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# h-vector

In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form. A characterization of the set of h-vectors of simplicial polytopes was conjectured by Peter McMullen[1] and proved by Lou Billera and Carl W. Lee[2][3] and Richard Stanley[4] (g-theorem). The definition of h-vector applies to arbitrary abstract simplicial complexes. The g-conjecture states that for simplicial spheres, all possible h-vectors occur already among the h-vectors of the boundaries of convex simplicial polytopes.

Stanley introduced a generalization of the h-vector, the toric h-vector, which is defined for an arbitrary ranked poset, and proved that for the class of Eulerian posets, the Dehn–Sommerville equations continue to hold. A different, more combinatorial, generalization of the h-vector that has been extensively studied is the flag h-vector of a ranked poset. For Eulerian posets, it can be more concisely expressed by means of a noncommutative polynomial in two variables called the cd-index.

## Definition

Let Δ be an abstract simplicial complex of dimension d − 1 with fi i-dimensional faces and f−1 = 1. These numbers are arranged into the f-vector of Δ,

${\displaystyle f(\Delta )=(f_{-1},f_{0},\ldots ,f_{d-1}).}$

An important special case occurs when Δ is the boundary of a d-dimensional convex polytope.

For k = 0, 1, …, d, let

${\displaystyle h_{k}=\sum _{i=0}^{k}(-1)^{k-i}{\binom {d-i}{k-i}}f_{i-1}.}$

The tuple

${\displaystyle h(\Delta )=(h_{0},h_{1},\ldots ,h_{d})}$

is called the h-vector of Δ. The f-vector and the h-vector uniquely determine each other through the linear relation

${\displaystyle \sum _{i=0}^{d}f_{i-1}(t-1)^{d-i}=\sum _{k=0}^{d}h_{k}t^{d-k}.}$

Let R = k[Δ] be the Stanley–Reisner ring of Δ. Then its Hilbert–Poincaré series can be expressed as

${\displaystyle P_{R}(t)=\sum _{i=0}^{d}{\frac {f_{i-1}t^{i}}{(1-t)^{i}}}={\frac {h_{0}+h_{1}t+\cdots +h_{d}t^{d}}{(1-t)^{d}}}.}$

This motivates the definition of the h-vector of a finitely generated positively graded algebra of Krull dimension d as the numerator of its Hilbert–Poincaré series written with the denominator (1 − t)d.

The h-vector is closely related to the h*-vector for a convex lattice polytope, see Ehrhart polynomial.

## Toric h-vector

To an arbitrary graded poset P, Stanley associated a pair of polynomials f(P,x) and g(P,x). Their definition is recursive in terms of the polynomials associated to intervals [0,y] for all yP, y ≠ 1, viewed as ranked posets of lower rank (0 and 1 denote the minimal and the maximal elements of P). The coefficients of f(P,x) form the toric h-vector of P. When P is an Eulerian poset of rank d + 1 such that P − 1 is simplicial, the toric h-vector coincides with the ordinary h-vector constructed using the numbers fi of elements of P − 1 of given rank i + 1. In this case the toric h-vector of P satisfies the Dehn–Sommerville equations

${\displaystyle h_{k}=h_{d-k}.}$

The reason for the adjective "toric" is a connection of the toric h-vector with the intersection cohomology of a certain projective toric variety X whenever P is the boundary complex of rational convex polytope. Namely, the components are the dimensions of the even intersection cohomology groups of X:

${\displaystyle h_{k}=\operatorname {dim} _{\mathbb {Q} }\operatorname {IH} ^{2k}(X,\mathbb {Q} )}$

(the odd intersection cohomology groups of X are all zero). The Dehn–Sommerville equations are a manifestation of the Poincaré duality in the intersection cohomology of X.

## Flag h-vector and cd-index

A different generalization of the notions of f-vector and h-vector of a convex polytope has been extensively studied. Let P be a finite graded poset of rank n − 1, so that each maximal chain in P has length n. For any S, a subset of {1,…,n}, let αP(S) denote the number of chains in P whose ranks constitute the set S. More formally, let

${\displaystyle |\cdot |:P\to \{0,1,\ldots ,n\}}$

be the rank function of P and let PS be the S-rank selected subposet, which consists of the elements from P whose rank is in S:

${\displaystyle P_{S}=\{x\in P:|x|\in S\}.}$

Then αP(S) is the number of the maximal chains in P(S) and the function

${\displaystyle S\mapsto \alpha _{P}(S)}$

is called the flag f-vector of P. The function

${\displaystyle S\mapsto \beta _{P}(S),\quad \beta _{P}(S)=\sum _{T\subseteq S}(-1)^{|S|-|T|}\alpha _{P}(S)}$

is called the flag h-vector of P. By the inclusion–exclusion principle,

${\displaystyle \alpha _{P}(S)=\sum _{T\subseteq S}\beta _{P}(T).}$

The flag f- and h-vectors of P refine the ordinary f- and h-vectors of its order complex Δ(P):

${\displaystyle f_{i-1}(\Delta (P))=\sum _{|S|=i}\alpha _{P}(S),\quad h_{i}(\Delta (P))=\sum _{|S|=i}\beta _{P}(S).}$

The flag h-vector of P can be displayed via a polynomial in noncommutative variables a and b. For any subset S of {1,…,n}, define the corresponding monomial in a and b,

${\displaystyle u_{S}=u_{1}\cdots u_{n},\quad u_{i}=a{\text{ for }}i\notin S,u_{i}=b{\text{ for }}i\in S.}$

Then the noncommutative generating function for the flag h-vector of P is defined by

${\displaystyle \Psi _{P}(a,b)=\sum _{S}\beta _{P}(S)u_{S}.}$

From the relation between αP(S) and βP(S), the noncommutative generating function for the flag f-vector of P is

${\displaystyle \Psi _{P}(a,a+b)=\sum _{S}\alpha _{P}(S)u_{S}.}$

Margaret Bayer and Lou Billera determined the most general linear relations that hold between the components of the flag h-vector of an Eulerian poset P. Fine noted an elegant way to state these relations: there exists a noncommutative polynomial ΦP(c,d), called the cd-index of P, such that

${\displaystyle \Psi _{P}(a,b)=\Phi _{P}(a+b,ab+ba).}$

Stanley proved that all coefficients of the cd-index of the boundary complex of a convex polytope are non-negative. He conjectured that this positivity phenomenon persists for a more general class of Eulerian posets that Stanley calls Gorenstein* complexes and which includes simplicial spheres and complete fans. This conjecture was proved by Kalle Karu.[5] The combinatorial meaning of these non-negative coefficients (an answer to the question "what do they count?") remains unclear.

## References

1. ^ McMullen, Peter (1971), "The numbers of faces of simplicial polytopes", Israel Journal of Mathematics, 9 (4): 559–570, doi:10.1007/BF02771471, MR 0278183.
2. ^ Billera, Louis; Lee, Carl (1980), "Sufficiency of McMullen's conditions for f-vectors of simplicial polytopes", Bulletin of the American Mathematical Society, 2 (1): 181–185, doi:10.1090/s0273-0979-1980-14712-6, MR 551759.
3. ^ Billera, Louis; Lee, Carl (1981), "A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes", Journal of Combinatorial Theory, Series A, 31 (3): 237–255, doi:10.1016/0097-3165(81)90058-3.
4. ^ Stanley, Richard (1980), "The number of faces of a simplicial convex polytope", Advances in Mathematics, 35 (3): 236–238, doi:10.1016/0001-8708(80)90050-X, MR 0563925.
5. ^ Karu, Kalle (2006), "The cd-index of fans and posets", Compositio Mathematica, 142: 701–718, doi:10.1112/S0010437X06001928, MR 2231198.


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Example 29.43.2. Let $S$ be a scheme. Let $\mathcal{A}$ be a quasi-coherent graded $\mathcal{O}_ S$-algebra generated by $\mathcal{A}_1$ over $\mathcal{A}_0$. Assume furthermore that $\mathcal{A}_1$ is of finite type over $\mathcal{O}_ S$. Set $X = \underline{\text{Proj}}_ S(\mathcal{A})$. In this case $X \to S$ is projective. Namely, the morphism associated to the graded $\mathcal{O}_ S$-algebra map

$\text{Sym}_{\mathcal{O}_ X}^*(\mathcal{A}_1) \longrightarrow \mathcal{A}$

is a closed immersion, see Constructions, Lemma 27.18.5.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

format: plain


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# Online talk: Tony Huynh (CMSA Seminar)

Next week, Tony Huynh is giving a talk in the Combinatorial Mathematics Society of Australasia Seminar which many of our readers may be interested in. Here is the info. The announcement for next week’s Graphs and Matroids talk will follow soon.

##### Tuesday, October 6,9pm ET (11am AEST)Tony Huynh, Monash UIdealness of k-wise intersecting familiesZoom/password: see CMSA website

Abstract:
A clutter is a hypergraph such that no hyperedge is contained in another hyperedge. It is $k$-wise intersecting if every $k$ hyperedges intersect, but there is no vertex contained in all the hyperedges. We conjecture that every $4$-wise intersecting clutter is not ideal. Idealness is an important geometric property, which roughly says that the minimum covering problem for the clutter can be efficiently solved by a linear program. As evidence for our conjecture, we prove it for the class of binary clutters. Our proof combines ideas from the theory of clutters, graphs, and matroids. For example, it uses Jaeger’s $8$-flow theorem for graphs, and Seymour’s characterization of the binary matroids with the sums of circuits property. We also show that $4$ cannot be replaced by $3$ in our conjecture, where the counterexample of course comes from the Petersen Graph.

This is joint work with Ahmad Abdi, Gérard Cornuéjols, and Dabeen Lee.

