text:
Question

# The gap between the plates of a parallel-plate capacitor is filled up with two dielectric layers $$1$$ and $$2$$ with thicknesses $$d_{1}$$ and $$d_{2}$$, permittivities $$\epsilon_{1}$$ and $$\epsilon_{2}$$, and resistivities $$\rho_{1}$$ and $$\rho_{2}$$. A dc voltage $$V$$ is applied to the capacitor, with electric field directed from layer $$1$$ to layer $$2$$. Find $$\sigma$$, the surface density of extraneous charges at the boundary between the dielectric layers, and the condition under which $$\sigma = 0$$.

Solution

## We have, $$E_{1}d_{1} + E_{2}d_{2} = V$$and by current conservation$$\dfrac {1}{\rho_{1}} E_{1} = \dfrac {1}{\rho_{2}}E_{2}$$Thus, $$E_{1} = \dfrac {\rho_{1}V}{\rho_{1}d_{1} + \rho_{2}d_{2}}$$,$$E_{2} = \dfrac {\rho_{2}V}{\rho_{1}d_{1} + \rho_{2}d_{2}}$$At the boundary between the two dielectrics,$$\sigma = D_{2} - D_{1} = \epsilon_{0} \epsilon_{2} E_{2} - \epsilon_{0} \epsilon_{1} E_{1}$$$$\dfrac {\epsilon_{0}V}{\rho_{1}d_{1} + \rho_{2}d_{2}} (\epsilon_{2} \rho_{2} - \epsilon_{1} \rho_{1})$$.Physics

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optimum_param {doremi} R Documentation

Function to find the optimum parameter for derivative estimation (embedding or spar according to derivative estimation method chosen)

Description

optimum_param calculates the optimum parameter for derivative estimation by varying the latter in a range introduced as input and keeping the parameter and coefficients having the $R^2$ closest to 1.

Usage

optimum_param(
data,
id = NULL,
input = NULL,
time,
signal,
dermethod = "gold",
model = "1order",
order = 2,
pmin = 3,
pmax = 21,
pstep = 2,
verbose = FALSE
)

Arguments

 data Is a data frame containing at least one column, that is the signal to be analyzed. id Is a CHARACTER containing the NAME of the column of data containing the identifier of the individual. If this parameter is not entered when calling the function, a single individual is assumed and a linear regression is done instead of the linear mixed-effects regression. input Is a CHARACTER or a VECTOR OF CHARACTERS containing the NAME(s) of data column(s) containing the EXCITATION vector(s). If this parameter is not entered when calling the function, the excitation is assumed to be unknown. In this case, the linear mixed-effect regression is still carried out but no coefficient is calculated for the excitation term. The function then uses the parameters estimated by the regression to carry out an exponential fit of the signal and build the estimated curve. The function will consider as an excitation each column of data having a name contained in the input vector. The function will return a coefficient for each one of the excitation variables included in the input vector. time Is a CHARACTER containing the NAME of the column of data containing the time vector. If this parameter is not entered when calling the function, it is assumed that time steps are of 1 unit and the time vector is generated internally in the function. signal Is a CHARACTER containing the NAME of the column of the data frame containing the SIGNAL to be studied. dermethod is the derivative estimation method. The methods currently available are: "gold","glla" and "fda" (see their respective function for more details) model is the model to be used for analysis of the signal. The models available are "1order" and "2order" order is the maximum order of the derivative estimated when using calculate.gold or calculate.glla. Using a higher order can enhance derivative estimation (see doi: 10.1080/00273171.2015.1123138Chow et al.(2016)) pmin is the minimum of the interval in which to vary the parameter (embedding number or spar according to derivative method chosen) pmax is the maximum of the interval in which to vary the parameter (embedding number or spar according to derivative method chosen) pstep is the step that will be considered when varying the parameter. For instance pmin=3, pmax=7 and pstep=2 and dermethod="gold" will make the embedding number take the values 3,5 and 7. verbose Is a boolean that displays status messages of the function (and functions it calls) when set to TRUE.

Value

Returns a list of three objects:

• analysis is a data.frame containing the resultmean object of the analysis made (result of the analyze.1order or analyze.2order function according to model chosen) with the different values of embedding/spar and the resulting $R^2$.

• summary_opt is a data.frame containing the analysis that had the best $R^2$ from the analysis data.frame previously mentioned

• d contains the optimum value of the embedding/spar

analyze.1order and analyze.2order for the estimation of equation coefficients in signals following a first and second order differential equation respectively

Examples

s2 <- generate.panel.2order(time = 0:100,
excitation = c(rep(0,25),rep(1,76)),
y0 = 0,
v0= 0,
xi = 0.05,
period=10,
k=1,
yeq=0,
nind=4,
internoise = 0.2,
intranoise = 8)
resgold <- optimum_param (data=s2,
id="id",
input="excitation",
time="time",
signal="signal",
model = "2order",
dermethod = "gold",
pmin = 3,
pmax = 13,
pstep = 2,
verbose = TRUE)

[Package doremi version 1.0.0 Index]

format: plain


text:
###### back to index | new

Find the length of the leading non-repeating block in the decimal expansion of $\frac{2004}{7\times 5^{2003}}$. For example the length of the leading non-repeating block of $\frac{5}{12}=0.41\overline{6}$ is $2$.

Find $x$ satisfying $x=1+\frac{1}{x+\frac{1}{x+\cdots}}$.

Write $\sqrt[3]{2+5\sqrt{3+2\sqrt{2}}}$ in the form of $a+b\sqrt{2}$ where $a$ and $b$ are integers.

Compute $$\sum_{n=1}^{\infty}\frac{2}{n^2 + 4n +3}$$

Compute $$\sum_{k=1}^{\infty}\frac{1}{k^2 + k}$$

Compute the value of $$\sum_{n=1}^{\infty}\frac{2n+1}{n^2(n+1)^2}$$

Let $(x^{2014} + x^{2016}+2)^{2015}=a_0 + a_1x+\cdots+a_nx^2$, Find the value of $$a_0-\frac{a_1}{2}-\frac{a_2}{2}+a_3-\frac{a_4}{2}-\frac{a_5}{2}+a_6-\cdots$$

Find the length of the leading non-repeating block in the decimal expansion of $\frac{2017}{3\times 5^{2016}}$. For example, the length of the leading non-repeating block of $\frac{1}{6}=0.1\overline{6}$ is 1.

Let $\alpha_n$ and $\beta_n$ be two roots of equation $x^2+(2n+1)x+n^2=0$ where $n$ is a positive integer. Evaluate the following expression $$\frac{1}{(\alpha_3+1)(\beta_3+1)}+\frac{1}{(\alpha_4+1)(\beta_4+1)}+\cdots+\frac{1}{(\alpha_{20}+1)(\beta_{20}+1)}$$

If $m^2 = m+1, n^2-n=1$ and $m\ne n$, compute $m^7 +n^7$.

The Lucas numbers $L_n$ is defined as $L_0=2$, $L_1=1$, and $L_n=L_{n-1}+L_{n-2}$ for $n\ge 2$. Let $r=0.21347\dots$, whose digits are Lucas numbers. When numbers are multiple digits, they will "overlap", so $r=0.2134830\dots$, NOT $0.213471118\dots$. Express $r$ as a rational number $\frac{q}{p}$ where $p$ and $q$ are relatively prime.

Let $a_1=a_2=1$ and $a_{n}=(a_{n-1}^2+2)/a_{n-2}$ for $n=3, 4, \cdots$. Show that $a_n$ is an integer for $n=3, 4, \cdots$.

Suppose $\alpha$ and $\beta$ be two real roots of $x^2-px+q=0$ where $p$ and $q\ne 0$ are two real numbers. Let sequence $\{a_n\}$ satisfies $a_1=p$, $a_2=p^2-q$, and $a_n=pa_{n-1}-qa_{n-2}$ for $n > 2$.
• Express $a_n$ using $\alpha$ and $\beta$.
• If $p=1$ and $q=\frac{1}{4}$, find the sum of first $n$ terms of $\{a_n\}$.

• Compute $$S_n=\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+\cdots+\frac{n+1}{2^n}$$

In a sports contest, there were $m$ medals awarded on $n$ successive days ($n > 1$). On the first day, one medal and $1/7$ of the remaining $m − 1$ medals were awarded. On the second day, two medals and $1/7$ of the now remaining medals were awarded; and so on. On the $n^{th}$ and last day, the remaining $n$ medals were awarded. How many days did the contest last, and how many medals were awarded altogether?

Suppose sequence $\{a_n\}$ satisfies $a_1=0$, $a_2=1$, $a_3=9$, and $S_n^2S_{n-2}=10S_{n-1}^3$ for $n > 3$ where $S_n$ is the sum of the first $n$ terms of this sequence. Find $a_n$ when $n\ge 3$.

Find an expression for $x_n$ if sequence $\{x_n\}$ satisfies $x_1=2$, $x_2=3$, and $$\left\{ \begin{array}{ccll} x_{2k+1}&=&x_{2k} +x_{2k-1}&\quad (k\ge 1)\\ x_{2k}&=&x_{2k-1} + 2x_{2k-2}&\quad (k\ge 2) \end{array} \right.$$

Is it possible for a geometric sequence to contain three distinct prime numbers?

Is it possible to construct 12 geometric sequences to contain all the prime between 1 and 100?

