text:
izlyforever's blog

By izlyforever, history, 3 weeks ago,

Successful hacks makes Codeforces better. Here are at least two reasons:

• A successful hack helped stable ProblemSet
• The defenders can quickly find bugs in their own code through the test provided by hackers

So hackers make contributions to the community, they deserve some contribution.

UDP1

VLamarca's number of hacks(number of problem hacks) also a good suggestion.

If it does increases contribution, $\frac{100 x}{100 + x}$ contribution may be simple nice, where $x$ is number of problem hacks.

Fade hacks mentioned by Real_Father_Of_Ash is really annoying, it does know how to improve, but I believe that people who are loving codeforces and care about contribution won't do like this.

Really hope admin: MikeMirzayanov and geranazavr555 could take it into consideration.

• +75

By izlyforever, history, 2 months ago,

nihal2001 posted a blog for asking the following question:

There are $n$ stones, two players take turn to choose $x$ stones, such that $1 \leq x \leq n$ and $x \And n = 0$. The one who cannot make choose lose.

Determine who is the winner, The first one or the second?

I proved that If $n$ belongs to https://oeis.org/A295897, the second player win(can be solved in $O(\log n)$).

My Question(Multiple piles version of above question):

There are $n_1, \cdots, n_m$ stones, two players take turn to choose an index $i$ and $x_i$ stones, such that $1 \leq i \leq m$, $1 \leq x_i \leq n_i$ and $x_i \And n_i = 0$. The one who cannot make choose lose.

Who will be the winner?

This turn out to compute Sprague-Grundy function for $n_1 \cdots, n_m$. The first player win if and only if $sg(n_1) \wedge \cdots \wedge sg(n_m) \neq 0$

I know how to compute $sg(n)$ in $O(n^2 \log n)$, but I can't give it a formula or compute efficiently like $O(\log n)$ or $O(\log^2 n)$

UPD: $O(n^{log_2 3} \log n)$ implement based on wery0's comment.
UPD2: $O(n^{log_2 3})$ implement based on wery0's talk.

format: plain


text:
489人阅读 评论(0)

# Equal Sum Partitions

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 551    Accepted Submission(s): 409

Problem Description
An equal sum partition of a sequence of numbers is a grouping of the numbers (in the same order as the original sequence) in such a way that each group has the same sum. For example, the sequence:
2 5 1 3 3 7
may be grouped as:
(2 5) (1 3 3) (7)
to yield an equal sum of 7.

Note: The partition that puts all the numbers in a single group is an equal sum partition with the sum equal to the sum of all the numbers in the sequence.

For this problem, you will write a program that takes as input a sequence of positive integers and returns the smallest sum for an equal sum partition of the sequence.

Input
The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. The first line of each data set contains the data set number, followed by a space, followed by a decimal integer M, (1 ≤ M ≤ 10000), giving the total number of integers in the sequence. The remaining line(s) in the dataset consist of the values, 10 per line, separated by a single space. The last line in the dataset may contain less than 10 values.

Output
For each data set, generate one line of output with the following values: The data set number as a decimal integer, a space, and the smallest sum for an equal sum partition of the sequence.

Sample Input
3
1 6
2 5 1 3 3 7
2 6
1 2 3 4 5 6
3 20
1 1 2 1 1 2 1 1 2 1
1 2 1 1 2 1 1 2 1 1

Sample Output
1 7
2 21
3 2

Source

Recommend

/*
题意:n个数，分成若干个集合，要求每个集合的数和相同，求集合最小值
思路：枚举当前集合判断是否满足条件

*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;

typedef __int64 ll;

#define N 10005
#define INF 0x3f3f3f3f

int sum[N];
int n;

bool fdd(ll temp)
{
int hh=0;
int pos=0;
while(pos!=n)
{
hh+=temp;
pos=upper_bound(sum+1,sum+n+1,hh)-(sum+1);
if(sum[pos]!=hh)
{
return false;
}
}
return true;
}

int main()
{
int i,j,t,ca;
sum[0]=0;
scanf("%d",&t);
while(t--)
{
scanf("%d%d",&ca,&n);
int x;
for(i=1;i<=n;i++)
{
scanf("%d",&x);
sum[i]=sum[i-1]+x;
}

for(i=1;i<=n;i++)
if(fdd(sum[i])) break;

printf("%d %d\n",ca,sum[i]);
}
return 0;
}

0
0

* 以上用户言论只代表其个人观点，不代表CSDN网站的观点或立场
个人资料
• 访问：180323次
• 积分：5680
• 等级：
• 排名：第4593名
• 原创：389篇
• 转载：9篇
• 译文：0篇
• 评论：14条
阅读排行
最新评论


text:
# Homogenization of systems with equi-integrable coefficients

Abstract : In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions due to Acerbi and Fusco combined with a Meyers $L^p$-estimate adapted to the functional ellipticity condition. The present framework includes in particular the elasticity case and the reinforcement by stiff thin fibers.
Keywords :
Type de document :
Article dans une revue
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2014, 20 (4), pp.1214-1223. 〈10.1051/cocv/2014013〉

Littérature citée [28 références]

https://hal.archives-ouvertes.fr/hal-01102183
Contributeur : Marc Briane <>
Soumis le : mercredi 6 décembre 2017 - 15:24:44
Dernière modification le : jeudi 21 juin 2018 - 01:22:15

### Fichier

cocv140013.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Citation

Marc Briane, Juan Casado-Diaz. Homogenization of systems with equi-integrable coefficients. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2014, 20 (4), pp.1214-1223. 〈10.1051/cocv/2014013〉. 〈hal-01102183〉

### Métriques

Consultations de la notice

## 206

Téléchargements de fichiers


text:
# sklearn.neighbors.NearestNeighbors¶

class sklearn.neighbors.NearestNeighbors(n_neighbors=5, radius=1.0, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, n_jobs=None, **kwargs)[source]

Unsupervised learner for implementing neighbor searches.

Read more in the User Guide.

Parameters: n_neighbors : int, optional (default = 5) Number of neighbors to use by default for kneighbors queries. radius : float, optional (default = 1.0) Range of parameter space to use by default for radius_neighbors queries. algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional Algorithm used to compute the nearest neighbors: ‘ball_tree’ will use BallTree ‘kd_tree’ will use KDTree ‘brute’ will use a brute-force search. ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit method. Note: fitting on sparse input will override the setting of this parameter, using brute force. leaf_size : int, optional (default = 30) Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem. metric : string or callable, default ‘minkowski’ metric to use for distance computation. Any metric from scikit-learn or scipy.spatial.distance can be used. If metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays as input and return one value indicating the distance between them. This works for Scipy’s metrics, but is less efficient than passing the metric name as a string. Distance matrices are not supported. Valid values for metric are: from scikit-learn: [‘cityblock’, ‘cosine’, ‘euclidean’, ‘l1’, ‘l2’, ‘manhattan’] from scipy.spatial.distance: [‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘correlation’, ‘dice’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’] See the documentation for scipy.spatial.distance for details on these metrics. p : integer, optional (default = 2) Parameter for the Minkowski metric from sklearn.metrics.pairwise.pairwise_distances. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used. metric_params : dict, optional (default = None) Additional keyword arguments for the metric function. n_jobs : int or None, optional (default=None) The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Notes

See Nearest Neighbors in the online documentation for a discussion of the choice of algorithm and leaf_size.

https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Examples

>>> import numpy as np
>>> from sklearn.neighbors import NearestNeighbors
>>> samples = [[0, 0, 2], [1, 0, 0], [0, 0, 1]]

>>> neigh = NearestNeighbors(2, 0.4)
>>> neigh.fit(samples)
NearestNeighbors(...)