# Online talk: Dan Cranston

##### Monday, September 28,3pm ET (8pm BST, 7am Tue NZST)Dan Cranston, Virginia Commonwealth UVertex Partitions into an Independent Set and a Forest with Each Component SmallYoutube

Abstract:
For each integer $k \ge 2$, we determine a sharp bound on $\text{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$, where $I$ is an independent set and $G[F_k]$ is a forest in which each component has at most $k$ vertices. For each $k$ we construct an infinite family of examples showing our result is best possible. Hendrey, Norin, and Wood asked for the largest function $g(a,b)$ such that if $\text{mad}(G)<g(a,b)$ then $V(G)$ has a partition into sets $A$ and $B$ such that $\text{mad}(G[A])<a$ and $\text{mad}(G[B])<b$. They specifically asked for the value of $g(1,b)$, which corresponds to the case that $A$ is an independent set. Previously, the only values known were $g(1,4/3)$ and $g(1,2)$. We find the value of $g(1,b)$ whenever $4/3<b<2$. This is joint work with Matthew Yancey.

# Online talk: Alexey Pokrovskiy (non-standard day & time!)

We’re really excited to have Alexey Pokrovskiy speak on his fantastic recent result on Rota’s Basis Conjecture this upcoming week. This talk has been moved to be a part of the Tutte Colloquium at Waterloo and so will be held at a different day and time than usual. Here are the full details.

##### Friday, September 25,1pm ET (6pm BST, 5am Tue NZST)Alexey Pokrovskiy, Birkbeck, University of LondonRota’s Basis Conjecture holds asymptoticallyYoutube

Abstract:
Rota’s Basis Conjecture is a well known problem, that states that for any collection of $n$ bases in a rank $n$ matroid, it is possible to decompose all the elements into $n$ disjoint rainbow bases. Here an asymptotic version of this is will be discussed – that it is possible to find $n – o(n)$ disjoint rainbow independent sets of size $n – o(n)$.

# Online talk: Oliver Lorscheid

Mon, September 14, 3pm ET (8pm BST, 7am Tue NZST)
Oliver Lorscheid, Instituto Nacional de Matemática Pura e Aplicada
Foundations of Matroids without Large Uniform Minors, Part 2


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# Primitive roots?

pivoxa15
Can a number have more than 1 primitive root?

Thanks

Last edited:

Staff Emeritus
Gold Member
This one's not too hard to work out for yourself: what's the defining property of a primitive root?

pivoxa15
From the name, I get the impression that there should be only one primitive root for each number but there are more due to the definition that a primitive root exists when the primitive root to the power of phi(n) has a remainder of 1 when divided by n.

Finding the primitive of a number, n (if it exists) is quiet a long process of trial and error is it not?

Staff Emeritus
Gold Member
The "primitive" part of saying that a is a primitive root modulo n means that that every number m relatively prime to n can be written as m = a^k (mod n) for some integer k.

As I recall, there are quite a lot of them, so you just try things randomly, and you'll find one fairly quickly.

pivoxa15
What do you mean by relatively prime?

How many numbers do have to try to ensure this number has no primitive roots?

Thanks Hurkyl

pivoxa15
Also, prime numbers always have at least one primitive root but do they have infinitely many?

Are one primitive root usually preferred to another?

pivoxa15
One excercise was find the primitive root of 12.

I did it by trying to find a number 'a' where the ord of the number 'a' to the base 12 equal phi(12)

phi(12) = 2

and so I found 5^2 is congruent to 1 (mod 12). The power of 5, that is 2 is also the smallest power for which 5^i is congruent to 1 (mod 12).

the gcd(5,12)=1

Hence i=phi(12)=ord5(mod12) which matches the definition of primitive root. 'a' or the primitive root therefore is 5.

But the back of the book said that 12 has no primitive root.

Is the book wrong or am I wrong?

Thanks

Last edited:


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# What is the empirical formula for the compound containing 13.5 g Ca, 10.8 g O, and 0.675 g H?

Dec 27, 2016

$C a {\left(O H\right)}_{2}$

#### Explanation:

We divide each given mass by the atomic mass of each individual element:

$\text{Calcium:}$ $\frac{13.5 \cdot g}{40.1 \cdot g \cdot m o {l}^{-} 1} = 0.337 \cdot m o l .$

$\text{Oxygen:}$ $\frac{10.8 \cdot g}{15.999 \cdot g \cdot m o {l}^{-} 1} = 0.675 \cdot m o l .$

$\text{Hydrogen:}$ $\frac{0.675 \cdot g}{1.008 \cdot g \cdot m o {l}^{-} 1} = 0.675 \cdot m o l .$

If we divide thru by the smallest atomic quantity, we get an empirical formula of, $C a {H}_{2} {O}_{2}$, i.e. $C a {\left(O H\right)}_{2}$.


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## anonymous one year ago The points shown on the graph represent the numbers in a geometric sequence. What is the initial value of the sequence?

1. anonymous

2. freckles

reading from left to right the initial point is the first point which is?

3. anonymous

1,2 @freckles

4. freckles

yep (1,2) 1 is where the initial value happens 2 is the actually the initial value

5. freckles

the geometric sequence you see there is... 2,4,8 where the common ratio is 2 and the initial value of sequence is 2 where the sequence can be described as : $a_n=2 (2)^{n-1} \\ \text{ and we see } a_1=2(2)^{1-1}=2(2)^{0}=2(1)=2 \\ \text{ the first number in the sequence is 2 given by n=1 }$


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# TDD implies higher quality code

I don’t mean just fewer errors, although that is definitely a happy side effect of TDD. I mean that the code is easier to read, maintain and has fewer leaky abstractions.

# Scaling Gitlab runners

Gitlab documents a method for auto-scaling a gitlab-runner. But what if you are not able to apply Docker Machine concepts to your cluster, or don’t need autoscaling and are content to scale manually? Read on for my solution to simple, manual scaling of Gitlab runners in a Docker swarm.

# Charting the multiport black box parameters of linear, time invariant electrical networks

This tutorial gives an overview of multiport black-box model theory and how it relates to commonly used parameters of linear, time invariant electrical networks. Expressions are also derived for the conversions between the various multiport parameters.

# Combining principles; Theorem 3

When each of the $$M$$ branch networks and source resistances are identical there is an equivalence between the multiport combiner with source resistance below and the single branch network also shown below, comprised of an effective source resistance $$R_{e}$$, a scaled branch network $$\mathbf{Y_{e}}$$ and the original trunk network $$\mathbf{Z_{t}}$$.

# Combining principles; Theorem 2

A combining network driven by multiple voltage sources as shown in the figure of Theorem 1 is equivalent to the same network driven by a single voltage source as shown below.