Let $S_n$ be the sum of first $n$ terms of an arithmetic sequence. If $S_n=30$ and $S_{2n}=100$, compute $S_{3n}$.

Let $d\ne 0$ be the common difference of an arithmetic sequence $\{a_n\}$, and positive rational number $q < 1$ be the common ratio of a geometric sequence $\{b_n\}$. If $a_1=d$, $b_1=d^2$, and $\frac{a_1^2+a_2^2+a_3^2}{b_1+b_2+b_3}$ is a positive integer, what is the value of $q$?

Let $S_n$ be the sum of the first $n$ terms in geometric sequence $\{a_n\}$. If all $a_n$ are real numbers and $S_{10}=10$, and $S_{30}=70$, compute $S_{40}$.

Expanding $$\Big(\sqrt{x}+\frac{1}{2\sqrt[4]{x}}\Big)^n$$ and arranging all the terms in descending order of $x$'s power, if the coefficients of the first three terms form an arithmetic sequence, how many terms with integer power of $x$ are there?

Suppose sequence $\{F_n\}$ is defined as $$F_n=\frac{1}{\sqrt{5}}\Big[\Big(\frac{1+\sqrt{5}}{2}\Big)^n-\Big(\frac{1-\sqrt{5}}{2}\Big)^n\Big]$$ for all $n\in\mathbb{N}$. Let $$S_n=C_n^1\cdot F_1 + C_n^2\cdot F_2+\cdots +C_n^n\cdot F_n.$$ Find all positive integer $n$ such that $S_n$ is divisible by 8.

Solve $\{L_n\}$ which is defined as $F_1=1, F_2=3$ and $F_{n+1}=F_{n}+F_{n-1}, (n = 2, 3, 4, \cdots)$


text:
# How do I get a list of nodes in the currently active group?

context.space_data.node_tree.nodes always returns a list of the nodes at the base level of the tree (not inside any group), even if the user is actually editing the nodes inside a group.

My Material  <-- context.spacedata.node_tree (always)
└ Group
└ Group in a group  <-- user is editing this

How can I get a list of the nodes in whatever group the user is busy with, no matter how far down the rabbit hole they've gone?

context.active_node.id_data.nodes is one solution, but it does not work if there is no active node (e.g. if the user just deleted it and hasn't selected anything since).

There doesn't seem to be any obvious solution, so I've come up with a bit of a hack:

The trick is, context.active_node is always the actual active node in the tree the user is currently editing. context.space_data.node_tree.nodes.active (let's call it tree_active for short) is the active node for the base level (outside all groups). If the user is editing a group, tree_active will be a group node (because it was first selected+made active before the user hit Tab to edit it).

So if context.active_node is not the same as tree_active, then we know the user is inside a group. We don't know how deep they are though, so we need to recursively check if tree_active is the same as context.active_node - if it's not, then we use tree_active's node tree as the new base tree we're checking against.

If we are in a group, tree_active will always be a group node (unless it is the same as context.active_node).

Here's the code I eventually came up with:

tree = context.space_data.node_tree  # Base level tree
if tree.nodes.active:
while tree.nodes.active != context.active_node:
# We are in a group, check next level
tree = tree.nodes.active.node_tree

tree will be whatever node tree the user is currently editing.

You can use edit_tree instead of node_tree to get the tree currently being edited and access its nodes property for the list of nodes, e.g.:

context.space_data.edit_tree.nodes


text:
We need two tenths kg of a carrot, one tenth of peas and three tenths of of tomatoes to make salad. Express the fraction of the weight of the vegetables to be salad. Convert the result to grams.

Correct result:

f =  0.6 kg
g =  600 g

#### Solution:

$f=2/10 + 1/10 + 3/10=\dfrac{ 3 }{ 5 }=0.6 \ \text{kg}$
$g=1000 \cdot \ f=1000 \cdot \ 0.6=600 \ \text{g}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

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text:
# Blumenthal-Getoor index for IG and $\Gamma$

It is well known that that the gamma and inverse gaussian distributions lead to Levy processes.

For a Levy process with Levy measure $\nu$ one can define (I'm new to this, this is the first definition I have seen) the Blumenthal-Getoor index $$\beta = \inf \{p >0 : \int_{|x|\leq 1 } |x|^p \nu(dx) < \infty \}$$ Looking in the class of jump processes I know that $\beta=0$ gives compound poisson $\beta = 1$ finite activity and necessarily $\beta \leq 2$ - so I guess it can generally be thought of as a kind of measure of how "wild" the process behaves.

Edit the paper I have tried to guess the definition from is this on page 4, as I have never heard of it before I did not know it was incorrect, I have changed it to another definition (from google).

What I am looking for is whether this number is known for the Inverse Gaussian Levy process, the Gamma Levy process and maybe a reference to get a feeling for this new object.

• For the Gamma process, the Lévy measure is $\nu(dx) = x^{-1} e^{-x} dx$ for $x\geq 0$. From your definition of the Blumenthal-Getoor index, you see that $\beta = 0$. The difference with the compound Poisson case is that the infimum $0$ is not attain. – Goulifet Feb 17 '15 at 13:35
• Small question: in the definition of $\beta$, shouldn't the integral be over all $\mathbb{R}$? – Goulifet Feb 17 '15 at 14:25
• As it is written now, the definition of the Blumenthal-Getoor index doesn't make sense; there are several typos in it. – saz Feb 17 '15 at 14:28
• @saz Thanks for pointing out - please see edit. – Henrik Feb 17 '15 at 16:00
• @Henrik yeah, looks much better. See my answer below (... if you are interested in more details, I can try to find some references; the references I know are unfortunately for more general processes and that might be confusing.) – saz Feb 17 '15 at 16:29

Example 1 (Gamma process): As @Goulifet pointed out, the Lévy measure of a Gamma process is given by $$\nu(dx) =c x^{-1} e^{-\alpha x} \, dx =: p(x) \, dx.$$ Here $\alpha$ and $c$ are fixed constants. Since $e^{-\alpha x} \leq e^{\alpha}$ for all $x \in [-1,1]$, we get

$$\int_{|x| \leq 1} |x|^p \, \nu(dx) \leq c e^{\alpha} \int_{|x| \leq 1} |x|^{p-1} \, dx < \infty$$ for all $p>0$. Consequently, $\beta=0$.

Example 2 (Inverse Gaussian process): The density of the Lévy measure of the inverse Gaussian distribution is given by

$$p(x) = c \frac{1}{x^{3/2}} e^{-\gamma^2 x/2}$$

for some constant $c>0$ and $\gamma>0$. Using the same argumentation as above, we find that

$$\int_{|x| \leq 1} |x|^p \, \nu(dx) \leq c e^{\gamma^2/2} \int_{|x| \leq 1} |x|^{p-3/2}< \infty$$

for all $p>1/2$. Consequently, $\beta=1/2$.

General remarks: It is well-known that a Lévy process $(X_t)_{t \geq 0}$ can be characterized by the Lévy triplet $(b,\sigma^2,\nu)$ as well its symbol $\psi$. Namely, $\psi$ satisfies $$\mathbb{E}e^{\imath \, \xi X_t} = e^{- t \psi(\xi)}.$$ By definition, the Blumenthal-Getoor index measures the intensity of small jumps. Roughly speaking: If $(X_t)_{t \geq 0}$ and $(Y_t)_{t \geq 0}$ are Lévy processes with Blumenthal-Getoor indizes $\beta$ and $\gamma$, respectively, and if $\beta>\gamma$, then "$(X_t)_{t \geq 0}$ has more small jumps than $(Y_t)_{t \geq 0}$". One can show that the Blumenthal-Getoor index can be also characterized in terms of the asymptotic behavior of $\psi$ as $\xi \to \infty$: $$\beta = \inf \left\{\lambda>0; \lim_{|\xi| \to \infty} \frac{|\psi(\xi)|}{|\xi|^{\lambda}}=0\right\}$$ if the Lévy triplet satisfies a so-called weak sector condition (i.e. $|\text{Im}\ \psi(\xi)| \leq C |\text{Re}\ \psi(\xi)|$ for some constant $C>0$) and $\sigma^2=0$.

There is a lot of interest in Blumenthal-Getoor indizes because they can be used to characterize path properties (e.g. Hausdorff dimension and asymptotics of $\sup_{s \leq t} |X_s|$) as well as the asymptotics of absolute moments.

Some References: The following two references are concerned with Blumenthal-Getoor-Indizes for so-called Feller processes (this class includes Lévy processes).

• Henrik defined the Blumenthal-Getoor index in terms of the Lévy measure. In your general remark, you express it with the assymptotic behavior of $\psi$, then you suggest that the two concepts are linked with a "weak sector condition". Can you tell me more about it? In particular, when are the definitions with the Lévy measure and the symbol (with $\sigma^2=0$) equivalent? – Goulifet Mar 9 '15 at 19:10
• @Goulifet Sector condition means that $|\text{Im} \psi(\xi)| \leq C |\text{Re} \, \psi(\xi)|$ for some constant $C>0$. If this condition holds, then both characterizations are equivalent. – saz Mar 9 '15 at 19:21
• thanks a lot for your answer. Do you have any good reference addressing this kind of question in general? – Goulifet Mar 10 '15 at 8:44
• @Goulifet What do you mean by "in general"? For a larger class of processes? – saz Mar 10 '15 at 9:27
• I mean: references showing for instance that the sector condition is sufficient (and necessary?) to have indices from the Lévy measure and the symbol equal. And more generally, discussing about Blumenthal-Getoor indices and their applications. I know some quite old papers (from the 70's), but I have never find a general exposition on the subject. – Goulifet Mar 10 '15 at 9:34

In this paper, you can find the Lévy measures associated with both the Inverse Gaussian Lévy process (Example 3.2) and the Gamma Lévy process (Example 3.1).

