

This document describes the contributions to Mail::Box realized with the generous grant of Stichting NLnet. After completion of this sponsored project, the module will continue to be supported on voluntary basis.

## Software Development

One of the areas covered by the project plan was pure software development, targeted to provide more "weight" to the library. Development took place on different aspects, of which the most important are listed below.

Main concerns during the development were

• What do people want to do with automated e-mail scripts?
• How to provide the user with an interface which is so simple that mistakes against the rules (the RFCs) are hard to make.
• How do people want to do things? There are many different ways to construct a reply message, but in the library they should be handled in one place with a uniform and simple interface. Designing this interface is one of the most complex aspects of software development.
• All actions are without any user interaction: it must be able to run in stand-alone scripts. This requires a flexible approach on the input. For instance, the user expects to create an "in-lined" reply on an arriving text message, however a nested multi-part message with only binary information comes in... Still, the reply should be correct and look nice.
• The implementation must be platform independent and secure.
• Everything must be documented, and the source code understandable.

These criteria are the main difference between the other e-mail related Perl modules and Mail::Box: other software only provides low level operations on simple messages, and expects users to create the smarter functionality.

### Releases

The software is released under the GNU Public License (GPL), which means that everybody is free to use and redistribute it. Fixes and extensions made to the software must be made public, which in this case actually resulted in some contributions.

As release model was chosen for a "release often" policy: new releases are made frequently. Each release contains bug-fixes and new features. Feedback about the release is swiftly handled to improve the next release.

For a project with only one developer, it is not practicle to use a system with a development branch and a stable branch. When a new release doesn't break existing code, the need for a stable branch is even lower. Mail::Box therefore used a single track release schedule.

When the NLnet project took off, Mail::Box 2.012 was current. At the end of the supported period, release 2.052 was reached. This gives an average of one release every two weeks, forty releases in total. Only a few of these releases were emergency fixes, which is a consequence of the release policy.

### New features

The next sections will give some details about major developments during the time span of the project funded by NLnet.

#### New folder types

Folders (also named mailboxes), are used to store groups of e-mail messages. When the project started, only the Mbox, MH were supported. These types are the most popular types on Unix systems. However, the target of Mail::Box is to create a folder type independent interface, which is usable on as many different platforms as possible.

Maildir support was the first one to be added. It was already in a rough implementation at the start of the project, and finished in one of the early releases: version 2.015, June 2002.

In a joined effort with Liz Mattijsen, a POP3 connector was implemented. This full implementation of the POP3 protocol has nice extra features, like invisibly reconnecting lost connections to the server. POP3 was first released with version 2.027, October 2002.

Likewise, based on software from Tassilo von Parseval, access to Outlook DBX folders was implemented. The closed nature of this Microsoft format makes it impossible to provide write access to these folders, but read access is enough to move e-mail archives away from Outlook into Open Source folder types. Included since version 2.042, May 2003.

David J. Kernen wrote an IMAP4 protocol handler. That handler was used to create a back-end to that popular folder type, were the messages resides on a remote server. Not all features are implemented yet, but an alpha version was released in December 2003.

The main complication of the implementation is the level of portability and auto-configuration which should take place. In general, with Mail::Box the user's program doesn't need to know how the messages are stored. At the same time, much effort is put in optimizing performance in folder type dependent ways.

#### Message construction

New ways to create and process messages were added. In all these extensions, the implementation tries to protect the user from mistakes against the official rules of the RFCs. It is hard to grasp the content of the (at least) five e-mail related standards, so people should be kept away from that when possible.

Next to the reply, forward, and build --which already existed but saw some improvements--, new read and rebuild actions were added. "Rebuild" can be used to add plain text alternatives to html message parts, remove structural complexity, and such. "Rebuild" was added in release 2.041, May 2003.

#### Unicode

Due to its origin in the United States, e-mail is using 7 bits ASCII. However, the current e-mail standards support the encoding of character sets used in other parts of the world. Mail::Box received a simple way to decode and encode these "foreign" characters, although this has a negative effect on performance. Unicode features have been added over time, and can not be pin-pointed to a certain release.

#### Field groups

Each (MIME compliant) e-mail message starts with a set of lines describing the content of the message and the transportation process. Mail::Box got ways to handle sets of these lines which are related.

For instance, a header may contain multiple Received} lines, showing the intermediate computers which were used to transport the message from the sender to the destination. These lines can be accompanied by a few more lines. The lines are not very useful, and can hence be removed per group or all together, saving disk space. But they can also easily be inspected and constructed. ResentGroups are included since release 2.023, September 2002.

Header fields added by mailing-list software can be recognized (and removed) as well as fields produced by spam-fighting software. A connection to the popular SpamAssassin software was made. More use in the area of spam-fighting software is expected, as result of the ever growing amount of unsolicited e-mail. ListGroups were introduced with release 2.044 in July 2003. SpamGroups were added in 2.048, released in August 2003.