text: Add a circle to the chart to highlight where f(x) and g(x) are equal. Use the TeX markup \pi for the Greek letter . Use the annotation function to add annotations to a chart. (Type plotedit again or click the icon again when you want to exit plot edit mode.) Then, access properties of the object using dot notation. % Create a textarrow annotation at the coordinates in data units, % the textarrow coordinates are given [end_x, head_x], [end_y, head_y]. I tried the following using minipage annotation('textbox', [0.5, 0.2, 0.1, 0.1], 'String', "hi") This places a text box with horizontal offset of 50% of the Figure's width, and vertical offset of 20% of the Figure's height. Starting in R2019b, you can display a tiling of plots using the tiledlayout and nexttile functions. In my case, I had many figures with a variable legend size, for each figure. annotation (lineType,x,y) creates a line or arrow annotation extending between two points in the current figure. If you specify the type as 'rectangle', 'ellipse', or 'textbox', then the second argument is the location and size. Other MathWorks country sites are not optimized for visits from your location. My goal was to keep the plot size constant in each figure and just changing the legend size (in particular the width, through the number of columns). Call the nexttile function to create the axes objects ax1 and ax2. How to add text labels and annotations to plots in MATLAB ® . Display an arrow pointing to the left by including the TeX markup \leftarrow. May be it is a Matlab bug. Now I would like to draw an arrow starting at 90 s, 0.04 concentration units and going to 120 s, 0.09 concentration units. This example first explains the different types of annotations, and then shows you how to add circles and text arrows to a chart. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. (HWHM + abs(min(xlim)))/diff(xlim) * pos(3) + pos(1) ]. I am plotting a time from 0 to 180 s on the x-axis and a concentration between 0 and 0.1 concentration units on the y-axis. I, is your independent variable vector. Other MathWorks country sites are not optimized for visits from your location. Use the TeX markup \pi for the Greek letter π. The third argument specifies the text. I then calculated the x-position of my 20s-marker in normalized coordinates as 20/(180*0.7750) (first normalizing to the length of the x-axis, then to the size of the plot with respect to the window. For example, annotation('line',[x_begin x_end],[y_begin y_end]). This does, however, not work, since 0 and 1 refer to points in the whole figure (the window in which the plot appears) and not to the area of the plot itself. So problem is the entire figure is not gracefully scalable. Previous versions of MATLAB ® allow annotations to extend into (or out of) the boundaries. You forgot to mention, if you want to display the text relative to an axes or to the figure, or absolute in the figure etc. If I get Matlab to show me the code for it, it gives. I am plotting a time from 0 to 180 s on the x-axis and a concentration between 0 and 0.1 concentration units on the y-axis. in the Command Window or by clicking the Edit Plot icon in the figure toolbar. Use the annotation function to add annotations to a chart. I simply drew the arrow by hand. By default, text supports a subset of TeX markup. To create a circle, use the 'ellipse' option for the annotation type. In this case, add text to the point . If you specify the type as 'line', 'arrow', 'doublearrow', or 'textarrow', then the second input is the starting and ending x positions of the annotation. I am including the plot which I am trying to annotate. I just included matlab figures using matlab2tikz. Customize the circle by setting properties of the underlying object. By default, text supports a subset of TeX markup. The first two input arguments to the textfunction specify the position. This will keep you intensely occupied for a few minutes! It serves as an identifier to users, so it should remain visible and readable when the plot is being rotated. Hello everyone, I am trying to annotate a plot which contains many line. Here's a quick illustration of what I mean. Annotations use normalized figure units and can span multiple axes in a figure. Finally, arrows, text and rectangular or elliptic boxes can be added to highlight parts of a plot using the annotation function. If possible i want to implement it into the tikz file(not in the latex file). I am more involved in the imaging side :), More information would be helpful, as would more illustrative example code, since we don’t know what you’re doing, and providing a context is always appropriate. You can customize the text arrow by setting properties of the underlying object. Also, is this robust to, You may receive emails, depending on your. Return the Ellipse object as an output argument from the annotation function. If it is not possible I need to insert text right below the legend. The first two input arguments to the textfunction specify the position. MathWorks is the leading developer of mathematical computing software for engineers and scientists. "line" accepts the same style. Annotations can be shown with or without an arrow. Is there a way by which I can write a code to label or annotate these lines. I have already considered to simply "normalize" those positions myself (e.g. [(yPosition - min(ylim))/diff(ylim) * pos(4) + pos(2). The uses of the basic text() will place text at an arbitrary position on the Axes. Annotations are extra information added to a chart to help identify important information. Customize the circle by setting properties of the underlying object. 90 s/180 s = 0.5 --> x-position in normalized coordinates). It can be positioned with respect to relative coordinates in the plot or with respect to the actual data coordinates of the graph. Select Arrow from the Insert menu. This comment is replaced with a way too long new comment which hopefully makes up for it since it also scales to negative x and hopefully isn't totally out of place here. Customize the circle by setting properties of the underlying object. While 99% of the figure is still okay, the arrows I placed are no longer properly positioned. Choose a web site to get translated content where available and see local events and offers. Settign the text location is easy, but it is hard to explain as long, as we have to guess, what you want exactly. E.g. annotation (lineType,x,y) creates a line or arrow annotation extending between two points in the current figure. Add a circle to the chart to highlight where f(x) and g(x) are equal. Is there a way the define the starting and end point of an annotation object such as an arrow in terms of the data being plotted and not as either "normalized" coordinates (x- and y-positions between 0 and 1) or a physical length measurement such as cm? Reload the page to see its updated state. MathWorks is the leading developer of mathematical computing software for engineers and scientists. For a full list of markup, see Greek Letters and Special Characters in Chart Text. Return the Ellipse object as an output argument from the annotation function. For a full list of markup, see Greek Letters and Special Characters in Chart Text. Display an arrow pointing to the left by including the TeX markup \leftarrow. By default, the grid is off and the border lines are on. For everyone, here's a short instruction: Looking up, as suggested by Star Strider, the 'Position' Property in the Axes Properties documentation, I found: The third element in the vector, 0.7750, corresponds to the default width of the plot within the figure in normalized coordinates (i.e. In this case, add text to the point (π,sin(π)). If you specify the type as 'line', 'arrow', 'doublearrow', or 'textarrow', then the second input is the starting and ending x positions of the annotation. To create a circle, use the 'ellipse' option for the annotation type. Plot random data in each axes. E.g. Choose a web site to get translated content where available and see local events and offers. Do you want to open this version instead? To display an annotation within a specific figure, uipanel, or … (Start(1) + abs(min(xlim)))/diff(xlim) * pos(3) + pos(1) ]. Add text next to a particular data point using the text function. Find the treasures in MATLAB Central and discover how the community can help you! (Start(2) - min(ylim))/diff(ylim) * pos(4) + pos(2)]); My orthopedic knowledge is, apart from my namesake, unfortunately rather lacking. But now I also want the annotations outside the plot in my latex file. Please consider donating to Black Girls Code today. Black Lives Matter. Greek Letters and Special Characters in Chart Text. Call the tiledlayout function to create a 2-by-1 tiled chart layout. Display an arrow pointing to the left by including the TeX markup \leftarrow. By default, text supports a subset of TeX markup. Accelerating the pace of engineering and science. Based on your location, we recommend that you select: . The third input is the starting and ending y positions of the annotation. Then, access properties of the object using dot notation. It gives the left lower corner coordinates and the width and height values. Why? https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#comment_404192, https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#answer_242121, https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#comment_404195, https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#comment_404199, https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#comment_486101, https://www.mathworks.com/matlabcentral/answers/310815-specify-annotation-position-with-respect-to-x-and-y-axes-values#comment_486104. Thank you in advance! I have annotations in my figures. A modified version of this example exists on your system. To create a circle, use the 'ellipse' option for the annotation type. Learn more about text, position, location, plot Specify x and y as two-element vectors of the form [x_begin x_end] and [y_begin y_end], respectively. For example, annotation('rectangle',[x y w h]). For example, set the String property to the desired text and the Color property to a color value. Web browsers do not support MATLAB commands. I need to place text string outside the axis in the figure. object you’re using. But whereas the Java glass-pane is a true transparent layer, on top of all other window components (examples), Matlab’s implementation only works for axes. Add text next to a particular data point using the text function. The third argument specifies the text. Specify x and y as two-element vectors of the form [x_begin x_end] and [y_begin y_end], respectively. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. How to add text labels and annotations to plots in MATLAB ® . But the moment I click on the "plot tools" button the picture becomes somewhat smaller due to the placement of all the plot tool components. the figure / the window containing the plot has a width of 1 length units). (HM - min(ylim))/diff(ylim) * pos(4) + pos(2)]); % The data units are rescaled to normalized units for x via, % x_norm = ( x_data + abs(min(xlim)))/diff(xlim) * pos(3) + pos(1), % and for y via ( does NOT work for negative values (see x for this), % y_norm = (y_data - min(ylim))/diff(ylim) * pos(4) + pos(2), % Also for negative number now :). Create a simple line plot and add a text box annotation to the figure. For a full list of markup, see Greek Letters and Special Characters in Chart Text. The first input to the function specifies the type of annotation you want to create. Automatically Position Text Annotations on a plot.. First enter plot edit mode, either by typing. With a few lines of code, you can normalise your arrow object positions with respect to them. plotedit. Circle Annotations. Matlab’s implementation of annotation is an attempt to replicate Java’s standard glass-pane mechanism. The first input to the function specifies the type of annotation you want to create. I would like to annotate various straight lines in a 3-D plot in MATLAB, by showing the line number in the middle of the line. but the end point's x-coordinate (0.2244...) does not correspond to the 20 s (20 s / 180 s = 0.1111...) where 180 s is the "length" of my x-axis in the units that I want to plot. Use the TeX markup \pi for the Greek letter . Currently, I am using this: Unable to complete the action because of changes made to the page. Then, experiment! The size of the box is 10% of Figure's height by 10% of Figure's width: See the documentation on. Return the Ellipse object as an output argument from the annotation function. Haven't tried it on this example but on another one, but I assume it works. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. An annotation is a text element that can be placed anywhere in the plot. The first two input arguments to the textfunction specify the position. Thanks heaps, I got it! Return the TextArrow object as an output argument from the annotation function. Hi, I got a similar problem when I had to put a legend - with variable size - outside the plot. Add text next to a particular data point using the text function. Scatter data is not constant all the time so the … Instead, they clip at the boundaries. This places a text box with horizontal offset of 50% of the Figure's width, and vertical offset of 20% of the Figure's height. Apparently, I did not get notified. Specify lineType as 'line', 'arrow', 'doublearrow', or 'textarrow'. Since plot axes are always obscured by uicontrols, so too is the annotation layer. Basic annotation ¶. Based on your location, we recommend that you select: . The functions grid and box may also be used to add grid and border lines to the plot. Edit: I am terribly sorry, both for writing things I could not make sense of a couple months later and for not replying sooner Star Strider. Add a text arrow to the chart using the 'textarrow' option for the annotation type. Accelerating the pace of engineering and science. The third argument specifies the text. In this case, add text to the point . Those objects are drawn in an invisible axes, on top of every other axes. Settign the text location is easy, but it is hard to … For example, set the Color property. The annotation data has to come from a vector suitable to each line. The size of the box is 10% of Figure's height by 10% of Figure's width: Circle Annotations. Type: cell array of struct where each struct has one or more of the keys listed below. [(xPosition + abs(min(xlim)))/diff(xlim) * pos(3) + pos(1). [(End(1) + abs(min(xlim)))/diff(xlim) * pos(3) + pos(1). My apologies in advance if it is. These annotations are outside the plot area to prevent overlap with the data. [(End(2) - min(ylim))/diff(ylim) * pos(4) + pos(2). You forgot to mention, if you want to display the text relative to an axes or to the figure, or absolute in the figure etc. Learn more about annotation, subplot, southeast, text box in plot, print value in subplot MATLAB A common use case of text is to annotate some feature of the plot, and the annotate() method provides helper functionality to make annotations easy. % Positins for the end of the Arrow in data units. Add a circle to the chart to highlight where f(x) and g(x) are equal. Now I would like to draw an arrow starting at 90 s, 0.04 concentration units and going to 120 s, 0.09 concentration units. 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The community can help you code, you may receive emails, depending on...., or 'textarrow ' option for the annotation because of changes made to the function specifies the of! Enter plot edit mode, either by typing are extra information added to highlight of. To come from a vector suitable to each line or click the icon when. On your default, text supports a subset of TeX markup \leftarrow current figure span multiple in... Are equal to annotate simply ` normalize '' those positions myself ( E.g there a way by which can! Also want the annotations outside the plot area to prevent overlap with the appropriate points on the axes software! As 'line ', or 'textarrow ' right below the legend figure is still okay, grid! Text function a code to label or annotate these matlab annotation outside plot the appropriate points on the axes mode ). One, but I assume it works uses of the figure my latex )... 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text:
## Illinois Journal of Mathematics

### $p$-groups of maximal class as automorphism groups

#### Abstract

We classify the (finite) $p$-groups of maximal class that are isomorphic to the full automorphism group of a (finite or infinite) group. The only such $p$-groups are the nonabelian groups of order $8$ and 3-groups in a certain family, whose structure is fully described. Up to isomorphism there is exactly one such 3-group for each even nilpotency class greater than $2$, and none for other classes.