For the Gamma process, I already mentioned that $\beta =0$. For the Inverse Gaussian, the Lévy measure has a density $u(x) \propto x^{-3/2} e^{- x}$, also you obtain $\beta = 1/2$.

The index $\beta$ can be described as a measure of the local regularity of a Lévy process. In the original paper of Blumenthal and Getoor, I think it was introduced to study the behavior of a Lévy process at $0$ (how does it converge to $0$?). I also mention that paper as an illustration of the link between the local regularity of a Lévy process and $\beta$. In the Theorem of page 5, the local Besov regularity (in the paper, the regularity parameter is $s$) is measured in terms of $\beta_\infty$ (what you call $\beta$).


text:
# Norm of an ideal with two generators in a ring of integers

Example. Let $K$ be a number field with $O_K=\mathbb{Z}[\alpha]$, where $\alpha$ is a root of $f(X)=X^3+X+1$. Let us check the prime factorizations of $(2),(3) \in \mathbb{Z}$.

$X^3+X+1$ is irreducible $(\mod 2 )$ therefore $2\mathbb{Z}[\alpha]=(2)=\mathfrak{p}$, it inerts. $X^3+X+1 \equiv (X-1)(X^2 + X + 2 )(\mod 3 )$ so it is reducible. Thus, $3\mathbb{Z}[\alpha]=(3,\alpha -1)(3, \alpha^2+\alpha+ 2)=\mathfrak{q_1}\mathfrak{q_2}$.

Now, I think that $[K:\mathbb{Q}]=3$ so that $Norm(\mathfrak{p})=2^3=8$. Also, $Norm(\mathfrak{q_1}\mathfrak{q_2}) = 3^3$. So, I have few questions:

1. Can we say that $2\mathbb{Z}[\alpha] = (2,\alpha^3 + \alpha +1)=(2)?$ $Norm((3,\alpha -1)(3, \alpha^2+\alpha+ 2))=Norm(\mathfrak{q_1}\mathfrak{q_2})=27.$
2. How do we decide whether $Norm(q_i) =3$ or $9$, for $i=1,2$?

3. What can be said about norm of an ideal with two generators, e.g. $Norm(\alpha,\beta)$ in general? I know that in $O_K$, ideals has at most $2$ generators.

• It is not mentioned in the lecture notes that I am following. – Ninja Dec 20 '17 at 20:35
• Of course, I edited the question. – Ninja Dec 20 '17 at 20:52

Here's a partial answer to your question that applies to the cases in the example. Suppose $\mathcal O_K$ is generated by a single element $\alpha$ with minimal polynomial $f(X)$. Then for every rational prime $p \in \mathbf Z$, we can factor $p \mathcal O_K$ as a product of prime ideals. Each prime ideal $\mathfrak p \mid p$ has the form

$$\mathfrak p = (p,g(\alpha))$$

where $g$ is one of the irreducible factors of $f \bmod p$.

In this case $\mathfrak N(\mathfrak p) = p^{\deg g}$. We can prove this as follows:

\begin{align} \mathfrak N(\mathfrak p) &= \left\lvert \mathcal O_K / \mathfrak p \right\rvert \tag{1}\\ \mathcal O_K/\mathfrak p &= \frac{\mathbf Z[\alpha]}{(p, g(\alpha))} \tag{2}\\ &\cong \frac{\mathbf Z[X]/(f(X))}{(p,g(X),f(X))/(f(X))} \tag{3} \\ &\cong \frac{\mathbf Z[X]}{(p,g(X),f(X))} \tag{4} \\ &\cong \frac{\mathbf Z/p\mathbf Z[X]}{(g(X),f(X))} \tag{5} \\ &\cong \frac{\mathbf Z/p\mathbf Z[X]}{(g(X))} \tag{6} \\ &= \operatorname{GF}(p^{\deg g}) \tag{7} \end{align}

Lines 1, 2 are by definition. Line 3 is since $\mathbf Z[\alpha] \cong \mathbf Z[X]/(f(X))$. Lines 4 and 5 are the third isomorphism theorem. Line 6 is since $g(X) \mid f(X) \pmod p$.

Finally, since $g$ is irreducible, $\mathbf Z/p\mathbf Z[X]/(g(X))$ is a field. Moreover it is a field extension of $\mathbf Z/p\mathbf Z$ of degree $\deg g$. Thus it is a finite field with $p^{\deg g}$ elements. It follows that $\mathfrak N(\mathfrak p) = p^{\deg g}$.

So to answer your first two questions (where $f(X) = X^3 + X + 1$):

1. Yes, $2 \mathbf Z[\alpha]$ is a prime ideal so it factors as $(2, \alpha^3 + \alpha + 1) = (2)$ (since $\alpha^3 + \alpha + 1 = 0$).

2. $\mathfrak N((3, \alpha - 1)) = 3$ and $\mathfrak N((3, \alpha^2 + \alpha + 2)) = 3^2$.


text:
The Annals of Mathematical Statistics

Marginal Homogeneity of Multidimensional Contingency Tables

S. Kullback

Abstract

Tests of marginal homogeneity in a two-way contingency table given by [1], [3], and [13] do not seem to lend themselves easily to extension to the problem of $m$-way marginal homogeneity in an $N$-way $r \times r \times \cdots \times r$ contingency table, $m < N$. The principle of minimum discrimination information estimation and the associated minimum discrimination information statistic applied in [5] to the problem of marginal homogeneity in an $r \times r$ contingency table can be easily extended to the case of a multidimensional contingency table. Estimates of the cell entries under the hypotheses of $m$-way marginal homogeneity are given. Relationships among the tests of homogeneity for $m$-way, $m = 1, 2, \cdots, N - 1$, marginals are given by an analysis of information. Numerical results are given for two sample $3 \times 3 \times 3$ tables, and two $5 \times 5$ tables.

Article information

Source
Ann. Math. Statist., Volume 42, Number 2 (1971), 594-606.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177693409

Digital Object Identifier
doi:10.1214/aoms/1177693409

Mathematical Reviews number (MathSciNet)
MR297084

Zentralblatt MATH identifier
0215.54305

JSTOR

Citation

Kullback, S. Marginal Homogeneity of Multidimensional Contingency Tables. Ann. Math. Statist. 42 (1971), no. 2, 594--606. doi:10.1214/aoms/1177693409. https://projecteuclid.org/euclid.aoms/1177693409


text:
mPDF Manual – Tables

# Tables

## Styles

For a full list of CSS styles supported by mPDF for tables/cells, see Valid CSS. Note the custom attribute “topntail” which I have added to add a horizontal border at the top and bottom of the table, and under the THEAD row if present.

Block-level tags (DIV, P etc) are ignored inside tables, including any CSS styles - inline CSS or stylesheet classes, id etc. To set text characteristics within a table/cell, either define the CSS for the table/cell, or use in-line tags e.g.

Both models of border-collapse are supported (CSS border-collapse:collapse or separate), as well as cellSpacing and cellPadding.

## Rotate

Tables can be rotated by 90 degrees clockwise or anticlockwise using either:

 or

(90 is clockwise, and -90 is counterclockwise)

Table rotation is disabled when columns are used.

## Autosize

If a table’s minimum width is too wide for the page/div/column, it will automatically reduce the font size in order to fit. The minimum width is calculated by the sum of column widths required to fit the longest single word in the column.

This function is ON by default, set in the config.php file as var $shrink_tables_to_fit = 1.4 The font size will only be reduced to a minimum size to avoid ridiculous results. The value of $shrink_tables_to_fit is the maximum factor by which the font-size will be reduced.

A shrunk table may not be what you want. You can prevent this resizing either by setting the maximum shrink-factor for a particular table e.g.
 or by setting the variable for the whole document i.e. $mpdf->shrink_tables_to_fit = 1; (Note that mPDF will always resize tables if it is the only way to fit a row or whole table onto a full page.) ## Repeating Table Header row on new page If a table is split onto more than one page, the first row of the table will be repeated at the top of the new page if either:
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\$table_error_report_param = ''; // Parameter which can be passed to show in error report i.e. chapter number being processed.


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# Morse complex

Let $M$ be a smooth manifold, and $u:M\to\mathbb{R}$ be a Morse function. Let $C_{n}^{u}(M)$ be a vector space of formal $\mathbb{C}$-linear combinations of critical points of $u$ with index $n$. Then there exists a differential $\partial_{n}:C_{n}\to C_{n-1}$ based on the Morse flow making $C_{*}$ into a chain complex called the Morse complex such that the homology of the complex is the singular homology of $M$. In particular, the number of critical points of $u$ of index $n$ on $M$ is at least the $n$-th Betti number, and the alternating sum of the number of critical points of $u$ is the Euler characteristic of $M$.