>>> neigh.kneighbors([[0, 0, 1.3]], 2, return_distance=False)
...
array([[2, 0]]...)

>>> nbrs = neigh.radius_neighbors([[0, 0, 1.3]], 0.4, return_distance=False)
>>> np.asarray(nbrs[0][0])
array(2)

Methods

 fit(X[, y]) Fit the model using X as training data get_params([deep]) Get parameters for this estimator. kneighbors([X, n_neighbors, return_distance]) Finds the K-neighbors of a point. kneighbors_graph([X, n_neighbors, mode]) Computes the (weighted) graph of k-Neighbors for points in X radius_neighbors([X, radius, return_distance]) Finds the neighbors within a given radius of a point or points. radius_neighbors_graph([X, radius, mode]) Computes the (weighted) graph of Neighbors for points in X set_params(**params) Set the parameters of this estimator.
__init__(n_neighbors=5, radius=1.0, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, n_jobs=None, **kwargs)[source]
fit(X, y=None)[source]

Fit the model using X as training data

Parameters: X : {array-like, sparse matrix, BallTree, KDTree} Training data. If array or matrix, shape [n_samples, n_features], or [n_samples, n_samples] if metric=’precomputed’.
get_params(deep=True)[source]

Get parameters for this estimator.

Parameters: deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators. params : mapping of string to any Parameter names mapped to their values.
kneighbors(X=None, n_neighbors=None, return_distance=True)[source]

Finds the K-neighbors of a point. Returns indices of and distances to the neighbors of each point.

Parameters: X : array-like, shape (n_query, n_features), or (n_query, n_indexed) if metric == ‘precomputed’ The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. n_neighbors : int Number of neighbors to get (default is the value passed to the constructor). return_distance : boolean, optional. Defaults to True. If False, distances will not be returned dist : array Array representing the lengths to points, only present if return_distance=True ind : array Indices of the nearest points in the population matrix.

Examples

In the following example, we construct a NeighborsClassifier class from an array representing our data set and ask who’s the closest point to [1,1,1]

>>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh = NearestNeighbors(n_neighbors=1)
>>> neigh.fit(samples)
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> print(neigh.kneighbors([[1., 1., 1.]]))
(array([[0.5]]), array([[2]]))

As you can see, it returns [[0.5]], and [[2]], which means that the element is at distance 0.5 and is the third element of samples (indexes start at 0). You can also query for multiple points:

>>> X = [[0., 1., 0.], [1., 0., 1.]]
>>> neigh.kneighbors(X, return_distance=False)
array([[1],
[2]]...)

kneighbors_graph(X=None, n_neighbors=None, mode='connectivity')[source]

Computes the (weighted) graph of k-Neighbors for points in X

Parameters: X : array-like, shape (n_query, n_features), or (n_query, n_indexed) if metric == ‘precomputed’ The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. n_neighbors : int Number of neighbors for each sample. (default is value passed to the constructor). mode : {‘connectivity’, ‘distance’}, optional Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, in ‘distance’ the edges are Euclidean distance between points. A : sparse matrix in CSR format, shape = [n_samples, n_samples_fit] n_samples_fit is the number of samples in the fitted data A[i, j] is assigned the weight of edge that connects i to j.

Examples

>>> X = [[0], [3], [1]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh = NearestNeighbors(n_neighbors=2)
>>> neigh.fit(X)
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> A = neigh.kneighbors_graph(X)
>>> A.toarray()
array([[1., 0., 1.],
[0., 1., 1.],
[1., 0., 1.]])

radius_neighbors(X=None, radius=None, return_distance=True)[source]

Finds the neighbors within a given radius of a point or points.

Return the indices and distances of each point from the dataset lying in a ball with size radius around the points of the query array. Points lying on the boundary are included in the results.

The result points are not necessarily sorted by distance to their query point.

Parameters: X : array-like, (n_samples, n_features), optional The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. radius : float Limiting distance of neighbors to return. (default is the value passed to the constructor). return_distance : boolean, optional. Defaults to True. If False, distances will not be returned dist : array, shape (n_samples,) of arrays Array representing the distances to each point, only present if return_distance=True. The distance values are computed according to the metric constructor parameter. ind : array, shape (n_samples,) of arrays An array of arrays of indices of the approximate nearest points from the population matrix that lie within a ball of size radius around the query points.

Notes

Because the number of neighbors of each point is not necessarily equal, the results for multiple query points cannot be fit in a standard data array. For efficiency, radius_neighbors returns arrays of objects, where each object is a 1D array of indices or distances.

Examples

In the following example, we construct a NeighborsClassifier class from an array representing our data set and ask who’s the closest point to [1, 1, 1]:

>>> import numpy as np
>>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh.fit(samples)
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> rng = neigh.radius_neighbors([[1., 1., 1.]])
>>> print(np.asarray(rng[0][0]))
[1.5 0.5]
>>> print(np.asarray(rng[1][0]))
[1 2]

The first array returned contains the distances to all points which are closer than 1.6, while the second array returned contains their indices. In general, multiple points can be queried at the same time.

radius_neighbors_graph(X=None, radius=None, mode='connectivity')[source]

Computes the (weighted) graph of Neighbors for points in X

Neighborhoods are restricted the points at a distance lower than radius.

Parameters: X : array-like, shape = [n_samples, n_features], optional The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. radius : float Radius of neighborhoods. (default is the value passed to the constructor). mode : {‘connectivity’, ‘distance’}, optional Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, in ‘distance’ the edges are Euclidean distance between points. A : sparse matrix in CSR format, shape = [n_samples, n_samples] A[i, j] is assigned the weight of edge that connects i to j.

Examples

>>> X = [[0], [3], [1]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh.fit(X)
NearestNeighbors(algorithm='auto', leaf_size=30, ...)

set_params(**params)[source]
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.


text:
# Expectation of log(1/X) when X follows inverse gaussian distribution

Can anybody help me in this question? How to derive the expectation of log(1/X) when X follows inverse Gaussian distribution?

Found out a type of approximation for $\mathbb{E}[\log(X)]$ while $X \sim \mathcal{N}(\mu,\sigma^2)$ in this link (Expected value and variance of log(a)). Can this be extended to the present case to get an approximate solution?

Any help will be appreciated.

• $\log(1/X)=-\log(X)$, did you consider that? – mpiktas Jul 21 '15 at 7:33


text:
# Problem with a simple physic simulation using python scripting

I am very new at blender and I want to make a simple simulation in blender.

I used boolean operation to model the bowl-like shape. And I dropped the cube into the bowl. When I play the simulation via "Alt-A", the cube is stucking on the invisible surface. But I want to see the cube drop into the bowl.

What is the thing that I should correct?