#### Article information

Source
Illinois J. Math., Volume 47, Number 1-2 (2003), 141-156.

Dates
First available in Project Euclid: 17 November 2009

https://projecteuclid.org/euclid.ijm/1258488144

Digital Object Identifier
doi:10.1215/ijm/1258488144

Mathematical Reviews number (MathSciNet)
MR2031311

Zentralblatt MATH identifier
1032.20024

#### Citation

Cutolo, Giovanni; Smith, Howard; Wiegold, James. $p$-groups of maximal class as automorphism groups. Illinois J. Math. 47 (2003), no. 1-2, 141--156. doi:10.1215/ijm/1258488144. https://projecteuclid.org/euclid.ijm/1258488144


text:
1. anonymous

The N71-90 virus will give an infected person a mild rash on their arms once the person has 1 billion of the virus cells in their body. After an initial infection with just one cell, each virus cell will divide into two cells every four hours. After 30 divisions there are 1,073,741,824 cells and the rash starts. Once the rash starts, the immune system kicks in and kills all of the virus cells within an hour. The number of virus cells in the body can be determined using the function

2. anonymous

@freckles

3. anonymous

@esamalaa @triciaal

4. anonymous

what is the question?

5. anonymous

6. anonymous

where h is the number of hours after infection. If Jolene is infected by one virus cell, how many virus cells will she have after 20 divisions?

7. IrishBoy123

$$20 \ divisions \ \rightarrow \ 4 \times 20 \ hours$$ use the equation


text:
## Algebra 2 (1st Edition)

We first go down the first column of the table and find the $z=1$ row. We then go over columns until we find $z=.4$. This is the z-score.


text:
# validity of convergent sequences with strict inequalities

• March 16th 2010, 06:06 PM
dgmath
validity of convergent sequences with strict inequalities
Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

I know that if xk >= yk for all k>=m, then x>=y.

However, if xk>yk for all k>=m, would x>y hold true as well?

I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.
• March 16th 2010, 06:09 PM
Drexel28
Quote:

Originally Posted by dgmath
Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

I know that if xk >= yk for all k>=m, then x>=y.

However, if xk>yk for all k>=m, would x>y hold true as well?

I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.

Of course not. $0<\frac{1}{n}$
• March 16th 2010, 06:33 PM
dgmath
Quote:

Originally Posted by Drexel28
Of course not. $0<\frac{1}{n}$

um, not sure I understand
• March 16th 2010, 06:34 PM
Drexel28
Quote:

Originally Posted by dgmath
um, not sure I understand

Define $x_n=0$ and $y_n=\frac{1}{n}$ then $x_n but $\lim\text{ }x_n=\lim\text{ }y_n=0$


text:
Elementary topology and machine learning

The machine learning bubble may be overinflated, but it is not about to burst. Interdisciplinary research in this field is grounded in sound theory and has numerous empirical breakthroughs to show for. As it finds more and more applications and concentrates public research funding, many of us are still wondering: how can mathematics contribute?
Case study of an interaction between elementary topology and machine learning’s binary classification problem. Following classical theorems, we obtain a topologically accurate solution.

Correction: It should be $\sup_{i,j}| E_{i,j}^n - (k+1)^2 \int_{R_{i,j}^n} f | = o(1/n)$ and $k=k(n)$ grow correspondingly slower with $n$.

PDF note here.


text:
# These clouds appear fibrous or curly. They are high, thin, white, feathery clouds made of ice crystals. They are associated with fair weather, but they can indicate approaching storms too. Which type of cloud is this?

###### Question:

These clouds appear fibrous or curly. They are high, thin, white, feathery clouds made of ice crystals. They are associated with fair weather, but they can indicate approaching storms too. Which type of cloud is this?

### Professor Smith examines the dating behaviors of college students. Smith decides to track the dating behaviors of college students throughout their college careers. She decides to begin her research using her introductory class. After explaining the study, she passes out a questionnaire to all students. She assures students that their responses will be confidential. The students complete her survey during class. Her research most clearly impinges on:________. a. deception. b. analysis and repor

Professor Smith examines the dating behaviors of college students. Smith decides to track the dating behaviors of college students throughout their college careers. She decides to begin her research using her introductory class. After explaining the study, she passes out a questionnaire to all stude...

### Is it possible for a triangle to have 10 for the base and 7 and 8 for the other sides

is it possible for a triangle to have 10 for the base and 7 and 8 for the other sides...

### On the model of a carbon atom below, label the protons, neutrons, and electrons in your model. Summarize what you have drawn in two sentences. Your response must include the charges of the subatomic particles in your model and their location.

On the model of a carbon atom below, label the protons, neutrons, and electrons in your model. Summarize what you have drawn in two sentences. Your response must include the charges of the subatomic particles in your model and their location....

### A report issued by the mayor's office states that city residents support building a new baseball stadium. The report is based on a survey of 150 city residents who were shopping at a sporting goods store. Participants were asked the question, "Do you think the city should replace its outdated stadium with a more modern stadium?" Select all statements that correctly evaluate the report question is not biased The sample is biased because it does not represent the population The sample is not biase

A report issued by the mayor's office states that city residents support building a new baseball stadium. The report is based on a survey of 150 city residents who were shopping at a sporting goods store. Participants were asked the question, "Do you think the city should replace its outdated stadiu...

### I need help with the questions that are blank

I need help with the questions that are blank...

### What is 10 x 42 – 6 x 3 + 3 ? Evaluating expressions with Exponents

what is 10 x 42 – 6 x 3 + 3 ? Evaluating expressions with Exponents...

### Help me on what is meant by 2cm to represent 1unit on the graph and give me examples.

Help me on what is meant by 2cm to represent 1unit on the graph and give me examples....

### Why did women serve in noncombat positions in the military and work in factories at home?

Why did women serve in noncombat positions in the military and work in factories at home?...

### I need help Asap!!!!!!!!!

I need help Asap!!!!!!!!!...

### How did it get away with flint's water crisis

how did it get away with flint's water crisis...

### The sum of a number and its double is 69. What is the number? a. 46.6 b. 34.5 c. 23 d. 20

The sum of a number and its double is 69. What is the number? a. 46.6 b. 34.5 c. 23 d. 20...

### If D is neutral liquid, which of the following is CheatMgCO3(A) + (B)C сMgCl2 + (D)

If D is neutral liquid, which of the following is CheatMgCO3(A) + (B)C сMgCl2 + (D)...

### A Buchner funnel uses _______ when separating a(n) _______ by filtration. A. heating, soluble solid B. vacuum, precipitate C. soluble solid, insoluble solid D. precipitate, vacuum

A Buchner funnel uses _______ when separating a(n) _______ by filtration. A. heating, soluble solid B. vacuum, precipitate C. soluble solid, insoluble solid D. precipitate, vacuum...

### Aye I need help a little, In the inequality -9 < 9, which number appears farther left on a number line and why? A. -9 appears farther left because -9 is smaller than 9. B. 9 appears farther left because 9 is larger than -9. C. 9 appears farther left because 9 is smaller than -9. D. -9 appears farther left because -9 is larger than 9.

aye I need help a little, In the inequality -9 < 9, which number appears farther left on a number line and why? A. -9 appears farther left because -9 is smaller than 9. B. 9 appears farther left because 9 is larger than -9. C. 9 appears farther left...

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### Pls explain the error

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### How many distinct permutations can be formed using the letters of the word prepared

how many distinct permutations can be formed using the letters of the word prepared...


text:
# Stack-sortable permutation

In mathematics and computer science, a stack-sortable permutation (also called a tree permutation)[1] is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees.

## Sorting with a stack

The problem of sorting an input sequence using a stack was first posed by Knuth (1968), who gave the following linear time algorithm (closely related to algorithms for the later all nearest smaller values problem):

• Initialize an empty stack
• For each input value x:
• While the stack is nonempty and x is larger than the top item on the stack, pop the stack to the output
• Push x onto the stack
• While the stack is nonempty, pop it to the output

Knuth observed that this algorithm correctly sorts some input sequences, and fails to sort others. For instance, the sequence 3,2,1 is correctly sorted: the three elements are all pushed onto the stack, and then popped in the order 1,2,3. However, the sequence 2,3,1 is not correctly sorted: the algorithm first pushes 2, and pops it when it sees the larger input value 3, causing 2 to be output before 1 rather than after it.

Because this algorithm is a comparison sort, its success or failure does not depend on the numerical values of the input sequence, but only on their relative order; that is, an input may be described by the permutation needed to form that input from a sorted sequence of the same length. Knuth characterized the permutations that this algorithm correctly sorts as being exactly the permutations that do not contain the permutation pattern 231: three elements x, y, and z, appearing in the input in that respective order, with z < x < y. Moreover, he observed that, if the algorithm fails to sort an input, then that input cannot be sorted with a single stack.

As well as inspiring much subsequent work on sorting using more complicated systems of stacks and related data structures,[2] Knuth's research kicked off the study of permutation patterns and of permutation classes defined by forbidden patterns.