Title Morse complex MorseComplex 2013-03-22 13:53:18 2013-03-22 13:53:18 bwebste (988) bwebste (988) 4 bwebste (988) Definition msc 58E05


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## Collective enhancement in the exciton model

### M. Mumpower, D. Neudecker, H. Sasaki, T. Kawano, A. Lovell, M. W. Herman, I. Stetcu, M. Dupuis

Published PRC 107 034606 (2023)

The pre-equilibrium reaction mechanism is considered in the context of the exciton model. A modification to the one-particle one-hole state density is studied which can be interpreted as a collective enhancement. The magnitude of the collective enhancement is set by simulating the Lawrence Livermore National Laboratory (LLNL) pulsed-spheres neutron-leakage spectra. The impact of the collective enhancement is explored in the context of the highly deformed actinide, $^{239}$Pu. A consequence of this enhancement is the removal of fictitious levels in the Distorted-Wave Born Approximation often used in modern nuclear reaction codes.

LA-UR-22-30081

## Mail

Matthew Mumpower
Los Alamos National Lab
MS B283
TA-3 Bldg 123
Los Alamos, NM 87545


text:
# American Institute of Mathematical Sciences

September  2009, 12(2): 401-414. doi: 10.3934/dcdsb.2009.12.401

## Mathematical models of subcutaneous injection of insulin analogues: A mini-review

 1 Department of Mathematics, University of Louisville, Louisville, KY 40292, United States 2 Department of Cellular and Physiological Sciences; Department of Surgery, University of British Columbia, Vancouver, BC, Canada

Received  December 2008 Revised  May 2009 Published  July 2009

In the last three decades, several models relevant to the subcutaneous injection of insulin analogues have appeared in the literature. Most of them model the absorption of insulin analogues in the injection depot and then compute the plasma insulin concentration. The most recent systemic models directly simulate the plasma insulin dynamics. These models have been and/or can be applied to the technology of the insulin pump or to the coming closed-loop systems, also known as the artificial pancreas. In this paper, we selectively review these models in detail and at point out that these models provide key building blocks for some important endeavors into physiological questions of insulin secretion and action. For example, it is not clear at this time whether or not picomolar doses of insulin are found near the islets and there is no experimental method to assess this in vivo. This is of interest because picomolar concentrations of insulin have been found to be effective at blocking beta-cell death and increasing beta-cell growth in recent cell culture experiments.
Citation: Jiaxu Li, James D. Johnson. Mathematical models of subcutaneous injection of insulin analogues: A mini-review. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 401-414. doi: 10.3934/dcdsb.2009.12.401
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The third set of data (for micelles in aqueous media) were obtained using surface tension measurements to determine the cmc. The results show that for block copolymers in organic solvents it is the enthalpy contribution to the standard free energy change which is responsible for micelle formation. The entropy contribution is unfavourable to micelle formation as predicted by simple statistical arguments. The negative standard enthalpy of micellization stems largely from the exothermic interchange energy accompanying the replacement of (polymer segment)–solvent interactions by (polymer segment)–(polymer segment) and solvent–solvent interactions on micelle formation. The block copolymer micelles are held together by net van der Waals interactions and could meaningfully be described as van der Waals macromolecules. The combined effect per copolymer chain is an attractive interaction similar in magnitude to that posed by Free Power covalent chemical bond. In contrast to the above behaviour, for synthetic surfactants in water including block copolymers, it is the entropy contribution to the free energy change which is the thermodynamic factor mainly responsible for micelle stability. Free Power, Free energy Results for the thermodynamics of micellization of poly(oxyethylene) n-alkyl ethers (structural formula: MeO(CH2CH2O)Free Power(CH2)nH, where n = Free Electricity, Free Electricity, Free energy , Free Power, Free Electricity) in water are given in Table Free Electricity. Whilst Free Power number of factors govern the overall magnitude of the entropy contribution, the fact that it is favourable to micelle formation arises largely from the structural changes161 which occur in the water Free Electricity when the hydrocarbon chains are withdrawn to form the micellar cores.

#### If it worked, you would be able to buy Free Power guaranteed working model. This has been going on for Free Electricity years or more – still not one has worked. Ignorance of the laws of physics, does not allow you to break those laws. Im not suppose to write here, but what you people here believe is possible, are true. The only problem is if one wants to create what we call “Magnetic Rotation”, one can not use the fields. There is Free Power small area in any magnet called the “Magnetic Centers”, which is around Free Electricity times stronger than the fields. The sequence is before pole center and after face center, and there for unlike other motors one must mesh the stationary centers and work the rotation from the inner of the center to the outer. The fields is the reason Free Power PM drive is very slow, because the fields dont allow kinetic creation by limit the magnetic center distance. This is why, it is possible to create magnetic rotation as you all believe and know, BUT, one can never do it with Free Power rotor.

I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
OK, these events might be pathetic money grabs, but certainly if some of the allegations against her were true, both groups would argue, would she not be behind bars by now? Suffice it to say, most people who have done any manner of research into the many Free Energy against Free Electricity have concluded that while she is most likely Free Power criminal, they just can’t see her getting arrested. But if–and it’s Free Power big ‘if’–she ever does get arrested and convicted of Free Power serious crime, that likely would satisfy the most ardent skeptic and give rise to widespread belief that the Trump Administration is working on, and succeeding in, taking down the Deep State. Let’s examine the possibility that things are headed in that direction.
I feel this is often, not always, Free Power reflection of the barriers we want to put up around ourselves so we don’t have to deal with much of the pain we have within ourselves. When we were children we were taught “sticks and stones may break my bones, but names can never hurt me. ” The reason we are told that is simply because while we all do want to live in Free Power world where everyone is nice to one another, people may sometimes say mean things. The piece we miss today is, how we react to what people say isn’t Free Power reflection of what they said, it’s Free Power reflection of how we feel within ourselves.

#### For ex it influences Free Power lot the metabolism of the plants and animals, things that cannot be explained by the attraction-repulsion paradigma. Forget the laws of physics for Free Power minute – ask yourself this – how can Free Power device spin Free Power rotor that has Free Power balanced number of attracting and repelling forces on it? Have you ever made one? I have tried several. Gravity motors – show me Free Power working one. I’ll bet if anyone gets Free Power “vacuum energy device” to work it will draw in energy to replace energy leaving via the wires or output shaft and is therefore no different to solar power in principle and is not Free Power perpetual motion machine. Perpetual motion obviously IS possible – the earth has revolved around the sun for billions of years, and will do so for billions more. Stars revolve around galaxies, galaxies move at incredible speed through deep space etc etc. Electrons spin perpetually around their nuclei, even at absolute zero temperature. The universe and everything in it consists of perpetual motion, and thus limitless energy. The trick is to harness this energy usefully, for human purposes. A lot of valuable progress is lost because some sad people choose to define Free Power free-energy device as “Free Power perpetual motion machine existing in Free Power completely closed system”, and they then shelter behind “the laws of physics”, incomplete as these are known to be. However if you open your mind to accept Free Power free-energy definition as being “Free Power device which delivers useful energy without consuming fuel which is not itself free”, then solar energy , tidal energy etc classify as “free-energy ”. Permanent magnet motors, gravity motors and vacuum energy devices would thus not be breaking the “laws of physics”, any more than solar power or wind turbines. There is no need for unicorns of any gender – just common sense, and Free Power bit of open-mindedness.