Here is my code:

import bpy

def make_cup():

cone1 = bpy.context.object
cone1.name = 'cone1'

cone2 = bpy.context.object
cone2.name = 'cone2'

mod_diff = cone1.modifiers.new('mod_diff', 'BOOLEAN')
mod_diff.operation = 'DIFFERENCE'
mod_diff.object = cone2
bpy.context.scene.objects.active = cone1
res1 = bpy.ops.object.modifier_apply(modifier = 'mod_diff')

cone2.select = True
bpy.ops.object.delete()

cone1.select = True
bpy.ops.transform.translate(value=(0, 0, 2))

if __name__ == "__main__":

for o in bpy.data.objects:
o.select = True if o.type == 'MESH' else False
bpy.ops.object.delete()

make_cup()

# floor

# square

Make the collision shape of your bowl mesh

The default collision shape for rigid bodies is convex hull. This is why there is an "invisible wall" at the concavity of the bowl

In your script you need to set it to mesh. Here is py console code that changes this property for the context object

 C.object.rigid_body.collision_shape = 'MESH'

do same for bowl in your script.

rigid bodies: sphere not falling into the "box"

Rigid body physics problem even a torus acts like it had no hole in it


text:
Problem: What is the focal length of the eye-lens system when viewing an object 32 cm from the eye? Assume that the lens-retina distance is 2.0 cm. Follow the sign conventions.

FREE Expert Solution

Lens equation:

$\overline{)\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{o}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{i}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbit{f}}}$

so = 32 cm

Problem Details

What is the focal length of the eye-lens system when viewing an object 32 cm from the eye? Assume that the lens-retina distance is 2.0 cm. Follow the sign conventions.


text:
# On which of the following techniques photo state machine works ?

On which of the following techniques photo state machine works?

(1) Magnetic Image-Making

(2) Thermal Image-Making

(3) Electrostatic Image-Making

(4) Electromagnetic Image-Making

Answer: (3) All Electrostatic Copiers work under the premise that a charge of electricity is placed on an Image Drum which has the ability to retain the electric charge much like a capacitor holds its charge but with the ability to hold or release the charge depending on how much light and darkness is applied to the Image Drum. A photocopier (also known as a copier or copy machine) is a machine that makes paper copies of documents and other visual images quickly and cheaply. Most current photocopiers use a technology called xerography, a dry process using heat. Copiers can also use other technologies such as inkjet, but xerography is standard for office copying.


text:
# Fourier Series

1. May 12, 2016

### Poirot

1. The problem statement, all variables and given/known data
The following function is periodic between -π and π:

f(x) = |x|
Find the Coefficients of the Fourier series and, by examining the Fourier series at x=π or otherwise, determine:
1 + 1/32 + 1/52 + 1/72 ... = Σj=1 1/(2j - 1)2

2. Relevant equations
f(x) = a0/2 + ∑n=1 ancos(nx) + bn sin(nx)

a0 = 1/π ∫π f(x) dx
an = 1/π ∫π f(x) cos(nx) dx
bn = 1/π ∫π f(x) sin(nx) dx
3. The attempt at a solution
So I've found the coefficients:
a0 = π
an = -2(1 - (-1)n)/πn2
bn = 0 (as even function)

and so f(x) = π/2 + ∑-2(1 - (-1)n)/πn2 cos(nx)

I don't know how to do the last bit however, I don't really understand if I'm meant to come out with a number or something...
Any help would be greatly appreciated thank you.

2. May 12, 2016

### stevendaryl

Staff Emeritus
Yes. Just plug $x=\pi$ into your expression. (You can see that when $n$ is even, you get 0, so you only have to consider the case for $n$ is odd.)

3. May 12, 2016

### Samy_A

Yes, they expect a value for $\displaystyle \sum_{n=1}^{\infty}\frac{1}{(2n-1)²}$.

You have computed the Fourier series, and found $\displaystyle |x|=\frac{\pi}{2}- \frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(1-(-1)^n)}{n²}\cos(nx)$.

What you have to do next is actually stated in the question: "examining the Fourier series at x=π". In other words, set x=π in your Fourier series.

Last edited: May 12, 2016
4. May 12, 2016

### Poirot

Ok, Yeah I've done that and get

π/2 +4/π∑1/n^2 (From n=1 to ∞ for n odd only)

And can't see how to get rid of the π/2 or 4/π

Thanks

5. May 12, 2016

Take another look at it: You have $\pi=\pi/2+(4/\pi)(...)$ The rest is algebra.


text:
>Business >An intro to indeterminate forms and L’Hospital’s Rule

### An intro to indeterminate forms and L’Hospital’s Rule

Indeterminate forms are typically encountered when assessing limits of functions, and limits in turn have a critical part within calculus and mathematics. They are critical for learning all about gradients, derivatives, Hessians, and a ton more.

In this guide by AICoreSpot, you will find out how to assess the limits of indeterminate forms and the L’Hospital’s rule for finding solutions to them.

After finishing this tutorial, you will be aware of:

• How to assess the limits of functions possessing indeterminate types of the form 0/0 and infinite/infinite
• L’Hospitals Rule for assessing indeterminate types
• How to translate more complicated indeterminate types and apply L’Hospital’s rule to them

Tutorial index

This guide is subdivided into two portions, they are:

1. The indeterminate forms of type 0/0 and infinity/infinity
1. How to apply L’Hospital’s rule to these types
2. Solved instances of these two indeterminate types
2. More complicated indeterminate types
1. How to translate the more complicated indeterminate types to 0/0 and infinity/infinity forms
2. Solved instances of such types

This guide necessitates a fundamental understanding of the following two subjects:

• Limits and Continuity
• Assessing limits

Don’t worry, we’ll be covering these in future posts on AICoreSpot.

What are indeterminate forms?

When assessing limits, we come across scenarios where the fundamental rules for assessing limits might fail. For instance, we can go about applying the quotient rule with regards to rational functions.

lim(x→a) f(x)/g(x) = (lim(x→a)f(x))/(lim(x→a)g(x))          if lim(x→a)g(x)≠0

The above specified rule can only have application if the expression in the denominator does not approach zero as x get close to a. A more complex scenario props up if both the numerator and denominator both approach zero as x approaches a. This is referred to as an indeterminate form of type 0/0. Likewise, there are indeterminate forms of the type ∞/∞ provided by:

lim(x→a) f(x)/g(x) = (lim(x→a)f(x))/(lim(x→a)g(x)) when lim(x→a)f(x)=∞ and lim(x→a)g(x)=∞

What is L’Hospitals Rule?

The L’Hospital Rule specifies the following:

Application of L’Hospital’s Rule

A critical point to observe is that L’Hospital’s rule is only relevant when the conditions for f(x) and g(x) are met. For instance:

• lim(𝑥→0) sin(x)/(x+1) Cannot apply L’Hospital’s rule as it’s not 0/0 form
• lim(𝑥→0) sin(x)/x Can apply the rule as it’s 0/0 form
• lim(𝑥→∞) (e^x)/(1/x+1) Cannot apply L’Hospital’s rule as it’s not ∞/∞ form
• lim(𝑥→∞) (e^x)/x Can apply L’Hospital’s rule as it is ∞/∞ form

Instances of 0/0 and ∞/∞

Some instances of these two variants, and how to find solutions to them are displayed underneath. You can also go about referring to the figure below to refer to these functions.