## Bijections and enumeration

The sequence of pushes and pops performed by Knuth's sorting algorithm as it sorts a stack-sortable permutation form a Dyck language: reinterpreting a push as a left parenthesis and a pop as a right parenthesis produces a string of balanced parentheses. Moreover, every Dyck string comes from a stack-sortable permutation in this way, and every two different stack-sortable permutations produce different Dyck strings. For this reason, the number of stack-sortable permutations of length n is the same as the number of Dyck strings of length 2n, the Catalan number

${\displaystyle C_{n}={\frac {1}{n+1}}{\binom {2n}{n}}.}$[3]
Bijection between binary trees (with nodes numbered left-to-right) and stack-sortable permutations, generated by listing the same node numbers in preorder

Stack-sortable permutations may also be translated directly to and from (unlabeled) binary trees, another combinatorial class whose counting function is the sequence of Catalan numbers. A binary tree may be transformed into a stack-sortable permutation by numbering its nodes in left-to-right order, and then listing these numbers in the order they would be visited by a preorder traversal of the tree: the root first, then the left subtree, then the right subtree, continuing recursively within each subtree. In the reverse direction, a stack-sortable permutation may be decoded into a tree in which the first value x of the permutation corresponds to the root of the tree, the next x − 1 values are decoded recursively to give the left child of the root, and the remaining values are again decoded recursively to give the right child.[1]

Several other classes of permutations may also be placed in bijection with the stack-sortable permutations. For instance, the permutations that avoid the patterns 132, 213, and 312 may be formed respectively from the stack-sortable (231-avoiding) permutations by reversing the permutation, replacing each value x in the permutation by n + 1 − x, or both operations combined. The 312-avoiding permutations are also the inverses of the 231-avoiding permutations, and have been called the stack-realizable permutations as they are the permutations that can be formed from the identity permutation by a sequence of push-from-input and pop-to-output operations on a stack.[4] As Knuth (1968) noted, the 123-avoiding and 321-avoiding permutations also have the same counting function despite being less directly related to the stack-sortable permutations.

## Random stack-sortable permutations

Rotem (1981) investigates the properties of stack-sortable permutations chosen uniformly at random among all such permutations of a given length. The expected length of the longest descending subsequence in such a permutation is ${\displaystyle {\sqrt {\pi n}}-O(1)}$, differing by a constant factor from unconstrained random permutations (for which the expected length is approximately ${\displaystyle 2{\sqrt {n}}}$). The expected length of the longest ascending sequence differs even more strongly from unconstrained permutations: it is ${\displaystyle (n+1)/2}$. The expected number of values within the permutation that are larger than all previous values is only ${\displaystyle 3-6/(n+2)}$, smaller than its logarithmic value for unconstrained permutations. And the expected number of inversions is ${\displaystyle \Theta (n^{3/2})}$, in contrast to its value of ${\displaystyle \Theta (n^{2})}$ for unconstrained permutations.

Every permutation defines a permutation graph, a graph whose vertices are the elements of the permutation and whose edges connect pairs of elements that are inverted by the permutation. The permutation graphs of stack-sortable graphs are trivially perfect.[4]

For each element i of a permutation p, define bi to be the number of other elements that are to the left of and greater than i. Then p is stack-sortable if and only if, for all i, bi − bi + 1 ≤ 1.[1]

## Algorithms

Knott (1977) uses the bijection between stack-sortable permutations and binary trees to define a numerical rank for each binary tree, and to construct efficient algorithms for computing the rank of a tree ("ranking") and for computing the tree with a given rank ("unranking").

Micheli & Rossin (2006) defined two edit operations on permutations: deletion (making a permutation pattern) and its inverse. Using the same correspondence between trees and permutations, they observed that these operations correspond to edge contraction in a tree and its inverse. By applying a polynomial time dynamic programming algorithm for edit distance in trees, they showed that the edit distance between two stack-sortable permutations (and hence also the longest common pattern) can be found in polynomial time. This technique was later generalized to algorithms for finding longest common patterns of separable permutations;[5] however, the longest common pattern problem is NP-complete for arbitrary permutations.[6]

## Notes

1. ^ a b c
2. ^ Tarjan (1972); Avis & Newborn (1981); Rosenstiehl & Tarjan (1984); Bóna (2002); Felsner & Pergel (2008). See also the many additional references given by Bóna.
3. ^
4. ^ a b
5. ^
6. ^


text:
# 1. Introduction

Welcome to the documentation for Pkg, Julia's package manager. The documentation covers many things, for example managing package installations, developing packages, working with package registries and more.

Throughout the manual the REPL interface to Pkg, the Pkg REPL mode, is used in the examples. There is also a functional API, which is preferred when not working interactively. This API is documented in the API Reference section.

## Background and Design

Pkg is a complete rewrite of Julia's old package manager[1] and was released together with Julia v1.0. Unlike traditional package managers, which install and manage a single global set of packages, Pkg is designed around “environments”: independent sets of packages that can be local to an individual project or shared and selected by name. The exact set of packages and versions in an environment is captured in a manifest file which can be checked into a project repository and tracked in version control, significantly improving reproducibility of projects. If you’ve ever tried to run code you haven’t used in a while only to find that you can’t get anything to work because you’ve updated or uninstalled some of the packages your project was using, you’ll understand the motivation for this approach. In Pkg, since each project maintains its own independent set of package versions, you’ll never have this problem again. Moreover, if you check out a project on a new system, you can simply materialize the environment described by its manifest file and immediately be up and running with a known-good set of dependencies.

Since environments are managed and updated independently from each other, “dependency hell” is significantly alleviated in Pkg. If you want to use the latest and greatest version of some package in a new project but you’re stuck on an older version in a different project, that’s no problem – since they have separate environments they can just use different versions, which are both installed at the same time in different locations on your system. The location of each package version is canonical, so when environments use the same versions of packages, they can share installations, avoiding unnecessary duplication of the package. Old package versions that are no longer used by any environments are periodically “garbage collected” by the package manager.

Pkg’s approach to local environments may be familiar to people who have used Python’s virtualenv or Ruby’s bundler. In Julia, instead of hacking the language’s code loading mechanisms to support environments, we have the benefit that Julia natively understands them. In addition, Julia environments are “stackable”: you can overlay one environment with another and thereby have access to additional packages outside of the primary environment. This makes it easy to work on a project, which provides the primary environment, while still having access from the REPL to all your usual dev tools like profilers, debuggers, and so on, just by having an environment including these dev tools later in the load path.

Last but not least, Pkg is designed to support federated package registries. This means that it allows multiple registries managed by different parties to interact seamlessly. In particular, this includes private registries which can live behind corporate firewalls. You can install and update your own packages from a private registry with exactly the same tools and workflows that you use to install and manage official Julia packages. If you urgently need to apply a hotfix for a public package that’s critical to your company’s product, you can tag a private version of it in your company’s internal registry and get a fix to your developers and ops teams quickly and easily without having to wait for an upstream patch to be accepted and published. Once an official fix is published, however, you can just upgrade your dependencies and you'll be back on an official release again.


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# Infinite series $\sum_{k=1}^\infty \frac{k}{2^k}$ and $\sum_{k=1}^\infty \frac{k^2}{2^k}$ [duplicate]

How to evaluate those infinite series? How are they called?

$$\sum_{k=1}^\infty \frac{k}{2^k} \quad \text{and} \quad \sum_{k=1}^\infty \frac{k^2}{2^k}$$

I'm really sorry for asking, but I can't figure out how to google such stuff when I even don't know the names/categories.

## marked as duplicate by Travis, Clement C., Aditya Hase, Santosh Linkha, NamasteDec 17 '14 at 15:13

• "differentiated geometric series" – David Mitra Dec 17 '14 at 14:34
• This may help you compute the sums. – David Mitra Dec 17 '14 at 14:35
• @DavidMitra Thanks a lot, that's all I need to know ;-) – NoBackingDown Dec 17 '14 at 14:37

$$\sum_{k=1}^{\infty}x^k=\frac{x}{1-x}\rightarrow\frac{d}{dx}\sum_{k=1}^{\infty}x^k=\sum_{k=1}^{\infty}kx^{k-1}=\frac{1}{(1-x)^2}\rightarrow \sum_{k=1}^{\infty}kx^{k}=\frac{x}{(1-x)^2}$$
Now let $x=\frac{1}{2}$, hence we have $\sum_{k=1}^{\infty}k({\frac{1}{2}})^{k}=\frac{0.5}{(1-0.5)^2}=2$
Now if we take the derivative, we will have $$\frac{d}{dx}\sum_{k=1}^{\infty}kx^{k}=\sum_{k=1}^{\infty}k^2x^{k-1}=\frac{d}{dx}(\frac{x}{(1-x)^2})=\frac{1+x}{(1-x)^3}\rightarrow \sum_{k=1}^{\infty}k^2x^{k}=\frac{x(1+x)}{(1-x)^3}$$ Now if you let $x=\frac{1}{2}$, then you have: $$\sum_{k=1}^{\infty}k^2(\frac{1}{2})^{k}=\frac{0.5(1+0.5)}{(1-0.5)^3}=\frac{1.5}{0.25}=6$$


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# Integrals

If you have an integral you can't solve, but think that someone else in the workshop might, try adding it on this page. Likewise, if you see an integral on this page which you know how to solve, write in the answer (or the procedure for solving it.) If you need help in adding math to a wikipage take a look at Math Mode on the practice page.