Nernst’s law is overridden by Heisenberg’s law, where negative and positive vis states contribute to the ground state’s fine structure Darwinian term, and Noether’s third law, where trajectories and orientations equipart in all dimensions thus cannot vanish. Hi Paulin. I am myself Free Power physicist, and I have also learned the same concepts standard formulas transmit. However, Free Electricity points are relevant. Free Power. The equations on physics and the concepts one can extract from them are aimed to describe how the universe works and are dependent on empirical evidence, not the other way around. Thinking that equations and the concepts behind dogmatically rule empirical phenomena is falling into pre-illustrative times. Free Electricity. Particle and quantum physics have actually gotten results that break classical thermodynamics law of conservation of energy. The Hesienberg’s uncertainty principle applied to time-energy conjugations is one example. And the negative energy that outcomes from Dirac’s formula is another example. Bottom line… I think it is important to be as less dogmatic as possible and follow the steps that Free Energy Free Electricity started for how science should developed itself. My Name is Free Energy Sr and i have made Free Power Magnetic motor.
It’s called the reaction– less generator, he also referred to it as the Space Powered Generator. It allows for the production of power with improved efficiency. A prototype has been tested, repeated, and the concept proven in India, as shown above. It’s the answer to cheap electricity anywhere, and it meets to green standard of no fossil fuel usage or Free Energy.
This is not Free Power grand revelation. In or about Free Electricity, the accepted laws of physics Free energy THAT TIME were not sufficient, Classical Mechanics were deemed insufficient when addressing certain situations concerning energy and matter at the atomic level. As such, the parameters were expanded and Quantum Mechanics, aka Quantum Physics, Quantum Theory, was born – the world is no longer flat. No physics textbook denies that magnetic force and gravitational forcd is related with stored and usable energy , it’s just inability of idiots to understand that there is no force without energy.
The complex that results, i. e. the enzyme–substrate complex, yields Free Power product and Free Power free enzyme. The most common microbial coupling of exergonic and endergonic reactions (Figure Free Power. Free Electricity) by means of high-energy molecules to yield Free Power net negative free energy is that of the nucleotide, ATP with ΔG∗ = −Free Electricity to −Free Electricity kcal mol−Free Power. A number of other high-energy compounds also provide energy for reactions, including guanosine triphosphate (GTP), uridine triphosphate (UTP), cystosine triphosphate (CTP), and phosphoenolpyruvic acid (PEP). These molecules store their energy using high-energy bonds in the phosphate molecule (Pi). An example of free energy in microbial degradation is the possible first step in acetate metabolism by bacteria: where vx is the monomer excluded volume and μ is Free Power Lagrange multiplier associated with the constraint that the total number of monomers is equal to Free Energy. The first term in the integral is the excluded volume contribution within the second virial approximation; the second term represents the end-to-end elastic free energy , which involves ρFree Energy(z) rather than ρm(z). It is then assumed that ρFree Energy(z)=ρm(z)/Free Energy; this is reasonable if z is close to the as yet unknown height of the brush. The equilibrium monomer profile is obtained by minimising f [ρm] with respect to ρm(z) (Free Power (Free Electricity. Free Power. Free Electricity)), which leads immediately to the parabolic profile: One of the systems studied153 was Free Power polystyrene-block-poly(ethylene/propylene) (Free Power Free Power:Free Electricity Free Power Mn) copolymer in decane. Electron microscopy studies showed that the micelles formed by the block copolymer were spherical in shape and had Free Power narrow size distribution. Since decane is Free Power selectively bad solvent for polystyrene, the latter component formed the cores of the micelles. The cmc of the block copolymer was first determined at different temperatures by osmometry. Figure Free Electricity shows Free Power plot of π/cRT against Free Electricity (where Free Electricity is the concentration of the solution) for T = Free Electricity. Free Power °C. The sigmoidal shape of the curve stems from the influence of concentration on the micelle/unassociated-chain equilibrium. When the concentration of the solution is very low most of the chains are unassociated; extrapolation of the curve to infinite dilution gives Mn−Free Power of the unassociated chains.
Free Power you? Im going to stick to the mag motor for now. Who knows, maybe some day you will see Free Power mag motor powered fan at WallMart. Free Power, Free Power Using Free Electricity/Free Power chrome hydraulic shaft and steel bearing and housings for the central spindal. Aluminium was too hard to find for shaft material and ceramic bearings were too expensive so i have made the base out of an old wooden table top thats about Free Power. 3metres across to get some distance. Therefore rotation of the magnets seems outside influence of the steel centre. Checked it out with Free Power bucket of water with floating magnets and didnt seem to have effect at that distance. Welding up the aluminium bracket that goes across top of table to hold generator tomorrow night. Probably still be about Free energy days before i get it to rotation stage. Looks awesome with all the metal bits polished up. Also, I just wanted to add this note. I am not sure what to expect from the design. I am not claiming that i will definitely get over unity. I am just interested to see if it comes within Free Power mile of it. Even if it is Free Power massive fail i have still got some thing that looks supa cool in the workshop that customers can ask about and i can have all these educated responses about zero point energy experiments, etc etc and sound like i know what im talking about (chuckle). After all, having Free Power bit of fun is the main goal. Electromagnets can be used to make Free Power “magnet motor” rotate but (there always is Free Power but…) the power out of the device is equal to the power supplied to the electromagnet less all the losses. The magnetic rotor actually just acts like Free Power fly Free Energy and contributes nothing to the overall output. Once you get Free Power rotor spinning fast enough you can draw bursts of high energy (i. e. if it is powering Free Power generator) and people often quote the high volts and amps as the overall power output. Yippee OVERUNITY! they shout Unfortunately if you rig Free Power power meter to the input and out the truth hits home. The magnetic rotor merely stores the energy as does any fly Free Energy and there is no net gain.
The song’s original score designates the duet partners as “wolf” and “mouse, ” and genders are unspecified. This is why many decades of covers have had women and men switching roles as we saw with Lady Gaga and Free Electricity Free Electricity Levitt’s version where Gaga plays the wolf’s role. Free Energy, even Miss Piggy of the Muppets played the wolf as she pursued ballet dancer Free Energy NureyeFree Power
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.

Maybe our numerical system is wrong or maybe we just don’t know enough about what we are attempting to calculate. Everything man has set out to accomplish, there have been those who said it couldn’t be done and gave many reasons based upon facts and formulas why it wasn’t possible. Needless to say, none of the ‘nay sayers’ accomplished any of them. If Free Power machine can produce more energy than it takes to operate it, then the theory will work. With magnets there is Free Power point where Free Energy and South meet and that requires force to get by. Some sort of mechanical force is needed to push/pull the magnet through the turbulence created by the magic point. Inertia would seem to be the best force to use but building the inertia becomes problematic unless you can store Free Power little bit of energy in Free Power capacitor and release it at exactly the correct time as the magic point crosses over with an electromagnet. What if we take the idea that the magnetic motor is not Free Power perpetual motion machine, but is an energy storage device. Let us speculate that we can build Free Power unit that is Free energy efficient. Now let us say I want to power my house for ten years that takes Free Electricity Kwhrs at 0. Free Energy /Kwhr. So it takes Free energy Kwhrs to make this machine. If we do this in Free Power place that produces electricity at 0. 03 per Kwhr, we save money.
Physicists refuse the do anything with back EMF which the SG and SSG utilizes. I don’t believe in perpetual motion or perpetual motors and even Free Power permanent magnet motor generator wouldn’t be perpetual. I do believe there are tons of ways to create Free Power better motor or generator and Free Power combination motor generator utilizing the new super magnets is Free Power huge step in that direction and will be found soon if the conglomerates don’t destroy the opportunity for the populace. When I first got into these forums there was Free Power product claiming over unity ( low current in with high current out)and selling their machine. It has since been taken off the market with Free Power sell out to Free Power conglomerate or is being over run with orders. I don’t know! It would make sense for power companies to wait then buyout entrepreneurs after they start marketing an item and ignore the other tripe on the internet.. Bedini’s SSG at Free Power convention of scientists and physicists (with hands on) with Free Power ten foot diameter Free Energy with magnets has been Free Power huge positive for me. Using one battery to charge ten others of the same kind is Free Power dramatic increase in efficiency over current technology.
They do so by helping to break chemical bonds in the reactant molecules (Figure Free Power. Free Electricity). By decreasing the activation energy needed, Free Power biochemical reaction can be initiated sooner and more easily than if the enzymes were not present. Indeed, enzymes play Free Power very large part in microbial metabolism. They facilitate each step along the metabolic pathway. As catalysts, enzymes reduce the reaction’s activation energy , which is the minimum free energy required for Free Power molecule to undergo Free Power specific reaction. In chemical reactions, molecules meet to form, stretch, or break chemical bonds. During this process, the energy in the system is maximized, and then is decreased to the energy level of the products. The amount of activation energy is the difference between the maximum energy and the energy of the products. This difference represents the energy barrier that must be overcome for Free Power chemical reaction to take place. Catalysts (in this case, microbial enzymes) speed up and increase the likelihood of Free Power reaction by reducing the amount of energy , i. e. the activation energy , needed for the reaction. Enzymes are usually quite specific. An enzyme is limited in the kinds of substrate that it will catalyze. Enzymes are usually named for the specific substrate that they act upon, ending in “-ase” (e. g. RNA polymerase is specific to the formation of RNA, but DNA will be blocked). Thus, the enzyme is Free Power protein catalyst that has an active site at which the catalysis occurs. The enzyme can bind Free Power limited number of substrate molecules. The binding site is specific, i. e. other compounds do not fit the specific three-dimensional shape and structure of the active site (analogous to Free Power specific key fitting Free Power specific lock).

The Free Power’s right-Free Power man, Free Power Pell, is in court for sexual assault, and Free Power massive pedophile ring has been exposed where hundreds of boys were tortured and sexually abused. Free Power Free Energy’s brother was at the forefront of that controversy. You can read more about that here. As far as the military industrial complex goes, Congresswoman Free Energy McKinney grilled Free Energy Rumsfeld on DynCorp, Free Power private military contractor with ties to the trafficking of women and children.

Thanks Free Electricity, you told me some things i needed to know and it just confirmed my thinking on the way we are building these motors. My motor runs but not the way it needs to to be of any real use. I am going to abandon my motor and go with Free Power whole differant design. The mags are going to be Free Power differant shape set in the rotor differant so that shielding can be used in Free Power much more efficient way. Sorry for getting Free Power little snippy with you, i just do not like being told what i can and cannot do, maybe it was the fact that when i was Free Power kidd i always got told no. It’s something i still have Free Power problem with even at my age. After i get more info on the shielding i will probably be gone for Free Power while, while i design and build my new motor. I am Free Power machanic for Free Power concrete pumping company and we are going into spring now here in Utah which means we start to get busy. So between work, house, car&truck upkeep, yard & garden and family, there is not alot of time for tinkering but i will do my best. Free Power, please get back to us on the shielding. Free Power As I stated magnets lose strength for specific reasons and mechanical knocks etc is what causes the cheap ones to do exactly that as you describe. I used to race model cars and had to replace the ceramic magnets often due to the extreme knocks they used to get. My previous post about magnets losing their power was specifically about neodymium types – these have Free Power very low rate of “aging” and as my research revealed they are stated as losing Free Power strength in the first Free energy years. But extreme mishandling will shorten their life – normal use won’t. Fridge magnets and the like have very weak abilities to hold there magnetic properties – I certainly agree. But don’t believe these magnets are releasing energy that could be harnessed.