#### Web-based clients

Maybe the most important application for Perl based e-mail scripting has to do with web-based mail applications. To simplify this task for system developers, the module HTML::FromMail was created. It provides template systems to implement a web-mail client, taking care of many complicated tasks. The thing left for the mail-client developer is to add interactivity and layout. HTML::FromMail saw daylight in October 2003.

### Performance

Various approaches were taken to improve performance. For one: many methods in the library implement alternatives, and the user can decide which alternative is fastest in his or her case. Usually, the automatic decision is the best.

A good example of this smart behavior, is the way a message's body is stored when the program is run. It can be stored as one large string, a set of lines, or as temporary file on disk. For the functionality it's all the same, but it depends on the size of the message and the way it is used which version of storage performs best. The best way to keep the body data, is simply remember where to find it, and not get it at all unless needed. This lazy behavior has been implemented in many of the library's features.

Besides the lazy implementation, there have been some real performance improvements. The two best gains (up to 20% gain each) were reached by rewriting existing Perl components. An optional message parser, implemented in C, has a benefit as well. The C parser's first release became available in December 2002.

Mail::Box was developed for automated e-mail handling, but is in the current state and on new PCs, fast enough for user applications. Some functionality required for interactive applications could be added to simplify the task of the user client developers.

## Documentation

The best way to improve the acceptance of software by a community, is with better documentation. Mail::Box has grown quite large, and it will never be easy to learn how to use such a large library. But without good documentation you are lost for sure.

The standard way of documenting Perl was not sufficient for a code base of this size. Therefore, Perl's documentation system was extended with new syntax and a new tool to produce an homogeneous set of manual pages. These pages are indexed in various ways, and contain many examples and detailed explanations of concepts. The statistics at the end of the project:

 Classes (and manuals) 128 Documented methods 931 Documented diagnostics 165 Shown examples 228

Probably the easiest way to find the right methods to do a certain task, is by browsing through the HTML version of the documentation. This was all realized during the project.

The documentation tool has been released as separate product, named OODoc: Object Oriented Documentation.

## Promotion

Providing a good implementation is one side of the story, but growing an user community is even more important for a successful product. Therefore, quite some promotional activities were initiated.

### Mailing-list

In an attempt to get people reacting on each other's use of Mail::Box a mailing-list was started. There is quite some activity on the list, but this is mainly related to mistakes in user code and bugs in the library. It did not really contribute to joint development.

The mailing-list started in May 2002. In February 2003, it had 70 members. At the end of the project in December 2003, 118 people followed the list.

 Jan 2003 132 messages Feb 2003 138 messages Mar 2003 92 messages (from May 20) Apr 2003 104 messages May 2002 7 messages May 2003 69 messages Jun 2002 73 messages Jun 2003 22 messages Jul 2002 25 messages Jul 2003 68 messages Aug 2002 79 messages Aug 2003 45 messages Sep 2002 53 messages Sep 2003 34 messages Oct 2002 76 messages Oct 2003 26 messages Nov 2002 57 messages Nov 2003 47 messages Dec 2002 64 messages Dec 2003 33 messages (till Dec 6)

The usage statistics of the list's archive , show a very irregular pattern, mainly driven by major changes in the library.

On the other hand, the mailing-list statistics are only showing a part of all traffic: to avoid boring other list members, bug hunts usually took place off-list. The mailing-list received 1244 messages, while Mark's personal archive adds up to 3500 (of which about half written by me). It is clear that answering messages consumed a lot of time... for the 19 months of the project, this means 8.8 message per workday, or 22 per sponsored workday.

### Conferences

Mail::Box was promoted in various ways, but mainly by giving talks on various (Perl) conferences. Preparations of the abstracts, papers, and slides consumed more time than planned for the project. NLnet sponsored mainly the travel and stay.

SANE 2002 in Maastricht, The Netherlands
a 45 minutes contribution on the use of Mail::Box for system administration, entitled "E-mail with Perl". (UNIX system and network administrators conference)
YAPC::Europe 2002 in Munich, Germany
A three hours tutorial "E-mail programming with Mail::Box", 45 minutes talk on software development of large libraries, and 7 minutes about the Mail::Box spin-off module Object::Realize::Later. (European Perl conference)
German Perl Workshop 2003 in Bonn
45 minutes talk on the Mail::Box spin-off User::Identity, 15 minutes about Unicode e-mail headers.
YAPC::NA 2003 in Boca Raton, Florida, USA
90 minutes tutorial on Mail::Box, 20 minutes for OODoc, and 5 minutes for Object::Realize::Later. (North-American Perl conference)
YAPC::EU 2003 in Paris, France
new 95 minutes tutorial on Mail::Box.