1) The hard integral
The integral below (the "hard" integral topology) appears in the two-loop expansion of the lightlike polygonal Wilson loop at weak coupling (see for example Equation (B.1) of this paper). It would be very interesting to have its analytic expression for generic values of the kinematic invariants. Here it is:

$\hspace{-0.5cm}f_{\rm Hard} (p_1,p_2,p_3;Q_1,Q_2,Q_3) \ := \ \nonumber \\ \\ {1 \over 8}\,{\Gamma (2-2\epsilon_\mathrm{UV}) \over \Gamma(1-\epsilon_\mathrm{UV})^2} \int_{0}^{1}\! \Big( \prod_{i=1}^{3} d\tau_i \Big) \int_{0}^{1}\!\Big(\prod_{i=1}^{3} \, d\alpha_i \Big) \delta ( 1 - \sum_{i=1}^3 \alpha_i ) \nonumber \\ \\ \ (\alpha_1 \alpha_2 \alpha_3)^{-\epsilon_\mathrm{UV}} { \mathcal{N} \over \mathcal{D}^{2-2\epsilon_\mathrm{UV}}}\ ,$

where

$\mathcal{D} := -\alpha_1 \alpha_2 (z_1 - z_2)^2 -\alpha_2 \alpha_3 (z_2 - z_3)^2 -\alpha_1 \alpha_3 (z_1 - z_3)^2 \ ,$

and

$\begin{equation*} \hspace{-0.54cm}(z_1 - z_2)^2 &=& Q_3^2 + 2 (p_1 p_2) (1 - \tau_1) \tau_2 + 2 (Q_3 p_1 ) ( 1 - \tau_1) + 2 (Q_3 p_2 ) \tau_2 \ , \\ \\ (z_2 - z_3)^2 &=& Q_1^2 + 2 (p_2 p_3) (1 - \tau_2) \tau_3 + 2 (Q_1 p_2 ) ( 1 - \tau_2) + 2 (Q_1 p_3 ) \tau_3 \ , \\ \\ (z_3 - z_1)^2 &=& Q_2^2 + 2 (p_3 p_1) (1 - \tau_3) \tau_1 + 2 (Q_2 p_3 ) ( 1 - \tau_3) + 2 (Q_2 p_1 ) \tau_1 \ .$

The numerator is given by

$\begin{equation*} \hspace{-0.54cm}\mathcal{N} &=& 2 (p_1 p_2) (p_1 p_3) \Big[ \alpha_1 \alpha_2 ( 1 - \tau_1) + \alpha_3 \alpha_1 \tau_1 \Big] \\ \\ &+& 2 (p_1 p_2) (p_2 p_3) \Big[ \alpha_2 \alpha_3 ( 1 - \tau_2) + \alpha_1 \alpha_2 \tau_2 \Big] \\ \\ &+& 2 (p_1 p_3) (p_2 p_3) \Big[ \alpha_3 \alpha_1 ( 1 - \tau_3) + \alpha_2 \alpha_3 \tau_3 \Big] \\ \\ &+& 2 \alpha_1 \alpha_2 \Big[ 2 (p_1 p_2) (p_3 Q_3) - (p_2 p_3) (p_1 Q_3) - (p_3 p_1 ) (p_2 Q_3) \Big] \\ \\ &+& 2 \alpha_2 \alpha_3 \Big[ 2 (p_2 p_3) (p_1 Q_1) - (p_3 p_1) (p_2 Q_1) - (p_1 p_2 ) (p_3 Q_1) \Big] \\ \\ &+& 2 \alpha_3 \alpha_1 \Big[ 2 (p_3 p_1) (p_2 Q_2) - (p_1 p_2) (p_3 Q_2) - (p_2 p_3 ) (p_1 Q_2) \Big] \ .$

The momenta

$\begin{equation*} p_1, p_2, p_3$

are lightlike, whereas in the most general configuration

$\begin{equation*} Q_i^2 \neq 0, \qquad i=1, 2, 3 \, .$

Finally,

$\epsilon_\mathrm{UV} >0 \, .$


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# Name your favourite BioFuel Technology

Discussion in 'Earth Science' started by Singularity, Feb 20, 2006.

1. ### erich_knightErich J. KnightRegistered Senior Member

Messages:
108
Concerning Charcoal:

I thought, I first read about these soils in " Botany of Desire " by Michael Pollen, or Dr. Jared Diamond's "Guns Germs &Steel" but I could not find reference to them. Wherever, I did not realize their potential.

Terra Preta' soils I feel has great possibilities to revolutionize sustainable agriculture into a major CO2 sequestration strategy. There is an ecology going on in these soils that is not completely understood, and if replicated and applied at scale would have multiple benefits for farmers and environmentalist. Basically we could have Bio-fuels and non oil dependent soil fertility too.

Here's the Cornell page for an over view:

http://www.css.cornell.edu/faculty/lehmann/biochar/Biochar_home.htm

http://forums.hypography.com/earth-science/3451-terra-preta-9.html

The Georgia Inst. of Technology page:

http://www.energy.gatech.edu/presentations/dday.pdf

As you will see the Japanese work with these soils is impressive, Especially with trees.

The new agricultural technology called marker-assisted selection, or MAS offers a sophisticated method to greatly accelerate classical breeding and it could be the key to the large scale development of Terra Preta agriculture.

http://www.washingtonpost.com/wp-dyn/content/article/2006/07/03/AR2006070300922.html

Or, We could get Dr. Ventor to design the bugs needed for our locals:
synthetic genomics, inc. http://www.syntheticgenomics.com/index.htm

I hope these efforts will lead to a larger systemic and holistic approach to sustainable agricultural development.

I've sent this thread to the researchers at M-Roots, who make Mycorisal fungus inoculations for acceleration of the reestablishment of the symbiotic fungal / root relationship. Here's the M-Roots site: http://www.rootsinc.com/

I also sent it to Dr. Jared Diamond, if he replies, I will probably have an orgasm!

If pre Columbian Indians could produce these soils up to 6 feet deep over 20% of the Amazon basin it seems that our energy and agricultural industries could also product them at scale.

Harnessing the work of this vast number of microbes and fungi changes the whole equation of EROEI for food and Bio fuels. I see this as the only sustainable agricultural strategy if we no longer have cheap oil for fertilizer.

I believe, to have results in northern climates, an M-Roots type fungus inoculent and local compost bugs would be needed to get this super community of wee beasties populated into their proper Soil horizon Carbon Condos.

On Bio Hydrogen:

Nanologix has got their first H2 Clostridia Bio-Reactor going at Welech's Foods in PA., Producesing 70% H2. Erie PA. Waste Water Treatment Plant has signed up also:
http://biz.yahoo.com/prnews/060622/clth058.html?.v=54

Erich J. Knight

3. ### erich_knightErich J. KnightRegistered Senior Member

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108
A variation of this process would also work as well for syn-fuels, and still sequester CO2 while building soils at large scales:

http://www.eprida.com/hydro/

Erich J. Knight

Messages:
1,287

7. ### erich_knightErich J. KnightRegistered Senior Member

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108
HOT DAMN!!!!!........We made it into Nature!!

If this doesn't get Terra Preta some real traction , I don't know what will.

News Feature
Nature 442, 624-626(10 August 2006) | doi:10.1038/442624a; Published online 9 August 2006

Putting the carbon back: Black is the new green
Emma Marris1

Emma Marris is a Washington correspondent for Nature.

Top of pageAbstractOne way to keep carbon dioxide out of the atmosphere is to put it back in the ground. In the first of two News Features on carbon sequestration, Quirin Schiermeier asked when the world's coal-fired power plants will start storing away their carbon. In the second, Emma Marris joins the enthusiasts who think that enriching Earth's soils with charcoal can help avert global warming, reduce the need for fertilizers, and greatly increase the size of turnips.

http://www.nature.com/nature/journal/v442/n7103/full/442624a.html

Erich J. Knight

8. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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23,198
And where do you think the roots of the cut sugar cane are? Answer: in the ground at ZERO fossil fuel energy cost to put them there.

Alcohol, from sugar cane grown in tropical countries, is the economically best way to store carbon. (Also a lot of carbon is stored in the growing cane - sort of like growing trees, but faster in removing carbon from the air.)

A million tons of carbon stored in cane fields (or in metal tanks full of alcohol) should get the same "carbon credits" as a million tons stored in growing trees that were planted.

Sugar cane beats the hell out of schemes that use pumps to inject CO2 into wells, aquifers, etc. - this seem to be the "answer" proponents "hydrogen power" like as many of them are opposed to nuclear energy. They want to burn coal for the energy needed to make hydrogen and pump the CO2 produced into the ground. Ecologically OK, but why not let nature do the work of removing the CO2 - ALREADY EXCESSIVE in the air?

BTW the first and largest photo of your reference:

http://www.nature.com/nature/journa...ll/442624a.html

is totally inappropriate and borderline dishonest in any article on storing carbon. From the mud dome hemisphere construction and the vegetation, I immediately recognized it. (I drive by several every time I go out of Sao Paulo to work on house I am building by myself.) Some very poor man, probably in Brazil, spends his days stealing forest wood, and burns/bakes it inside this structure and get a few sacks of charcoal to sell. - 100% of what was carbon stored in the trees he stole, is released as CO2 into the air. That is why I think to include such a photo in that article is "borderline dishonest." Such dishonesty makes everthing there questionable, at least for me.

Last edited by a moderator: Sep 16, 2006

Messages:
1,287
10. ### erich_knightErich J. KnightRegistered Senior Member

Messages:
108
That sugar cane is at best Co2 Neutral, Terra preta is carbon negitive :

"The remarkable thing about this process is that, even after the fuel has been burned, more carbon dioxide is removed from the atmosphere than is put back. Traditional biofuels claim to be 'carbon neutral', because the carbon dioxide assimilated by the growing biomass makes up for the carbon dioxide given off by the burning of the fuel. But as Lehmann points out, systems such as Day's go one step further: "They are the only way to make a fuel that is actually carbon negative".

I want to post the Brasilian embassy and ask why they don't creat Terra Preta in the cane fields!??

What about getting all these microbes and fungi working working for us ??

What about the tripling soil fertility, without NPK??

"According to Glaser's research, a hectare of metre-deep terra preta can contain 250 tonnes of carbon, as opposed to 100 tonnes in unimproved soils from similar parent material.
The extra carbon is not just in the char — it's also in the organic carbon and enhanced bacterial biomass that the char sustains.