Example 1.1: 0/0

Assess lim(𝑥→2) ln(x-1)/(x-2) (Observe the left graph in the figure)

Example 1.2 : ∞/∞

Evaluate lim(𝑥→∞) ln(x)/x (See the right graph in the figure)

Even more indeterminate forms

The L’Hospital rule informs us how to handle 0/0 or ∞/∞ forms. But, there are additional indeterminate forms that consist of products, differences, and powers. So, how do we tackle the remainder? We can leverage some smart tricks within mathematics to convert products, differences, and powers into quotients. This can facilitate us to easily apply L’Hospital Rule to nearly all indeterminate forms. The table underneath displays several intermediate forms and how to handle them.

Instances

The following instances display how you can convert one indeterminate for to either 0/0 or ∞/∞ form and go about applying L’Hopsital’s rule to solve the limit. After the worked out instances, you can also observe the graphs of all the functions whose limits have been calculated.

### Example 2.1: 0.∞

Evaluate lim(𝑥→∞) x.sin(1/x) (See the first graph in the figure)

### Example 2.2: ∞-∞

Evaluate lim(𝑥→0) 1/(1-cos(x)) – 1/x (See the second graph in the figure below)

Example 2.3: Power Form

Evaluate lim(𝑥→∞) (1+x)^(1/x) (See the third graph in the figure below)

Extensions

This section details a few ideas and concepts for extending the guide that you may desire to explore.

• Cauchy’s Mean Value Theorem
• Rolle’s Theorem


text:
New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education

The Classification of the Finite Simple Groups, Number 3
Daniel Gorenstein, Richard Lyons, Rutgers University, New Brunswick, NJ, and Ronald Solomon, Ohio State University, Columbus, OH
 SEARCH THIS BOOK:
Mathematical Surveys and Monographs
1998; 419 pp; hardcover
Volume: 40
ISBN-10: 0-8218-0391-3
ISBN-13: 978-0-8218-0391-2
List Price: US$96 Member Price: US$76.80
Order Code: SURV/40.3

This book offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings and automorphisms. The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups. While the purpose of the book is to provide the background for the proof of the classification of the finite simple groups--dictating the choice of topics--the subject matter is covered in such depth and detail that the book should be of interest to anyone seeking information about the structure of the finite simple groups.

This volume offers a wealth of basic facts and computations. Much of the material is not readily available from any other source. In particular, the book contains the statements and proofs of the fundamental Borel-Tits Theorem and Curtis-Tits Theorem. It also contains complete information about the centralizers of semisimple involutions in groups of Lie type, as well as many other local subgroups.

Graduate students and research mathematicians interested in the subgroup structure of the finite simple groups of Lie type, the alternating groups and the sporadic simple groups.

Reviews

"This is the third volume in a series in which the authors aim to write down a complete proof of the classification of simple finite groups. This third volume concentrates entirely on various basic properties of the known finite simple groups. The volume is written in the careful, clear and thorough style we have come to expect from the authors. Quite apart from its role in the series, it contains a wealth of information about the known simple groups which is essential for use in applications of finite group theory. For this reason, it will surely stand on its own as a standard text on simple groups."

-- Bulletin of the London Mathematical Society

"The book is carefully written and much of the material presented has uses well beyond the task at hand. There is a wealth of information in this volume, including quite a number of useful tables ... will be a valuable reference for future generations of mathematicians."

-- Mathematical Reviews

• Some theory of linear algebraic groups
• The finite groups of Lie type
• Local subgroups of groups of Lie type. I
• Local subgroups of groups of Lie type. II
• The alternating groups and the twenty-six sporadic groups
• Coverings and embeddings of quasisimple $$\mathcal {K}$$-groups
• General properties of $$\mathcal {K}$$-groups
• Background references
• Expository references
• Errata for numbers 1 and 2
• Glossary
• Index


text:
Lemma 15.125.6. Let $(A, \mathfrak m, \kappa )$ be a Noetherian normal local domain of dimension $2$. If $a \in \mathfrak m$ is nonzero, then there exists an element $c \in A$ such that $A/cA$ is reduced and such that $a$ divides $c^ n$ for some $n$.

Proof. Let $\text{div}(a) = \sum _{i = 1, \ldots , r} n_ i \mathfrak p_ i$ with notation as in the proof of Lemma 15.125.5. Choose $c \in \mathfrak p_1 \cap \ldots \cap \mathfrak p_ r$ with $A/cA$ reduced, see Lemma 15.125.5. For $n \geq \max (n_ i)$ we see that $-\text{div}(a) + \text{div}(c^ n)$ is an effective divisor (all coefficients nonnegative). Thus $c^ n/a \in A$ by Algebra, Lemma 10.157.6. $\square$

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).


text:
• Abstract

A Low Energy Two-Step Successive Approximation Algorithm for ADC Design

This paper presents a new method for switching the capacitors in the DAC capacitor array of a successive approximation register (SAR) ADC. By separating the decoding of the most significant bits and the least significant bits, and using two different capacitor arrays with unequal size to determine their values, respectively, the average switching energy of the capacitor arrays is dramatically reduced compared to the traditional switching methods. Calibration registers are used to reduce the error of the most significant bits conversion due to the usage of a smaller capacitor array. Experiments were carried out on a 10-bit SAR-ADC designed using TSMC 0.18 μm CMOS process. HSPICE simulations show that significant reduction in energy consumption is achieved using the proposed design.

SECTION I

Introduction

The successive-approximation (SA) ADC is one of the most popular architectures for data-acquisition applications, especially when high-resolution, low power and medium speed are required. In some applications such as wireless sensor nodes, designing low power, and low energy ADC is one of the major challenges. For SAADC, the dominant power dissipation sources are the comparator and the switching in the DAC capacitor array.

Traditional successive-approximation ADC uses a well-known binary tree search method to determine the bit values during the conversion [1], [2], [3]. The conversion starts from the MSB and continues towards the LSB. The first conversion step is to charge up the whole capacitor array to half Vref where Vref is the reference voltage of the maximum detecting input range. Depending on the value of the input, the individual capacitor in the array is charged/discharged in the subsequent conversion cycles. For a 10-bit system, the switching energy of decoding the MSB would be as large as 255 times as of decoding the LSB, due to the larger size of the capacitor at the MSB.

A traditional successive-approximation ADC architecture is shown in Fig. 1. The converter consists of a comparator latch, a successive approximation register (SAR), and a binary weighted capacitors DAC. The output of the DAC (Vy) is charged by connecting the bottom plate of the capacitors to either ground or Vref, and the decoding bit is then determined by checking whether the voltage of the capacitor array (Vy) is greater or smaller than the reference ground (Vx). The process is repeated for the other bits moving towards the LSB, until all the bits are decoded.

Fig. 1. Traditional successive approximation architecture based on a charge redistribution principle.

In [4], Lampinen et al. proposed a double SA algorithm, which has two phases, to reduce the switching energy. The first phase is a nonlinear range selection in which the coarse level of the signal is found in a logarithmic fashion and it is not necessary to go through all the upper bits as in the traditional SA algorithm. The second phase is a linear binary tree search phase similar to the traditional method. In the nonlinear range selection phase, if the input voltage level is low, less number of capacitors is charged up and hence the switching energy is reduced. However, it is still needed to charge up the whole capacitor array with higher voltage, when the input is comparatively high.