### Attracting external developers

Op

en Source projects must have a community to be successful. They do not only require a group of users --supporting each other with the use of software--, but should also have a group of developers which can supplement each other in the development process. A project which is developed by only one person, like Mail::Box, may collapse when that one person stops development, for instance by illness or lack of time.

In the ideal situation, a group of active developers with comparable influence are in control. This can be found in FreeBSD, Gnome, and KDE development teams. However, the Linux kernel development has only a very small group of people on top, which do not call themselves {\it a team}. But that also shows to work. Many smaller applications depend on the effort of one person. When that developer stops its work, the product starts to faint away, which may take many years. For instance, the XV image displayer hasn't been changed since 1994, but is still distributed with the latest SuSE Linux.

During this Mail::Box project, effort was made to attract developers for the module, to try to shape {\it a team}. Time was reserved to encourage people to participate in development. However, this did not succeed.

One way to get people helping a hand, is by explicitly tackling their problems with the existing code. That way, a person relation is built, which may grow active developers. Every few months, the members of the mailing-list were asked for their needs. This always brought some life to the list, and some ideas to work on, but no code contributions.

Furthermore, each time someone spoke about their own application using Mail::Box, that person was invited to contribute the code as part of the module. People were not unwilling, but the conversion from an application which suites personal needs into code which is usable for other people is huge: much higher requirements on configuration, documentation, and automated testing. In some cases, the employer did not permit the contribution.

As test-case, it was planned to find someone to implement IMAP4 support. No less than four people offered to implement this, over time. Still, each time the good intentions faded when the complexity of the required code came clear to the volunteer. The POP3 protocol was much easier. Liz Mattijsen offered to implement it, and (once started) there was an full implementation within two weeks.

An other complication to get spontaneous code contributions, is the size of Mail::Box. Combined with its Object Oriented coding style, with up to 5 levels of inheritance, it is not easy to get a good feeling about the internals. It is hard to figure-out what the best spot for a new functionality is, and often some existing functionality has to be rewritten, redesigned, or relocated.

Many programmers do not feel capable enough to write code which is usable by other people: they hesitate to show their programs. To be honest: usually they are right. Getting them to release code requires a lot of guidance; many long e-mails explaining how to produce better code. Only a few reach a publishable level.

After 19 months, the number of received code patches has increased, but these are all quite small patches: never more than a few lines. No-one has offered to join core code development. Which is a shame.

### Deployment

Mail::Box has found deployment in different areas. Most of these applications are hidden to the outside world: it is in most cases part of a company's internal infrastructure. Often, it is used to clean-up e-mail archives or handle databases containing messages.

To name a few applications:

• In Taiwan, a Pen-Pal mailing system has been created to connect secondary school pupils. Mail::Box is used to shape virtual groups.
• The YMB Antispam Project is one of many experimental spam filter tools which are based on Mail::Box.
• PerlWebmail implements (as its name implies) a web-based e-mail client. It does not use HTML::FromMail, for one because that module did not exist at the moment of its design.
• Conversion is on its way for tkMail, a Perl/Tk graphical e-mail client. It was based on older Perl e-mail libraries, but needed the Unicode features --new versions of the Tk library have full support for Unicode. (The tkMail command is distributed as part of Perl's Tk library release.)
\end{itemize}

## Spin-offs

The Mail::Box development has resulted in a few modules which can also be used with other applications than purely e-mail related. These modules are

MIME::Types
is a collection of knowledge about MIME types, which can be used to map file-name extensions to types, vice versa.
OODoc
is a system to document complex (probably large, often Object Oriented) modules.
Object::Realize::Later
is a tricky module to implement lazy (delayed) creation of objects, which improves performance. This attracted a lot of attention from hard-core Perl programmers,
User::Identity
plays smart about user information, like deriving someone's probable language preference from an e-mail address. Or discovering a person's gender from a full name description in multiple languages.

## Acknowledgements

Special gratitude to Stichting NLnet for offering me the chance to work on this free software package. With the help of NLnet, the Perl software base is enriched with a powerful library, which in time, may become the basis of the next generation e-mail applications.

The following people contributed. Some contributed documentation, other send in patches or bug reports. Major contributors are marked with (*).