That difference of 150 tonnes is greater than the amount of carbon in a hectare's worth of plants. That means turning unimproved soil into terra preta can store away more carbon than growing a tropical forest from scratch on the same piece of land, before you even start to make use of its enhanced fertility. "

Harnessing the work of this vast number of microbes and fungi changes the whole equation of EROEI for food and Bio fuels. I see this as the only sustainable agricultural strategy if we no longer have cheap fossil fuels for fertilizer.

We need to get this super community of wee beasties to work with us by populating them into their proper Soil horizon Carbon Condos.

I feel Terra Preta soil technology is the greatest of Ironies since Tobacco.
That is: an invention of pre-Columbian American culture, destroyed by western disease, may well be the savior of industrial western society. As inversely Tobacco, over time has gotten back at same society by killing more of us than the entire pre-Columbian population.

Erich J. Knight

11. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
100% False.

Sugar cane to ethanol fuel carbon cycle is ALWAYS and IMMEDIATELY a net removal of CO2 from the air. Not only is part of the carbon immediately sequester in the growing cane and for years in the soil as roots, but the crushed cane can be processed in a "bio factory" (cow) that not only cost nothing to build but can be sold for human food (beef) at significant profit. The waste products of this four legged bio factory can be:

(1) Burnt for fuel. (It provides most of the fuel used for cooking in most of rural India and other poor parts of Asia.) or
(2) Used to enrich the soil, like the "terra preta" produced by expensive mechanical factories, which can neither be sold at a profit not used as human food but require significant fossil fuel (for making steel etc) to build. In contrast, cows are “built” naturally and run on solar energy (grass stored).

Use (1) should be discouraged when possible without causing too much human suffering as use (2) is much more beneficial in the long run. Use (1) instead of use (2) is a major factor causing the regions where use (1) is dominate to remain poor, but as they are poor, people using (1) can not afford to invest this “cow produced asset” for the year or two required to gain much more productivity. - They have an immediate need to cook tonight’s dinner, etc. (In some parts of India, this fuel asset is so competitively and desperately sought, that it never hit’s the ground but is caught by small children following the cow and then sun-dried until it can be used as fuel.)

In addition to the sequestering of carbon in the cane roots much more carbon is removed from the air by the growing cane (very economically as cane to alcohol produces both profit and lots of low skill requirement jobs.)*

In contrast to this economically productive cane-to-alcohol carbon sequestering and air clean up (of CO2) process, the production of terra preta will for about 500 years INCREASE the CO2 in the air and ALWAYS (FOR EVER) release poisonous CO into the air! The terra preta plant will of course some require energy and by its very nature release great amounts of heat, which is not economically feasible source ot the required energy. In contrast the crushed cane not only can provide 100% of the energy required for cane crushing and distillation but there is a surplus which at the larger plants is burnt to generate and sell electric power (the excess over local motors requirements etc.) Obviously the cane burnt for energy does not go to the cow. Cow food comes only from the smaller alcohol production plants.

The expensive terra preta mechanical factory releases, by "smoldering," into the air more than one ton of CO2 for every ton of carbon char it produces, and this does not include either the CO2 released to bring the cellulose to the terra preta plant nor the CO2 released by the tractors etc that must bury it to keep it from blowing or washed away by rain into the stream, eventually becoming sequestered on the ocean floor. (This lost to the oceans is doubly disastrous as not only does the soil not get enriched, but once on the ocean floor microorganism convert it to CH4 and CO2. The CH4 is then stored as methane hydrate if the deposit location is cold and deep, as often will be the case.)

Production of terra preta INCREASES the CO2 in the air as it is a combustion process ("smoldering" with too little oxygen to convert 100% into CO2, but producing a lot of poisonous CO, which will later in the atmosphere becomes CO2.) At best, approximately half of the carbon in the feed stock to the terra pret plant will end up in the "char" produced. For example, if one starts with 1000 pounds of carbon ALREADY SAFELY STORED in the celulose 500 or less pounds can be stored in the soil as char on the first attempt. Note the more than 500 pounds now released to the air, was safely stored in cellulose, which could have been buried for immediate storage of 100% of the carbon, not half or less.

As the years pass, the 500 or more pounds of C first released from safe storage in cellulous, by the terra preta plant can be again captured by living plants and brought back again to the terra preta plant. Then an additional 250 or less of the original 1000 pounds can also get stored in the soil. After many years, many cycles thru the trerra preta plant, most of the original 1000 pounds can be stored in the soil, but NEVER all of the inital 1000 pounds as each cycle does burn fuel to bring the cellulose to the terra preta plant and to bury it. If this fuel consumption requires 5 pounds (for 1000 pounds processed in many sequential cycle) then AT BEST the terra preta process can put 995 pounds out of every 1000 pounds processed in multiple cycles into the soil. Thus with modern means (not using only the manual labor of the Amazon Indians who may have been able to store 100%) the terra preta can not achieve net removal of CO2 for many, many years (I would guess 500 years.)

Much better than this very slow process to achieve net sequestering is to construct a methane recovery land fill with almost immediate displacement of some the combustion of petroleum and natural gas with methane made, at very low incremental cost to a common trash dump. This achieves significant and almost immediate net reduction in the CO2 as the fossil fuel consumption is reduced (replaced by carbon that the plant making the cellulose removed from the air.) - For example trees remove CO2, are made into paper that ends up the methane producing landfill. Then the methane is burn and the carbon returns to the air is again made into trees etc. To the extent this is done, the fossil fuel remains in the ground as chemical feed stock for future generations*

SUMMARY:
Erich_knight HAS IT EXACTLY WRONG. Terra preta will be INCREASING the CO2 in the air for many years (perhaps 500) and cane-to-alcohol system immediately reduces the CO2 in the air. Note I did not adequately mention the billions of tons of carbon that is stored in the cane still growing in the fields or after it is converted (a small faction) into alcohol, the millions of tons of carbon stored in steel tanks of the alcohol distributor.

Erich knight’s confusion on this is, I think, fundamentally caused by not recognizing that terra preta, unlike sugar cane does not directly remove one gram of CO2 from the air.** Terra preta is a STORAGE SYSTEM***, not a removal system. This is similar to the mistake proponent of the "hydrogen economy" make - hydrogen is an energy storage chemical, not an energy source. It is highly doubt full that terra preta can economically compete with other carbon storage system such as methane producing land fills and sugar cane, which is not only an economically viable CARBON STORAGE system, but also a SOIL ENRICHMENT system, and a ENERGY SOURCE (or actually the most economically efficient means currently available of capturing and storing solar energy for liquid fuel, which displaces oil consumption to give a double reduction effect in the air's CO2 content.) and a FOOD SOURCE, both directly as sugar and indirectly as beef, and a low skill JOBS SOURCE.

In contrast, man making terra preta is only a continuous source of poisonous carbon monoxide! and prehaps 1% as many jobs.

---------------------------------
*Perhaps even more economically important is fact that the alcohol fueled car is not burning a very valuable chemical feed stock material that future generation will need to make plastic etc., economically. The cost of not having economical oil to make plastics etc from will be enormous for some not too distant set of our descendents. It is a major crime against them to burn up this chemical complex we call petroleum, simply for heat! Also by doing so, we may be leaving them a world too hot to sustain life, if the methane hydrates of the ocean floors are destabilized. No greater crime than that is possible! That is not genocide, but “speciescide”, for many species!)

**Terra preta is actually a weak SOURCE of CO2, as are all organtic materials in the soil, it is slowly oxidized. The more that is there, the more CO2 it will produce.

***Terra preta is a very good storage system, better than wood construction in houses, and worse than either CO2 injection into aquifers, or a liquid fuel system economy using alcohol from sugar cane (or from any grown cellulous when and if that becomes possible) to keep constantly many millions of tons of carbon either in the growing cane or in the alcohol in the distributor's storage tanks or in the soil, after passing thru a cow, or even in the cow itself!

Final note:
I assume that like beef, one can eat terra preta, (for the proteins in the microorganisms in it and /or its ability to absorb digestive gas), but doubt it is as nutritious or tastes as good.

Last edited by a moderator: Sep 18, 2006
12. ### CarcanoValued Senior Member

Messages:
6,865
On a side note, I was doing some reading last night about Henry Ford's investigations of Bio-plastic for use in the construction of car panels. He ended up building an entire car using just the protein and carb content of soybeans and hemp fibre. The body panels were not only ten times more resistant to denting, but were also only 2/3 the weight of steel panels. Heres a pic of Ford taking an axe to the car to demostrate how strong the new material was:

http://altahemp.com/hempinfo.html

13. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
Interesting. Note also Ford never made car parts from these renewable sources, despite the advantage you mention. I presume because that would have cost more, which is the point I was trying to make about it being a crime to burn up petroleum for heat instead of use it only as a chemical feed stock, and pehaps for some critical lubrications, but as synthetic oils are already in use and better, perhaps there is no such need to use natural oils as lubricants.

As Paul Dixon would say:
"Your children will thank you" (for not using up their cheap plastic source - oil.)

14. ### CarcanoValued Senior Member

Messages:
6,865
Perhaps not, Ford was dead serious about mass producing cars with plastic parts, but this was right about the time when car production was halted due to the war, and there may be other reasons as well, such as the ban on hemp production.
http://virtualfactory.blogspot.com/2006/04/official-and-unofficial-story-of.html

The focus on bioplastics now seems to be polylactic resin derived from corn and sugar cane.

15. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
Even more interesting. Thanks. I am not (at least not yet) buying WWII beginning the reason why Ford never make use of bio plastics in production line cars, for two reasons:

(1)With steel in short supply for the war machines that should have made it easier to turn to bioplastics, if they were both practical and economic.