In [5], Ginsburg et al. proposed a split capacitor array architecture which splits the largest capacitor of the array into a binary scaled sub-array to maximize the energy savings during switching. By carefully design, the split array avoids throwing away charge that has been stored onto the array by charge recycling during “down” transition. For “down” transition in which the voltage of the capacitor array decreases, switching energy is reduced significantly. So for output codes with smaller values where more “down” transitions occur in the array during the conversion, high switching energy saving can be achieved. However, for other codes that have larger output value, more “up” transitions occur and the energy saving would then be minimal.

In this work, we want to tackle the following problem: “Can we further reduce the switching energy regardless of the input voltage value while at the same time maintaining the requirements of the conversion resolution?”. We propose to use two-capacitor-arrays architecture to reduce the switching energy. A smaller size of capacitor array is used to determine the MSB conversion. For LSB conversion, a full size capacitor array is used and the temporal correlation of the signal is exploited to reduce the switching energy. Correction phase and calibration registers are introduced to eliminate the error at the MSB conversion due to the use of a smaller DAC capacitor array.

SECTION II

Motivation

We use a 6-bit SA-ADC as an example for illustration. For traditional conversion algorithm, the Vref is divided into 64 equal size regions, in which the input is compared with and then digitized into. The conversion can be viewed as composed of two parts: the first is the decoding of the upper 3 bits (MSBs) and the second is the decoding of the lower 3 bits (LSBs). As an example of ZERO Volt, the total switching energy in the first part is 55Co(Vref)2, based on the capacitance of 32Co (MSB, b5), 16Co (b4) and 8Co (b3), and the total capacitance of the capacitor array of 64Co.

One way we can reduce the switching energy of the first part is to use smaller size of capacitors for b5, b4 and b3, as shown in Fig. 2. The total switching energy is (55/8)Co(Vref)2. It can be seen that the energy is reduced by 8 times because a capacitor array of 8 times smaller size is used for the MSB conversion. The energy saving is achieved regardless of the input values. From the above argument, it is shown that we can use a separate and smaller size of weighted capacitors DAC to convert the MSBs, and use a traditional weighted capacitors DAC to do the LSBs conversion. Significant switching energy can then be saved. Fig. 3 shows that switching energy consumption for the traditional and the proposed method.

Fig. 2. Size-reduced weight capacitor DAC for first part.
Fig. 3. (a) Over-estimation error (estimated code = 101, correct code = 100). (b) Under-estimation error (estimated code = 101, correct code = 100).

In this work, we propose a novel two-step search algorithm and a split-capacitor architecture using two binary-weighted capacitor arrays with unequal sizes to reduce the switching power. This method can reduce the switching energy for all range of input voltage level without changing the conversion resolution requirement. It separates the operation into two phases. In the first phase, smaller-sized capacitors are used for the coarse-level-search to determine the values of the most significant bits. In the second phase, typically-sized capacitors are used for fine-level-search to determine the values of the least significant bits where the voltage resolution in each step is finer. The switching energy is reduced dramatically.

SECTION III

Proposed SA Conversion Algorithm

The proposed architecture is shown in Fig. 4. The converter consists of a SAR with control logic, two sets of binary weighted capacitors DAC and two comparator latches (one for coarse-search and one for fine-search), a sample-and-hold circuit, and memory storage.

Fig. 4. Proposed two-step successive approximation ADC with correction.

One of the issues to use a small size capacitor for the coarse-level conversion is the accuracy and resolution issue due to the parasitic capacitance and also the comparator offset. With a n-bit binary weighted capacitor array, we can assume the accuracy and resolution is up to ± 1 LSB which is equal to (1/2n)Vref. For traditional SA-ADC, this resolution and accuracy is acceptable. However, for our 2-phase approach, in the first phase, the small-size capacitance array is used to determine the m-bit MSB. The error can be up to 1/2(nm))Vref and this will seriously affect the accuracy performance of the ADC. Fig. 5 shows an example. In (a), assume the first phase generate a 3-bit MSB code with 101. Ideally, it means Vin is within the range of 0.625Vref and 0.75Vref. However, if due to the accuracy and resolution issue, the actual output voltage Vcoarse of the ADC array is not 0.625Vref for code 101, but is smaller, e.g., 0.57Vref (within ± 1 LSB error of the coarse-level conversion), then when the Vin is equal to 0.59Vref phase-1 will still generate a 101 code. In phase-2, even when a larger-size DAC is used for a better resolution, the best decoding result is 101000. The correct decoding value should be 100101 and the error introduced is large. Similar error will occur when the actual output voltage Vcoarse of the DAC array is higher than that represented by the first phase decoded output, as shown in Fig. 5(b), noted as an underestimation error.

Fig. 5. Energy curve for Traditional Method and Proposed Method.

To solve this accuracy and resolution issue, we add a correction phase between the phase-1 coarse-level conversion and phase-2 fine-level conversion. In the first three clock cycles, the MSBs (b5, b4, b3) are estimated by the coarse-level DAC array. In the 4th and 5th cycle, we test whether the estimated MSB has under-estimation or over-estimation error. We load the estimated MSBs to the large-size fine-search DAC array and assign zeros at the LSBs (b2, b1, b0). The voltage of the DAC array (Vfine) is compared with Vin. If Vin is smaller than Vfine, this indicates that there is an over-estimation issue, then we subtract the estimated MSB by 1 and reload into the fine-search DAC array in the next clock cycle. Otherwise, in the 5th clock cycle, we test whether there is under-estimation by assigning ones at the LSBs (b2, b1, b0) in the fine-search DAC array. The voltage of the DAC array (Vfine) is again compared with Vin. If Vin is larger than Vfine, it indicates there is an under-estimation issue, then we increase the estimated MSB in the fine-search DAC array. After that we go into the fine-search second phase to obtain the LSBs conversion. The MSBs are already available in this phase, and the fine-search conversion is carried out in a similar fashion as the traditional method.

From the above discussion, we add an intermediate phase, which consists of 2 cycles to determine whether there is under-estimate or over-estimate error and correct back the MSBs if there are errors. Note that in each conversion, the MSBs of the fine-search DAC are loaded from the estimated values obtained from the coarse-level conversion. Different from the traditional conversion, they are not reset to zero at the end of the conversion. Instead, the previous values are kept. This is crucial for the energy saving as for most of the data conversion, the data is temporally correlated and the value of the data between two sampling periods are usually close to each other. Thus the MSBs of two consecutive data are close to each other and when we reload the MSBs at the fine-search capacitor array, most of the time the charge/discharge status of the capacitors are not changed and hence the switching of these large capacitors are much reduced.

The two additional cycles for the intermediate phase pose some energy overhead as additional comparison is required. To reduce the energy overhead we want to reduce the average number of additional comparison. When a particular digital code (xyz) has the coarse-above-fine characteristics, i.e., Vy,coarse (xyz) > Vy,fine (xyz000) over-estimation error will not occur because if Vin is larger than Vy,coarse (xyz), it will always larger than Vy,fine (xyz). Similar situation applied for under-estimation error checking. Thus if we know the characteristic of the voltage relationship between the fine and coarse-level of DAC output for each code, sometimes we can omit the over-estimation and under-estimation checking and this can save the overhead of the additional comparison. For each MSBs' digital code, we use a 2-bit memory to store the above voltage characteristic. The register value represents three different situations for the code, UN-ASSIGNED, COARSE-BELOW-FINE [Fig. 5(a)] and COARSE-ABOVE-FINE [Fig. 5(b)]. The values of the register are updated during the conversion process and they only need to be updated once. Depending on the value of the memory for the particular code and adjacent codes, the error-checking process in the intermediate phase can be bypassed and the number of additional comparison is reduced.