 Adam Augustine Gilles Darold Mike Cudmore Adam Byrtek 'alpha' Greg Matheson* Mike Mimic Alan Kelm* James Sanford Nick Ing-Simmons Albert Schueller Jan Stapel Nik Clayton Alex Liberman Jason Woodward Paul Simons alex Jeff Squyres Phil Hagen Alexander Bauer Jeffrey Friedl Phil Holden Andre Schultze Jeremy Banks Pjotr Prins Andreas Fitzner Jerrad Pierce Rob Holland Andreas M. Riechert Joe Junkin Robin Berjon Andreas Piper John B Batzel Ron Savage Anthony D. Urso Jon Thomason Ronnie Paskin asta Jost Krieger Sebastian Krahmer Beirne Konarski Karen Craven Sebastian Willert Benjamin Pineau Kees Dekker Shagren Bernd Patolla Kingpin Simon Cozens Bill Moseley Liz Mattijsen* Simon von Janowsky Blair Zajac* Lutz Gehlen Slaven Rezic Brian Grossman Marcel Gruenauer Stefan Wolfsheimer Christoph Dahl Marcel de Boer Steve Lewis Conrad Heiney Mark Ethan Trostler Steven Benson Constantin Khatsckevich Mark Weiler Supriya Jagadeesh Cory Johns Martin Thurn Swapnil Khabiya Darrell Fuhriman Marty J. Riley Tassilo von Parseval* David A. Golden* Marty Pauley Terrence Brennon David Coppit* Matthew Darwin Tim Sellar David Favor Matthew Lockner Todd Richmond Dimitris Glynos Matthew Walker Tom Allison Edward Wildgoose* Max Maischein Tony Bowden Emmet Cailfield Max Poduhoroff Walery Studennikov Eric Wheeler Melvyn Sopacua Wiggins d'Anconia Eugene Eric Kim Michael D Richards Yuval Kojman Evan Borgstrom Michael Reece Francois Petillon Michael de Beer


text:
# Write as a Function of b ((2xy)^4)/(4xy)=4x^ay^b

The equation cannot be rewritten as a function because there are more than two variables.
Cannot rewrite
Write as a Function of b ((2xy)^4)/(4xy)=4x^ay^b


text:
This post was originally featured as a guest post on InsideScoop, the San Francisco Chronicle food blog.

A “camper” is a guest that spends far too long at a table. Restaurants that value service would never aggressively rush the guest, but at the same time, conscientious guests should be aware of their impact on the staff, restaurant, and other diners. Camping is a big pet peeve of waiters and most people are aware it generally has a negative impact on the restaurant’s bottom line. Here is some data from a single restaurant in San Francisco that illustrates the impact of a camper (you’ll have to believe us when we say this is representative).

For this sample restaurant about 75% of the guests finish in less than 2 hours. Let’s consider the guests who spend more than 2 hours at the table to be campers.

The first thing to notice was that the campers tend to significantly outspend non-campers:

$50 Camper spending average$35 Non-Camper spending average

But at a busy restaurant, the restaurant will be seating someone else as soon as diners get up. So it’s important to consider the average amount of guest-spending per hour. On this metric, the non-campers are much better:

$52 Camper spending per hour$66 Non-Camper spending per hour

If this is a 100-seat restaurant that is open for 5 hours, the restaurant would make $14,368 a day if everyone was a non-camper and$9,270 a day if everyone camped. That’s a huge difference.

Conscientious guests should also be mindful of the waitstaff. Based on our research, there is no connection between tip percentage and camping. In other words, campers tend to tip the same rate as non-campers. What this means is that even though the waiter is spending more time with a table, they are compensated less when the table spends longer dining:

$3.20 Camper average guest tipping per hour$4.88 Non-Camper average guest tipping per hour

For a table of two people, that’s less than minimum wage to be split among the waiter, busboy and food runner. There’s no need to rush at restaurants, but rest assured that restaurants appreciate when guests are conscientious of other guests and their impact on business.

This analysis was conducted by CoPilot, a restaurant analytics company acquired by OpenTable in August which has become OpenTable Insights.


text:
## The Annals of Probability

### Universal Donsker Classes and Metric Entropy

R. M. Dudley

#### Abstract

Let $(X, \mathscr{A})$ be a measurable space and $\mathscr{F}$ a class of measurable functions on $X. \mathscr{F}$ is called a universal Donsker class if for every probability measure $P$ on $\mathscr{A}$, the centered and normalized empirical measures $n^{1/2}(P_n - P)$ converge in law, with respect to uniform convergence over $\mathscr{F}$, to the limiting "Brownian bridge" process $G_P$. Then up to additive constants, $\mathscr{F}$ must be uniformly bounded. Several nonequivalent conditions are shown to imply the universal Donsker property. Some are connected with the Vapnik-Cervonenkis combinatorial condition on classes of sets, others with metric entropy. The implications between the various conditions are considered. Bounds are given for the metric entropy of convex hulls in Hilbert space.

#### Article information

Source
Ann. Probab., Volume 15, Number 4 (1987), 1306-1326.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991978

Digital Object Identifier
doi:10.1214/aop/1176991978

Mathematical Reviews number (MathSciNet)
MR905333

Zentralblatt MATH identifier
0631.60004

JSTOR