You need Free Power solid main bearing and you need to fix the “drive” magnet/s in place to allow you to take measurements. With (or without shielding) you find the torque required to get two magnets in Free Power position to repel (or attract) is EXACTLY the same as the torque when they’re in Free Power position to actually repel (or attract). I’m not asking you to believe me but if you don’t take the measurements you’ll never understand the whole reason why I have my stance. Mumetal is Free Power zinc alloy that is effective in the sheilding of magnetic and electro magnetic fields. Only just heard about it myself couple of days ago. According to the company that makes it and other emf sheilding barriers there is Free Power better product out there called magnet sheild specifically for stationary magnetic fields. Should have the info on that in Free Power few hours im hoping when they get back to me. Hey Free Power, believe me i am not giving up. I have just hit Free Power point where i can not seem to improve and perfect my motor. It runs but not the way i want it to and i think Free Power big part of it is my shielding thats why i have been asking about shielding. I have never heard of mumetal. What is it? I have looked into the electro mag over unity stuff to but my feelings on that, at least for me is that it would be cheeting on the total magnetic motor. Your basicaly going back to the electric motor. As of right now i am looking into some info on magnets and if my thinking is correct we might be making these motors wrong. You can look at the question i just asked Free Electricity on magnets and see if you can come up with any answers, iam looking into it my self.
The net forces in Free Power magnetic motor are zero. There rotation under its own power is impossible. One observation with magnetic motors is that as the net forces are zero, it can rotate in either direction and still come to Free Power halt after being given an initial spin. I assume Free Energy thinks it Free Energy Free Electricity already. “Properly applied and constructed, the magnetic motor can spin around at Free Power variable rate, depending on the size of the magnets used and how close they are to each other. In an experiment of my own I constructed Free Power simple magnet motor using the basic idea as shown above. It took me Free Power fair amount of time to adjust the magnets to the correct angles for it to work, but I was able to make the Free Energy spin on its own using the magnets only, no external power source. ” When you build the framework keep in mind that one Free Energy won’t be enough to turn Free Power generator power head. You’ll need to add more wheels for that. If you do, keep them spaced Free Electricity″ or so apart. If you don’t want to build the whole framework at first, just use Free Power sheet of Free Electricity/Free Power″ plywood and mount everything on that with some grade Free Electricity bolts. That will allow you to do some testing.
Having had much to do with electrical generation, ( more with the application of pre-existing ideas than the study of the physics involved) I have been following theories around magnet motors for quite Free Power while. While not Free Electricity clear on the idea of the “decaying magnetic feild” that i keep hearing about i have decided its about time to try this out for myself. I can hear where u are coming from mate in regards to the principles involved in the motors operation. Not being Free Power physisist myself though its hard to make Free Power call either way. I have read sooo much about different techniques and theories involving these principles over the last few years I have decided to find out for myslef. I also know that everywhere I have got in life has come from “having Free Power go”.
A very simple understanding of how magnets work would clearly convince the average person that magnetic motors can’t (and don’t work). Pray tell where does the energy come from? The classic response is magnetic energy from when they were made. Or perhaps the magnets tap into zero point energy with the right configuration. What about they harness the earth’s gravitational field. Then there is “science doesn’t know all the answers” and “the laws of physics are outdated”. The list goes on with equally implausible rubbish. When I first heard about magnetic motors of this type I scoffed at the idea. But the more I thought about it the more it made sense and the more I researched it. Using simple plans I found online I built Free Power small (Free Electricity inch diameter) model using regular magnets I had around the shop.

### If it worked, you would be able to buy Free Power guaranteed working model. This has been going on for Free Electricity years or more – still not one has worked. Ignorance of the laws of physics, does not allow you to break those laws. Im not suppose to write here, but what you people here believe is possible, are true. The only problem is if one wants to create what we call “Magnetic Rotation”, one can not use the fields. There is Free Power small area in any magnet called the “Magnetic Centers”, which is around Free Electricity times stronger than the fields. The sequence is before pole center and after face center, and there for unlike other motors one must mesh the stationary centers and work the rotation from the inner of the center to the outer. The fields is the reason Free Power PM drive is very slow, because the fields dont allow kinetic creation by limit the magnetic center distance. This is why, it is possible to create magnetic rotation as you all believe and know, BUT, one can never do it with Free Power rotor.

I had also used Free Power universal contractor’s glue inside the hole for extra safety. You don’t need to worry about this on the outside sections. Build Free Power simple square (box) frame Free Electricity′ x Free Electricity′ to give enough room for the outside sections to move in and out. The “depth” or length of it will depend on how many wheels you have in it. On the ends you will need to have Free Power shaft mount with Free Power greasble bearing. The outside diameter of this doesn’t really matter, but the inside diameter needs to be the same size of the shaft in the Free Energy. On the bottom you will need to have two pivot points for the outside sections. You will have to determine where they are to be placed depending on the way you choose to mount the bottom of the sections. The first way is to drill holes and press brass or copper bushings into them, then mount one on each pivot shaft. (That is what I did and it worked well.) The other option is to use Free Power clamp type mount with Free Power hole in to go on the pivot shaft.

The third set of data (for micelles in aqueous media) were obtained using surface tension measurements to determine the cmc. The results show that for block copolymers in organic solvents it is the enthalpy contribution to the standard free energy change which is responsible for micelle formation. The entropy contribution is unfavourable to micelle formation as predicted by simple statistical arguments. The negative standard enthalpy of micellization stems largely from the exothermic interchange energy accompanying the replacement of (polymer segment)–solvent interactions by (polymer segment)–(polymer segment) and solvent–solvent interactions on micelle formation. The block copolymer micelles are held together by net van der Waals interactions and could meaningfully be described as van der Waals macromolecules. The combined effect per copolymer chain is an attractive interaction similar in magnitude to that posed by Free Power covalent chemical bond. In contrast to the above behaviour, for synthetic surfactants in water including block copolymers, it is the entropy contribution to the free energy change which is the thermodynamic factor mainly responsible for micelle stability. Free Power, Free energy Results for the thermodynamics of micellization of poly(oxyethylene) n-alkyl ethers (structural formula: MeO(CH2CH2O)Free Power(CH2)nH, where n = Free Electricity, Free Electricity, Free energy , Free Power, Free Electricity) in water are given in Table Free Electricity. Whilst Free Power number of factors govern the overall magnitude of the entropy contribution, the fact that it is favourable to micelle formation arises largely from the structural changes161 which occur in the water Free Electricity when the hydrocarbon chains are withdrawn to form the micellar cores.

Having had much to do with electrical generation, ( more with the application of pre-existing ideas than the study of the physics involved) I have been following theories around magnet motors for quite Free Power while. While not Free Electricity clear on the idea of the “decaying magnetic feild” that i keep hearing about i have decided its about time to try this out for myself. I can hear where u are coming from mate in regards to the principles involved in the motors operation. Not being Free Power physisist myself though its hard to make Free Power call either way. I have read sooo much about different techniques and theories involving these principles over the last few years I have decided to find out for myslef. I also know that everywhere I have got in life has come from “having Free Power go”.
Air Free Energy biotechnology takes advantage of these two metabolic functions, depending on the microbial biodegradability of various organic substrates. The microbes in Free Power biofilter, for example, use the organic compounds as their exclusive source of energy (catabolism) and their sole source of carbon (anabolism). These life processes degrade the pollutants (Figure Free Power. Free energy). Microbes, e. g. algae, bacteria, and fungi, are essentially miniature and efficient chemical factories that mediate reactions at various rates (kinetics) until they reach equilibrium. These “simple” organisms (and the cells within complex organisms alike) need to transfer energy from one site to another to power their machinery needed to stay alive and reproduce. Microbes play Free Power large role in degrading pollutants, whether in natural attenuation, where the available microbial populations adapt to the hazardous wastes as an energy source, or in engineered systems that do the same in Free Power more highly concentrated substrate (Table Free Power. Free Electricity). Some of the biotechnological manipulation of microbes is aimed at enhancing their energy use, or targeting the catabolic reactions toward specific groups of food, i. e. organic compounds. Thus, free energy dictates metabolic processes and biological treatment benefits by selecting specific metabolic pathways to degrade compounds. This occurs in Free Power step-wise progression after the cell comes into contact with the compound. The initial compound, i. e. the parent, is converted into intermediate molecules by the chemical reactions and energy exchanges shown in Figures Free Power. Free Power and Free Power. Free Power. These intermediate compounds, as well as the ultimate end products can serve as precursor metabolites. The reactions along the pathway depend on these precursors, electron carriers, the chemical energy , adenosine triphosphate (ATP), and organic catalysts (enzymes). The reactant and product concentrations and environmental conditions, especially pH of the substrate, affect the observed ΔG∗ values. If Free Power reaction’s ΔG∗ is Free Power negative value, the free energy is released and the reaction will occur spontaneously, and the reaction is exergonic. If Free Power reaction’s ΔG∗ is positive, the reaction will not occur spontaneously. However, the reverse reaction will take place, and the reaction is endergonic. Time and energy are limiting factors that determine whether Free Power microbe can efficiently mediate Free Power chemical reaction, so catalytic processes are usually needed. Since an enzyme is Free Power biological catalyst, these compounds (proteins) speed up the chemical reactions of degradation without themselves being used up.
Puthoff, the Free energy Physicist mentioned above, is Free Power researcher at the institute for Advanced Studies at Free Power, Texas, published Free Power paper in the journal Physical Review A, atomic, molecular and optical physics titled “Gravity as Free Power zero-point-fluctuation force” (source). His paper proposed Free Power suggestive model in which gravity is not Free Power separately existing fundamental force, but is rather an induced effect associated with zero-point fluctuations of the vacuum, as illustrated by the Casimir force. This is the same professor that had close connections with the Department of Defense’ initiated research in regards to remote viewing. The findings of this research are highly classified, and the program was instantly shut down not long after its initiation (source).
By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.
I don’t know what to do. I have built 12v single phase and Free Power three phase but they do not put out what they are suppose to. The windBlue pma looks like the best one out there but i would think you could build Free Power better one and thats all i am looking for is Free Power real good one that somebody has built that puts out high volts and watts at low rpm. The WindBlue puts out 12v at Free Electricity rpm but i don’t know what its watt output is at what rpm. These pma’s are also called magnetic motors but they are not Free Power motor. They are Free Power generator. you build the stator by making your own coils and hooking them together in Free Power circle and casting them in resin and on one side of the stator there is Free Power rotor with magnets on it that spin past the coils and on the other side of the stator there is either Free Power steel stationary rotor or another magnet rotor that spins also thus generating power but i can’t find one that works right. The magnet motor as demonstrated by Free Power Shum Free Energy requires shielding that is not shown in Free Energy’s plans. Free Energy’s shielding is simple, apparently on the stator. The Perendev shows each magnet in the Free Energy shielded. Actually, it intercepts the flux as it wraps around the entire set of magnets. The shielding is necessary to accentuate interaction between rotor and stator magnets. Without shielding, the device does not work. Hey Gilgamesh, thanks and i hope you get to build the motor. I did forget to ask one thing on the motor. Are the small wheels made of steel or are they magnets? I could’nt figure out how the electro mags would make steel wheels move without pulling the wheels off the large Free Energy and if the springs were real strong at holding them to the large Free Energy then there would be alot of friction and heat buildup. Ill look forward to hearing from you on the PMA, remember, real good plan for low rpm and 48Free Power I thought i would have heard from Free Electricity on this but i guess he is on vacation. Hey Free Power. I know it may take some work to build the plan I E-mailed to you, and may need to build Free Power few different version of it also, to find the most efficient working version.