(2)I suspect they were neither. 70 years later they are still "being developed" (but quick search now make me think they can be made practical) The economics I have not seen any information on yet, but will try some more. Your reference above does touch on a long standing concern of mine - What I think is the primary defect in the "free market system" - Namely the need for government to try to include the cost to society of production processes that the maker of products can duck. The most gross of these cost is now at least partially included - for example if your business is to reprocess old lead acid car batteries, you can no long being the process by dumping the liquid out into the stream behind the plant and the stacking them in big pile to burn an collect the melting lead with God knows what pollution (lead vapors certainly) going into the air. You still can of course make a product (almost anything) and ignore the end of cycle disposal costs.

Almost the only industry that does not avoid the disposal costs is the nuclear power industry. Some day the computer I am pounding now will hit the trash can and the battery in it plus a lot of other things, if lucky will end up in some poor country polluting their air after some component are salvaged by hand when it is burned or chemically processed to recover the small amount of gold in it.

If cars made of soybeans instead of steel are not (and I suspect they are not by a big factor) economically competitive now, perhaps the government including more of the currently avoided cost can help. Disposing of cars is not much of a cost. It certainly pays, even with high US labor cost to strip out the electric motors for their copper and all the steel is easily recycled (after “chunking” to small pieces) with magnetic separation) but the full cost of getting the steel from iron ore and coke to the environment is certainly not included as much of this cost is "dumped" on some third world count.

As China is still “coal-power” it certainly can not be held up as a current model for an economic system that does include most of the true cost of production They do not have great quantities of drinking water and yet are polluting what they do have in their "great leap forward" (the current expansion, not the non-sense of the same name Chairman Mao attempted) but with at least 30 modern nuclear plants in construction and the world’s largest (plus dozens of smaller) hydro-electric dams coming on line in a planned economy that can include all the costs, they will transform from a pollution center more rapidly than say Pittsburgh, PA did. (I can remember when even a brief visit there might cause serious lung problems, and certainly a hacking cough. No Chinese city is worse than Pittsburgh’s valley was in WWII’s steel and coke production peak.)

16. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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23,198
Alcohol is now (in Brazil) slightly less than half the price of gasoline! Recognizing it has only about 70% of the energy content by volume, and that you can buy more than two gallons for every gallon of gas that means you can go a little more than 40% farther with alcohol than with gasoline for the same expenditure. 2x0.7= 1.4

Reason why alcohol is now so cheap is that Brazil and soon India (worlds second producer) had very good growing seasons and record crops. (Only when the government is holding down the price of gasoline and supply of alcohol is low is alcohol driving same cost as using gasoline. - Alcohol has many dozens of independent competing producers, but PetroBras is essentially the only gasoline source and is government controlled, especially as national elections approach.)

US places US$0.14 on each liter imported from Brazil and quota restrictions also, but they never are important as with 3.75L/gallon, that is 52.5 cents extra cost per gallon or when the 0.7 energy factor is considered, that is$0.75/gallon handicap for Brazil company trying to export to US. There is also a 55 cent / gallon "kick back" (of your tax money) to US producers of alcohol. So US's support of "free trade" is BS as the "playing field" is tilted $1.30/gallon to aid US producers of alcohol. I do not include here the fact that corn the US alcohol producers buy is the largest of all the farm subsidies! - More of your taxes go there to make a very few, very rich, like the Cargill family, much richer each year. (Cargill is largest privately held company in US if not the world, but they have big campaign contribution expenses - US has best government money can buy.) Also interesting is fact that the import duty on oil is$0.00/ gallon so the rich enemies of the US in Mid East can also have a 52.5 cent /gallon advantage over poor friends - the truely needy population of Africa, India and South America. Just like in book 1984, US government needs an “enemy,” even if US needs to help prop it up financially.

When you know the facts, surely you can smell this giant rotten rat* that is causing Joe American to pay higher taxes for the privilege of paying more for his car's fuel than need be.

If I may combine and paraphrase GWB & Paul Dixon's closing line:

Stay the course - The Saudi and Cargill families and all the Ex-oil companies CEOs in US government will thank you.
----------------------------------------------
*Not to mention causing more deaths in Iraq each month than 9/11, making it unsafe for Americans to freely travel in much of the world, etc.

Last edited by a moderator: Sep 21, 2006
17. ### erich_knightErich J. KnightRegistered Senior Member

Messages:
108
Concerning Terra Preta:

Dear Billy

Did you even look at the EPRIDA site? http://www.energy.gatech.edu/presentations/dday.pdf & http://www.eprida.com/hydro/

They are a social purpose firm, designing equipment and business a model that will not cost the farmer anything out of pocket and create a many fold increase in rural high pay employment.

Did you study the data presented at the 2004 EACU conference and the recent World Soils Conference in Philly?

Johannes list the publications on his site :
http://www.css.cornell.edu/faculty/lehmann/terra_preta/TerraPretahome.htm

With all respect, Erich

18. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
To Erich_knight
Thanks for links. I have now looked at http://www.energy.gatech.edu/presentations/dday.pdf

Its 54 pages are mainly two parts: bio fuel & & terra preta.

The bio-fuels section is OK, but is mainly hopes and dreams and ignores alcohol which is real, economic, and enviromentally friendly.

On terra preta section:

Page 45 gives the relative carbon release by many fuels, showing all, even solar photovotatics, make some release (and they are correct when producing them and set up in field is included) and only terra preta as carbon negative. For reasons I detailed, in earlier post they are not entirely honest here. Yes, terra preta stores for reasonably long times (less than C02 injection into aquifer or raising clams etc as I mentioned in prior post) but each pass thru the char plant sends less than half of the carbon input into char for terra preta. Thus, if instead of using methane producing land dump to process 200 tons of bio-waste and by avoiding oil use, removes and /or store more than 200 tons in about one year, the char plant will put more than 100 tons of CO2 into the air for every 100 tons it stores, and part of that dumped into the air may be posionous CO initially. Their terra preat enthusasm is causing dishonesty.

Probably the same reason they failed to even include alcohol (of any type) in their page 45 chart -it is better, cheaper and much quicker than char at least as world converts and stores carbon in growing cane and alcohol storage tanks. After 1000 years or so, char can store more carbon than cane and alcohol.

You have quick and strong enthusiasm for many new technology but IMHO are not critical enough in your examination of them. Let me respectively suggest that you compare the results of processing 100 tons of wood chips and old news paper by two different processes. (methane land fill plant vs. Terra preta production and storage plant) in terms of how much (include oil displacement) the CO2 in air is changed by both and which removes more carbon form the carbon cycle for 100 years. I think you will find that the terra preta plant does not reduce oil consumption (adds slightly to it) and removes less than 50 tons of carbon from the carbon cycle and is not economically feasible without tax payer support. I.e. loses on all counts compared to the methane producing land fill.

Later by edit: I have visited the other two links now - not much new or different from first and I again not the almost activie ingnoring of ethanol and methane land fill alternatives. Also I know little about it, but is it not possible that Brazil's terra preta is natural, not man made? Obvious nature can make coincentrated carbon deposits (we call hem coal). Obviously vegitation in some areas, like Brazil, grows so fast and dies that it burries earlier half rotten vegitation. etc. Fact that some brokne potteryis found in it etc is not proof that it ws intentional made made soild addative. Perhaps tribal man's only role was to agee to sue one location as the dump. Back then it would not have old TV, tires, bottles and batteries, just vegitation and some pottery chards. The vegitation would generate heat (have you ever opened a big compost pile?) and with inadequate oxygen be largely reduced to carbon and oils (call that char) I like this natural carbon deposit theory alternative as I know peat is good for making scotch

Last edited by a moderator: Sep 22, 2006

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20. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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23,198
Thanks for link - It talks, for two pages, even about getting alcohol from tulip popular trees yet never even mentions sugar cane, worlds largest and best source. The only liquid fuel source that is cheaper than gasoline, has 30 + years of use in million of cars, and also cleans the air of CO2! Amazing - must be written by an American, who like most, can not understand there is an advanced world beyond the US borders.

21. ### SingularityBannedBanned

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1,287
Let them do the RnD

We will then use the results to Modify the SugarCane.

I hope we can create Ethanol from Genetically modified Forest Tree Basks (outer coverings of trees). So that somehow we will get our Jungles back instead of BioFuel Farm feilds.

22. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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23,198
I strongly recommend you hear and see slides of Dupont 3Oct06 presentation at 'Ethanol on The Cob' Biofuels Conference at:

www.veracast.com/webcasts/citigroup/biofuels06/98102254.cfm

Especially hear the questions.
Answer to one was approximately: “Yes a cellulose source is even more attractive in Brazil as their plants only produce ethanol 8 months of the year because they can not store the juice pressed from the cane. The crushed cane could fill in the other 4 months, increasing both the profits and greatly increasing yields per acre. Even today Brazil can compete with 20dollar / barrel petroleum.

Brazil’s climate is not good for wheat production. This year’s crop is less than usual and Brazil will import 80% of its needed wheat. Adam Smith’s lessons about the virtues of trading sadly are still ignored. A wheat for alcohol trade between Brazil and US would benefit both - greatly benefiting the US, but not the politically well connected current vested interests in US who care only for the profits they can milk from the tax payers.

US shoulld be importing bio-fuels from tropical lands where they are more efficiently* and economically produced and avoiding extra cost both when buying fuel at the “gas station” for your car and when paying taxes to support the large subsidies required for corn based fuel to compete.

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*Production of ethanol in Brazil from sugar cane yields 8 units of energy for 1 unit of petroleum energy input, whereas production from Iowa corn yields only 1.25 units of energy produced for 1 unit of petroleum energy input. (Some researchers still maintain Iowa’s net energy yield is negative!)

Last edited by a moderator: Oct 4, 2006
23. ### Chathabig brown was screwed upRegistered Senior Member

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1,867
H2 and O2. You can get these two with hydrolysis and perioxides, and they are efficient, more efficient and pure than ethanol.