When the over-estimation or under-estimation error is detected, the MSBs in DAC array (Vfine) is required to be subtracted or added one. If the MSB is 100 and required to be subtracted by one, all three MSBs have to be toggled. It would consume a large amount of switching energy, due to the large capacitance in MSBs. To reduce the energy overhead for addition and subtraction, the MSBs capacitors are split into the pattern that would only require one capacitor charged/discharged for the operation of the addition or subtraction, regardless of the code values. Fig. 6(a), (b) shows the original MSBs capacitor and the split-version. In (b), the ADD is the active HIGH signal of addition; the SUB is the active LOW signal of subtraction and the SP1 is to control number of capacitor required to be connected to Vref. For example, if the MSB is 110, in (a), the b5 and b4 are connected to Vref, and the total capacitance would be 48Co(32Co+16Co). In (b), the b5, b4, SP1 and SUB are connected to Vref, the total capacitance would be also 48Co(24Co+ 8Co + 8Co + 8Co). However, the addition operation is performed by changing the ADD signal from zero to Vref. And the subtraction operation is performed by changing the SUB signal from Vref to Gnd. The switching energy for addition and subtraction is fixed, regardless of code values.

Fig. 6. (a) Original MSBs, (b) the split version of MSB in fine-search capacitor array, for addition and subtraction.
SECTION IV

Switching Energy Analysis

From Fig. 1, Vin is first sampled into the DAC capacitor array. The energy required to charge the whole capacitor array with the voltage of Vin is TeX Source $$E_0 = {1 \over 2}C_{\rm total}V^2_{\rm in}=\left({1 \over 2}\right)2^nC_oV^2_{\rm in}\eqno{\hbox{(1)}}$$E1 for checking the MSB is equal to [5] TeX Source $$E_1 = -C_nV_{\rm ref}V_{\Delta (n)[1 < -0]} = \left({1}\over {4}\right)2^nC_oV^2_{\rm ref}\eqno{\hbox{(2)}}$$where VΔ (n)[1 < −0] is the voltage difference across the capacitor Cn between time-1 and time-0. At time-2, the (n−1)th bit is decoded. Either “up” transition or “down” transition occurs. E2down is given by [5]: TeX Source \eqalignno{E_{2({\rm down})} & = -C_{n-1}V_{\rm ref} V_{\Delta(n-1)[2 < -1]} = \left({5 \over 16}\right)2^nC_oV^2_{\rm ref}\quad {\hbox{(3)}}\cr E_{2({\rm up})} & = \left({1 \over 16}\right)2^nC_oV^2_{\rm ref}\quad {\hbox{(4)}}}

The energy consumption for decoding the rest of the bits can be analyzed using the same method. In [5] charge recycling and split capacitor techniques are used to reduce the down conversion energy and E2up and E2down are given by: TeX Source $$E_{2({\rm up})} = E_{2({\rm down})} = \left({1 \over 16}\right)2^nC_oV^2_{\rm ref}\eqno{\hbox{(5)}}$$

B. Proposed Two-Step SR-ADC

From Fig. 4, Vin is sampled into Cs initially. The energy required to charge up Cs to Vin is TeX Source $$E_0 = {1 \over 2}C_sV^2_{\rm in}\eqno{\hbox{(6)}}$$The calculation of the switching energy is similar to the traditional approach, except that the sizes of the capacitors are different. Simply, the E1 of charging up the bottom plate of Cn to Vref, can be expressed as [5] TeX Source $$E_1 = -C_nV_{\rm ref}V_{\Delta(n)[1 < -0]} = 2^{(n-m-2)}C_oV^2_{\rm ref}\eqno{\hbox{(7)}}$$For “Up transition” and “Down transition”, the E2up and E2down are expresses as: TeX Source \eqalignno{E_{2({\rm down})} & = -C_{n-1}V_{\rm ref}V_{\Delta(n-1)[2 < -1]} = 2^{(n-m-4)}5C_oV^2_{\rm ref}\quad \hbox{(8)}\cr E_{2({\rm up})} & = 2^{(n-m-4)}C_oV^2_{\rm ref}\quad \hbox{(9)}}

We can see that the energy consumption due to the “up” and “down” transition is much lower than the traditional approach, due to the reduction of the capacitance.

In the detection phase-1 and phase-2, when the over-estimation error or under-estimation error is detected. The MSBs are required to be subtracted or added by one, and the switching energy of subtraction Esub and of addition Eadd are given by: TeX Source \eqalignno{E_{\rm sub} & =\left({1 \over 2}\right)2^{(n-m)}C_oV^2_{\rm ref}\quad \hbox{(10)}\cr E_{\rm add} & =\left({1 \over 2}\right)\left(2^{(n-m-1)}-1\right)C_oV^2_{\rm ref}\quad \hbox{(11)}}

In the detection phase-2, the LSBs are required to set the ONEs for checking the under-estimation. Since the bit-(n-m) will be eventually set to ONE for decoding, the switching energy Eones for setting LSBs to ONEs is given by: TeX Source $$E_{\rm ones} = \left({1 \over 2}\right)\left(2^{(n-m-1)}-1\right)C_oV^2_{\rm ref}\eqno \hbox{(12)}$$

We compared the switching energy consumption of the traditional, charge recycling [5] and proposed approaches using MATLAB for a 10-bit capacitor array. The input data is swept from 0 to 1023 consecutively. The results are shown in Fig. 7. We can see that using the charge recycling approach [5], the energy saving is diminishing when the output code is large. For the proposed two-step approach, since the switching capacitance is dramatically reduced, the energy saving is much significant. At the smallest and largest output codes, the switching energy saving over the traditional SA-ADC and the charge-recycle SA-ADC are 93.3% and 87.7%, and 83.4% and 87.7%, respectively. The average switching energy saving over all the output code, when comparing with the traditional SA-DAC and the charge-recycle SA-ADC, are 92.4% and 87.9%, respectively. We also used real example data to simulate the actual energy saving. Instead of using continuously swept input data, we collected the sampled data at 44 kHz from a musical file and used the data as the input to the ADC. Fig. 7 summarizes the switching energy for the three different ADC architecture. From Fig. 7, we can see that the proposed 2-step approach consume much less energy than the other two approaches.

Fig. 7. (a) Switching energy versus input code for a 10-bit capacitor array, (b) Switching energy versus music file.
SECTION V

Simulation Results

A 10-bit capacitor array using the proposed two-step search approach was designed using TSMC 0.18 μm CMOS technology with metal-insulator-metal capacitor. We divided the bits into two equal groups of 5, i.e., the number of bits in the coarse-search phase (MSBs, b9-b5) and the fine search phase (LSBs, b4-b0) regions are all equal to 5 (m = 5). We also implemented a design using traditional approach. The simple sequencer and code register designs are used, with the custom made Flip-flop, which built on the C2MOS register. The simple P-type comparator latches with power gating switch are used. The proposed and traditional designs were implemented into a single chip to share with the same capacitor array and comparators, as shown in Fig. 8. The proposed two-step approach is occupied 11% more layout area than the traditional, due to the capacitors in coarse-search, memory storage with logic and one comparator.