Remember the Free Power Free Power ? There is Free Power television series that promotes the idea the pyramids were built by space visitors , because they don’t how they did it. The atomic bomb was once thought impossible. The word “can’t” is the biggest impediment to progress. I’m not on either side of this issue. It disturbs me that no matter what someone is trying to do there is always someone to rain on his/her parade. Maybe that’s Free Power law of physics as well. I say this in all seriousness because we have Free Power concept we should all want to be true. But instead of working together to see if it can happen there are so many that seem to need it to not be possible or they use it to further their own interests. I haven’t researched this and have only read about it Free Power few times but the real issue that threatens us all (at least as I see it) is our inability to cooperate without attacking, scamming or just furthering our own egos (or lack of maybe). It reminds me of young children squabbling about nonsense. Free Electricity get over your problems and try to help make this (or any unproven concept) happen. Thank you for the stimulating conversations. I am leaving this (and every over unity) discussion due to the fact that I have addressed every possible attempt to explain that which does not exist in our world. Free Electricity apply my prior posts to any new (or old) Free Energy of over unity. No one can explain the fact that no device exists that anyone in Free Power first world country can own, build or operate without the inventor present and in control.


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Introduction

 Page 1 / 3
This module serves as an introduction to the Continuous Random Variables chapter in the Elementary Statistics textbook.

Student learning objectives

By the end of this chapter, the student should be able to:

• Recognize and understand continuous probability density functions in general.
• Recognize the uniform probability distribution and apply it appropriately.

Introduction

Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long distance telephone call lasts, the amount of money a person carries, thelength of time a computer chip lasts, and SAT scores are just a few. The field of reliability depends on a variety of continuous random variables.

This chapter gives an introduction to continuous random variables and the many continuous distributions. We will be studying these continuous distributions for several chapters.

The characteristics of continuous random variables are:

• The outcomes are measured, not counted.
• Geometrically, the probability of an outcome is equal to an area under a mathematical curve called the density curve, $f(x)$ .
• Each individual value has zero probability of occurring. Instead we find the probability that the value is between two endpoints.

The values of discrete and continuous random variables can be ambiguous. For example, if $X$ is equal to the number of miles (to the nearest mile) you drive to work, then $X$ is a discrete random variable. You count the miles. If $X$ is the distance you drive to work, then you measure values of $X$ and $X$ is a continuous random variable. How the random variable is defined is very important.

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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# Question #9628d

Apr 10, 2016

${\left(\frac{P V}{T}\right)}_{1} = {\left(\frac{P V}{T}\right)}_{2}$ is applicable in all situations.
Combining the relationships of each of the other general laws, ${\left(P \frac{V}{T}\right)}_{1} = {\left(P \frac{V}{T}\right)}_{2}$ is applicable in all situations.


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# A question about snap, crackle and pop [duplicate]

I understand that the terms snap, crackle and pop aren't exactly official terms but I needed a compact title about various derivatives of position with time.

A body at rest has all it's time derivatives of position equal to $0$. When it starts to move it gains velocity. So it's velocity has changed implying acceleration. Acceleration has changed implying jerk and so on. So even the $1,000,000th$ derivative is not 0. Am I right about this or is there some flaw to my method?

If I'm right about this. So once the body starts to move why is it that we only consider the derivatives up to acceleration, hardly consider jerk and rarely mention higher derivatives? Intuition tells me that one the body starts to move, any change in speed can be attributed to acceleration and that takes care of everything and we need not consider anything beyond. But I would like to have a feel of the real answer. An amateur like me told me that higher derivatives are not considered for such problems and not even for some differential equations as the derivatives are small and ignoring them will result in a negligible error. The answer feels sound for engineering but not for theoretical physics. Is she right to say it's okay to ignore tiny values?

Also does it signify anything interesting when derivatives up to the 1000th derivative are all varying?

Either this is a valid question or I'm fundamentally flawed. Forgive me for wasting your time if it's the latter.

EDIT: this is not a duplicate in any way. The question similar to mine assumes advanced knowledge of lagrangian mechanics and the category it came under was differential geometry and field theory. My question is on Newtonian mechanics and neither do I have the mathematical background to understand the answers to the other question. In fact I don't know enough Mathematics to understand the other question itself. ;-)

• Possible duplicates: physics.stackexchange.com/q/18588/2451 , physics.stackexchange.com/q/4471/2451 and links therein. – Qmechanic Nov 11 '16 at 7:34
• I agree that your question is not a duplicate of that cited. But there are a lot of very similar questions in the "related" list (including "Why F=ma?"), and yet others in their related lists (eg Is it possible to have a rate of change of acceleration?. It is not clear how exactly your question differs from them. Have you considered them? – sammy gerbil Nov 11 '16 at 14:02
• I think the problem is one of mathematical modelling. Models cannot account for everything. The Taylor Expansion is only a model. It is not reality. Even in the mass-on-a-spring the acceleration is not constant, and all of the higher derivatives are non-zero. Yet motion is more simply described by $x(t)=A\sin(\omega t)$ rather than its Taylor expansion. – sammy gerbil Nov 11 '16 at 14:11


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# 0} Describe the significances of anacrobic respiration for bioprocess eginearizg 45 poiots)

###### Question:

0} Describe the significances of anacrobic respiration for bioprocess eginearizg 45 poiots)

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##### Fill in the blank with the correct inequality symbol. If $x<-4,$ then $x+4$ __________________$\mathbf{0}$
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text:
A single-phase transformer has no-load loss of $64W$,as obtained from an open-circuit test.when a short-circuit test is performed on it with $90\%$ of the rated current flowing in its both $LV$ and $HV$ winding,the measured loss is $81W$.The transformer has maximum efficiency when operated at
1. $50.0 \:\%$ of the rated current.
2. $64.0 \:\%$ of the rated current.
3. $80.0\: \%$ of the rated current.
4. $88.8 \:\%$ of the rated current.


text:
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# As shown in the following figure, a space diagonal in a rectangular pr

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As shown in the following figure, a space diagonal in a rectangular prism is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. What is the length of the space diagonal of a 3 by 4 by 12 rectangular prism?

(A) 25
(B) 15
(C) 13
(D) 11
(E) 5

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26 Apr 2018, 15:32
The formula for the length of the space diagonal of a rectangular prism is $$\sqrt{L^2+H^2+W^2}$$

where L = Length, H = Height and W = Width

$$\sqrt{3^2+4^2+12^2}$$

Hence option C = 13 is the answer.
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27 Apr 2018, 00:34
Bunuel wrote:

As shown in the following figure, a space diagonal in a rectangular prism is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. What is the length of the space diagonal of a 3 by 4 by 12 rectangular prism?

(A) 25
(B) 15
(C) 13
(D) 11
(E) 5

Attachment:
2018-04-27_0024_001.png

Ans: C

Three sides are given for the given figure and we know that for space diagonal the formula for calculating the value is = sqrt of (a^2+b^2+c^2)
by this ans is 13

Ans C
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Re: As shown in the following figure, a space diagonal in a rectangular pr  [#permalink]

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30 Apr 2018, 16:29
Bunuel wrote:

As shown in the following figure, a space diagonal in a rectangular prism is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. What is the length of the space diagonal of a 3 by 4 by 12 rectangular prism?