Fig. 8. SA-ADC chip layout (traditional and proposed approaches implemented using the same capacitor array).

For the proposed approach, since the detecting resolution required is 5-bit and 10-bit: (1/32)Vdd and (1/1024)Vdd in the coarse-search and fine-search respectively. The required biasing current for the comparator latch used in coarse-search, is smaller than the one used in fine-search. We use simple control logic for testing the over-estimation and under-estimation errors, and use the simple register bank for storing 32 digital codes characteristic.

HSPICE simulation were done to verify the function and compare the energy consumption of the two architecture. The designed parameters are as follows: n = 10 bit, Vdd = 1 V, Vref = 0.65, the unit capacitor Co = 23.2 fF, sampling frequency (fs) = 128 kHz. A data swept from 0 to 1023 was used as the input to the ADC for energy consumption comparison. The simulation results of the energy consumption for different inputs of the traditional and proposed approaches are shown in Fig. 9. The energy components of the comparator, digital controller and the capacitor array are shown. The comparator power of the traditional approach is larger than of the proposed approaches, due to the comparator in the coarse-search would consume less power. The controller power of the proposed approach is larger than of the traditional, due to the additional logic control for detecting phase, and additional memory access in the proposed approach. The capacitor switching power is much more in the traditional approach, due to the large capacitance in the MSBs. From Fig. 8, the average energy saving over all the output code is 51.8% when compared with the traditional SA-ADC.

Fig. 9. HSPICE simulation of traditional and proposed approaches.
SECTION VI

Conclusion

A low energy two-step successive approximation algorithm for ADC is proposed utilizing a two-capacitor-arrays architecture to reduce the switching energy. An ADC with a resolution of 10-bit was designed, and its operations was verified by HSPICE simulation.

Footnotes

R. Y.-K. Choi, C.-Y. Tsui are with the Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong, China eericky@ust.hk, eetsui@ust.hk.

References

1. An ultra-low power ADC for distributed sensor networks

M. D. Scott, B. E. Boser, K. S. J. Pister

Solid-State Circuits Conference, 2002-09, 255–258

2. A 6 b 600 MHz 10 mW ADC array in digital 90 nm CMOS

D. Draxelmayr

IEEE ISSCC 2004, vol. 1, p. 264–527, 2004-02

3. A 1 V supply successive approximation ADC with rail-to-rail input voltage range

T. Yoshida, M. Akagi, M. Sasaki, A. Iwata

ISCAS, vol. 1, p. 192–195, 2005

4. Novel successive-approximation alogrithms

H. Lampinen, P. Perala, O. Vainio

Int. Symp. Circuits and Systems, 2005, vol. 1, 188–191

5. An energy-efficient charge recycling approach for a SAR converter with capacitive DAC

B. P. Ginsburg, A. P. Chandrakasan

Int. Symp. Circuits and System, 2005, vol. 1, 184–187

Cited By

No Citations Available

Keywords

INSPEC: Controlled Indexing

capacitors, analogue-digital conversion, capacitor switching

INSPEC: Non-Controlled Indexing

No Keywords Available

Authors Keywords

No Keywords Available

More Keywords

No Keywords Available

No Corrections

Media

No Content Available
This paper appears in:
International Symposium on Circuits and Systems
Issue Date:
2009
On page(s):
17 - 20
ISBN:
N/A
Print ISBN:
978-1-4244-3827-3
INSPEC Accession Number:
10760256
Digital Object Identifier:
10.1109/ISCAS.2009.5117674
Date of Current Version:
26 Jun, 2009


text:
## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x\approx 0.2524$
Solving $\mathrm{a}^{t}=b$ FOR $t$ ... Take the logarithm (either natural or common) on both sides. $\log(3^{5x})=\log 4\qquad$ ... apply $\log_{a}M^{p}=p\cdot\log_{a}M$ $5x\cdot\log 3=\log 4 \qquad$ ... divide with $(5\log 3)$ $x=\displaystyle \frac{\log 4}{5\log 3}\approx 0.252371901429$ $x\approx 0.2524$


text:
# Pythagorean Theorem

on . Posted in Geometry

The hypotenuse is the sum of the squares of the other two sides in a right triangle.

## Pythagorean Theorem formula

$$\large{ c^2= a^2+b^2 }$$

Tags: Surveying Equations


text:
• April 8th 2008, 02:40 PM
lilikoipssn
Car A and Car B leave the origin at noon. Car A travels north at 66 mph and car B travels east at 112 mph.
(a) How far apart are they after 1 hour?
(b) How far apart are they after http://homework.math.ucsb.edu/webwor...5b59f2bc11.png hours?
(c) When are they 1300 miles apart?

I know (a) is 130 miles. But I can't seem to get b, and therefore i can't do c. If anyone can help I'd greatly appreciate it =)
• April 8th 2008, 02:59 PM
topher0805
What you are looking for is distance (D) as a function of time (t).

$D(t)$

Well, we know the equations that give us the distance of Car A and Car B from the origin:

$
D_A(t)=66t$

$
D_B(t)=112t$

And we know that to get the distance between the two we use Pythagoras Theorem.

So, we have that:

$D_{AB}(t)=\sqrt {(D_A)^2+(D_B)^2}$

We then add in our knowledge of $D_A$ and $D_B$ to get:

$D_{AB}(t)=\sqrt {(66t)^2+(112t)^2}$
• April 8th 2008, 03:25 PM
lilikoipssn
Thank you so much!
• April 8th 2008, 03:26 PM
Soroban
Hello, lilikoipssn!

Quote:

Car A and Car B leave the origin at noon.
Car A travels north at 66 mph and car B travels east at 112 mph.

(a) How far apart are they after 1 hour?
(b) How far apart are they after $t$ hours?
(c) When are they 1300 miles apart?

We can solve all the problems at once . . .
Code:

P *
|  *
|    *  d
66t |        *
|          *
|              *
* - - - - - - - - *
O      112t

Car $A$ drives north at 66 mph.
. . In $t$ hours, it has gone $66t$ miles to point $P$

Car $B$ drives east at 112 mph.
. . In $t$ hours, it has gone $112t$ miles to point $Q.$

Their distance $d$ is the hypotenuse of right triangle $POQ.$

. . $d \;=\;\sqrt{(66t)^2 + (112t)^2} \;=\;\sqrt{16900t^2} \;=\;130t$ miles.

(a) When $t = 1\!:\;\;d \:=\:130(1) \:=\:130$ miles.

(b) At time $t$, their distance is: . $d \:=\:130t$ miles.