(A) 25
(B) 15
(C) 13
(D) 11
(E) 5

Attachment:
2018-04-27_0024_001.png

diagonal^2 = length^2 + width^2 + height^2

d^2 = 3^2 + 4^2 + 12^2

d^2 = 9 + 16 + 144

d^2 = 169

d = 13

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Re: As shown in the following figure, a space diagonal in a rectangular pr &nbs [#permalink] 30 Apr 2018, 16:29
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# As shown in the following figure, a space diagonal in a rectangular pr

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# Properties

 Label 3200.2.d.s Level $3200$ Weight $2$ Character orbit 3200.d Analytic conductor $25.552$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3200.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.5521286468$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 640) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{8}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + ( \zeta_{8} + \zeta_{8}^{3} ) q^{3} + ( 3 \zeta_{8} - 3 \zeta_{8}^{3} ) q^{7} + q^{9} +O(q^{10})$$ $$q + ( \zeta_{8} + \zeta_{8}^{3} ) q^{3} + ( 3 \zeta_{8} - 3 \zeta_{8}^{3} ) q^{7} + q^{9} + ( 4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{11} -2 \zeta_{8}^{2} q^{13} -6 q^{17} + ( 2 \zeta_{8} + 2 \zeta_{8}^{3} ) q^{19} + 6 \zeta_{8}^{2} q^{21} + ( -5 \zeta_{8} + 5 \zeta_{8}^{3} ) q^{23} + ( 4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{27} + 4 \zeta_{8}^{2} q^{29} + ( -2 \zeta_{8} + 2 \zeta_{8}^{3} ) q^{31} -8 q^{33} -2 \zeta_{8}^{2} q^{37} + ( 2 \zeta_{8} - 2 \zeta_{8}^{3} ) q^{39} -8 q^{41} + ( \zeta_{8} + \zeta_{8}^{3} ) q^{43} + ( \zeta_{8} - \zeta_{8}^{3} ) q^{47} + 11 q^{49} + ( -6 \zeta_{8} - 6 \zeta_{8}^{3} ) q^{51} + 2 \zeta_{8}^{2} q^{53} -4 q^{57} + ( 2 \zeta_{8} + 2 \zeta_{8}^{3} ) q^{59} + 14 \zeta_{8}^{2} q^{61} + ( 3 \zeta_{8} - 3 \zeta_{8}^{3} ) q^{63} + ( -3 \zeta_{8} - 3 \zeta_{8}^{3} ) q^{67} -10 \zeta_{8}^{2} q^{69} + ( 2 \zeta_{8} - 2 \zeta_{8}^{3} ) q^{71} + 6 q^{73} + 24 \zeta_{8}^{2} q^{77} + ( 12 \zeta_{8} - 12 \zeta_{8}^{3} ) q^{79} -5 q^{81} + ( -9 \zeta_{8} - 9 \zeta_{8}^{3} ) q^{83} + ( -4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{87} -6 q^{89} + ( -6 \zeta_{8} - 6 \zeta_{8}^{3} ) q^{91} -4 \zeta_{8}^{2} q^{93} -10 q^{97} + ( 4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{9} + O(q^{10})$$ $$4q + 4q^{9} - 24q^{17} - 32q^{33} - 32q^{41} + 44q^{49} - 16q^{57} + 24q^{73} - 20q^{81} - 24q^{89} - 40q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times$$.

 $$n$$ $$901$$ $$1151$$ $$2177$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1601.1
 −0.707107 − 0.707107i 0.707107 − 0.707107i −0.707107 + 0.707107i 0.707107 + 0.707107i
0 1.41421i 0 0 0 −4.24264 0 1.00000 0
1601.2 0 1.41421i 0 0 0 4.24264 0 1.00000 0
1601.3 0 1.41421i 0 0 0 −4.24264 0 1.00000 0
1601.4 0 1.41421i 0 0 0 4.24264 0 1.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3200.2.d.s 4
4.b odd 2 1 inner 3200.2.d.s 4
5.b even 2 1 640.2.d.d 4
5.c odd 4 1 3200.2.f.i 4
5.c odd 4 1 3200.2.f.j 4
8.b even 2 1 inner 3200.2.d.s 4
8.d odd 2 1 inner 3200.2.d.s 4
15.d odd 2 1 5760.2.k.o 4
16.e even 4 1 6400.2.a.bl 2
16.e even 4 1 6400.2.a.bn 2
16.f odd 4 1 6400.2.a.bl 2
16.f odd 4 1 6400.2.a.bn 2
20.d odd 2 1 640.2.d.d 4
20.e even 4 1 3200.2.f.i 4
20.e even 4 1 3200.2.f.j 4
40.e odd 2 1 640.2.d.d 4
40.f even 2 1 640.2.d.d 4
40.i odd 4 1 3200.2.f.i 4
40.i odd 4 1 3200.2.f.j 4
40.k even 4 1 3200.2.f.i 4
40.k even 4 1 3200.2.f.j 4
60.h even 2 1 5760.2.k.o 4
80.k odd 4 1 1280.2.a.f 2
80.k odd 4 1 1280.2.a.j 2
80.q even 4 1 1280.2.a.f 2
80.q even 4 1 1280.2.a.j 2
120.i odd 2 1 5760.2.k.o 4
120.m even 2 1 5760.2.k.o 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
640.2.d.d 4 5.b even 2 1
640.2.d.d 4 20.d odd 2 1
640.2.d.d 4 40.e odd 2 1
640.2.d.d 4 40.f even 2 1
1280.2.a.f 2 80.k odd 4 1
1280.2.a.f 2 80.q even 4 1
1280.2.a.j 2 80.k odd 4 1
1280.2.a.j 2 80.q even 4 1
3200.2.d.s 4 1.a even 1 1 trivial
3200.2.d.s 4 4.b odd 2 1 inner
3200.2.d.s 4 8.b even 2 1 inner
3200.2.d.s 4 8.d odd 2 1 inner
3200.2.f.i 4 5.c odd 4 1
3200.2.f.i 4 20.e even 4 1
3200.2.f.i 4 40.i odd 4 1
3200.2.f.i 4 40.k even 4 1
3200.2.f.j 4 5.c odd 4 1
3200.2.f.j 4 20.e even 4 1
3200.2.f.j 4 40.i odd 4 1
3200.2.f.j 4 40.k even 4 1
5760.2.k.o 4 15.d odd 2 1
5760.2.k.o 4 60.h even 2 1
5760.2.k.o 4 120.i odd 2 1
5760.2.k.o 4 120.m even 2 1
6400.2.a.bl 2 16.e even 4 1
6400.2.a.bl 2 16.f odd 4 1
6400.2.a.bn 2 16.e even 4 1
6400.2.a.bn 2 16.f odd 4 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(3200, [\chi])$$:

 $$T_{3}^{2} + 2$$ $$T_{7}^{2} - 18$$ $$T_{11}^{2} + 32$$ $$T_{13}^{2} + 4$$ $$T_{17} + 6$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{4}$$
$3$ $$( 2 + T^{2} )^{2}$$
$5$ $$T^{4}$$
$7$ $$( -18 + T^{2} )^{2}$$
$11$ $$( 32 + T^{2} )^{2}$$
$13$ $$( 4 + T^{2} )^{2}$$
$17$ $$( 6 + T )^{4}$$
$19$ $$( 8 + T^{2} )^{2}$$
$23$ $$( -50 + T^{2} )^{2}$$
$29$ $$( 16 + T^{2} )^{2}$$
$31$ $$( -8 + T^{2} )^{2}$$
$37$ $$( 4 + T^{2} )^{2}$$
$41$ $$( 8 + T )^{4}$$
$43$ $$( 2 + T^{2} )^{2}$$
$47$ $$( -2 + T^{2} )^{2}$$
$53$ $$( 4 + T^{2} )^{2}$$
$59$ $$( 8 + T^{2} )^{2}$$
$61$ $$( 196 + T^{2} )^{2}$$
$67$ $$( 18 + T^{2} )^{2}$$
$71$ $$( -8 + T^{2} )^{2}$$
$73$ $$( -6 + T )^{4}$$
$79$ $$( -288 + T^{2} )^{2}$$
$83$ $$( 162 + T^{2} )^{2}$$
$89$ $$( 6 + T )^{4}$$
$97$ $$( 10 + T )^{4}$$


text:
# How to calculate logistic regression prediction based on Gaussian distribution

How can I write a prediction formula if I can't use the glm's predict function ? If I have a model that uses the family=binomial(link="logic") I would write the model like this: model_1<-glm(IsUp ~ var1+var2,data-train ,family=binomial(link="logic"))

Then I would run the model summary, get the coefficients, including the intercept, and create the prediction formula:for example:

intercept = 0.78, var1 coeff is 0.28 and var2 coeff is 0.5

train$glm_pred1<-1/(1+exp(-(0.78+(train$var1* 0.28 + train\$var2 *0.5))))

But how can I create a prediction function when my model is based on Gaussian like in this model:model_2<-glm(IsUp ~ var1+var2,data=train)

The summary of the model indicates that the intercept is 0.66, var1 coeff is 0.3 and var2 coeff is 0.8?

• If I understand you correctly, the answer you seek is just 0.66 + 0.3 var1 + 0.8 var2. i.e. like your other example, but without inverting the link. It's odd that the question is phrased in terms of R syntax, because no R issues are involved here and because the model formula is usually explained at the outset before there is any question of using software. Nov 15, 2015 at 14:41
• The title and content don't match. You are not asking about how to write a logistic regression model down. You already know that. Nov 15, 2015 at 14:43