(c) If $d = 1300$, we have: . $130t \:=\:1300 \quad\Rightarrow\quad t \:=\: 10$ hours.


text:
Upper critical field and location of surface nucleation of superconductivity
Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, pp. 145-181.
@article{AIHPC_2003__20_1_145_0,
author = {Helffer, Bernard and Pan, Xing-Bin},
title = {Upper critical field and location of surface nucleation of superconductivity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {145--181},
publisher = {Elsevier},
volume = {20},
number = {1},
year = {2003},
zbl = {1060.35132},
mrnumber = {1958165},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_2003__20_1_145_0/}
}
TY  - JOUR
AU  - Helffer, Bernard
AU  - Pan, Xing-Bin
TI  - Upper critical field and location of surface nucleation of superconductivity
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2003
DA  - 2003///
SP  - 145
EP  - 181
VL  - 20
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPC_2003__20_1_145_0/
UR  - https://zbmath.org/?q=an%3A1060.35132
UR  - https://www.ams.org/mathscinet-getitem?mr=1958165
LA  - en
ID  - AIHPC_2003__20_1_145_0
ER  -
%0 Journal Article
%A Helffer, Bernard
%A Pan, Xing-Bin
%T Upper critical field and location of surface nucleation of superconductivity
%J Annales de l'I.H.P. Analyse non linéaire
%D 2003
%P 145-181
%V 20
%N 1
%I Elsevier
%G en
%F AIHPC_2003__20_1_145_0
Helffer, Bernard; Pan, Xing-Bin. Upper critical field and location of surface nucleation of superconductivity. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, pp. 145-181. http://archive.numdam.org/item/AIHPC_2003__20_1_145_0/

[1] Agmon S., Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operators, Princeton University Press, 1982. | MR | Zbl

[2] Bauman P., Phillips D., Tang Q., Stable nucleation for the Ginzburg-Landau system with an applied magnetic field, Arch. Rational Mech. Anal. 142 (1998) 1-43. | MR | Zbl

[3] Bernoff A., Sternberg P., Onset of superconductivity in decreasing fields for general domains, J. Math. Phys. 38 (1998) 1272-1284. | MR | Zbl

[4] Bolley C., Helffer B., An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material, Ann. Inst. Henri Poincaré, Physique Théorique 58 (1993) 189-233. | Numdam | MR | Zbl

[5] Chapman S.J., Nucleation of superconductivity in decreasing fields, European J. Appl. Math. 5 (1994), part 1, 449-468; part 2, 469-494. | MR | Zbl

[6] Chapman S.J., Howison S.D., Ockendon J.R., Macroscopic models for superconductivity, SIAM Rev. 34 (1992) 529-560. | MR | Zbl

[7] Dauge M., Helffer B., Eigenvalues variation, I, Neumann problem for Sturm-Liouville operators, J. Differential Equations 104 (1993) 243-262. | MR | Zbl

[8] De Gennes P.G., Superconductivity of Metals and Alloys, Benjamin, New York, 1966. | Zbl

[9] Del Pino M., Felmer P., Sternberg P., Boundary concentration for eigenvalue problems related to the onset of superconductivity, Comm. Math. Phys. 210 (2000) 413-446. | MR | Zbl

[10] Du Q., Gunzburger M., Peterson J., Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Rev. 34 (1992) 45-81. | MR | Zbl

[11] Ginzburg V., Landau L., On the theory of superconductivity, Soviet Phys. JETP 20 (1950) 1064-1082.

[12] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal. 30 (1999) 341-359. | MR | Zbl

[13] Helffer B., Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, 1336, Springer-Verlag, 1988. | MR | Zbl

[14] Helffer B., Mohamed A., Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal. 138 (1996) 40-81. | MR | Zbl

[15] Helffer B., Morame A., Magnetic bottles in connection with superconductivity, J. Funct. Anal. 185 (2001) 604-680. | MR | Zbl

[16] Lu K., Pan X.-B., The first eigenvalue of Ginzburg-Landau operator, in: Bates , (Eds.), Differential Equations and Applications, International Press, 1997, pp. 215-226. | MR | Zbl

[17] Lu K., Pan X.-B., Gauge invariant eigenvalue problems in R2 and in R2+, Trans. Amer. Math. Soc. 352 (2000) 1247-1276. | MR | Zbl

[18] Lu K., Pan X.-B., Eigenvalue problems of Ginzburg-Landau operator in bounded domains, J. Math. Phys. 40 (1999) 2647-2670. | MR | Zbl

[19] Lu K., Pan X.-B., Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Phys. D 127 (1999) 73-104. | MR | Zbl

[20] Lu K., Pan X.-B., Surface nucleation of superconductivity in 3-dimension, J. Differential Equations 168 (2000) 386-452. | MR | Zbl

[21] Lu K., Pan X.-B., Surface nucleation of superconductivity, Methods and Applications of Analysis 8 (2001) 279-300. | MR | Zbl

[22] Saint-James D., De Gennes P., Onset of superconductivity in decreasing fields, Phys. Lett. 6 (5) (1963) 306-308.

[23] Saint-James D., Sarma G., Thomas E.J., Type II Superconductivity, Pergamon Press, Oxford, 1969.

[24] Tinkham M., Introduction to Superconductivity, McGraw-Hill, New York, 1975.


text:
# GUTTERFLOWER TOUR DIARY

## News

• June 2, 2002
GUTTERFLOWER TOUR DIARY

GUTTERFLOWER TOUR DIARY. . . . . . . .composed from a small but pricy hotel room nestled amongst the 24 hour excitement that is Manhattan. . . . . .yesterday's KISS CONCERT in Boston went off without a hitch. . . . .got to say hello to our new friend Michelle Branch. . . . . . . .ran into some folks from Vanessa Carlton's camp who'll be out with us all this summer w/ Third Eye Blind. . . . . . .did some TV, radio, print, took some nice photos, AND made some big rock in New England. . . . . . . . full day. . . . . . . .click on the photos and video above to get in on some of the days events. . . . . . .thanks to Boston for all of the love. . . . . see you this summer. . . . . . . . . . .

Today. . . . . on the road to ZOOTOPIA. . . . . .and a short set at GIANTS STADIUM !!!!!!!. . . . . . .we'll be ridin' over with a couple of winners from Z-100. . . . ..they'll be spendin' most of the day with us. . . . . . .photos for you tomorrow. . . . . . . . .and . . . . . . .idon't forget . . . . . . .tomorrow. . . . . . . .THE LATE SHOW WITH DAVID LETTERMAN. . . . . . . .all of you can get in on this one. . . . . . .CBS. . . . . . .check your local listings. . . . . . . . .

That does it for another GUTTERFLOWER TOUR DIARY. . . . . .oh, don't forget the GUTTERFLOWER disc has a special internet section which allows you access to GUTTERFLOWER TOUR tickets before the show goes on sale to the public. . . . . check the TOUR section of the site for details. . . . . . . . . .boom. . . . . . . .that's how this one ends. . . . . .see you tomorrow with Zootopia coverage. . . . . . . .til then. . . . .

be cool. . . . .

byebye

love

goo

on June 2, 2002 - 12:00am

GUTTERFLOWER TOUR DIARY. . . . . . . .composed from a small but pricy hotel room nestled amongst the 24 hour excitement that is Manhattan. . . . . .yesterday's KISS CONCERT in Boston went off without a hitch. . . . .got to say hello to our new friend Michelle Branch. . . . . . . .ran into some folks from Vanessa Carlton's camp who'll be out with us all this summer w/ Third Eye Blind. . . . . . .did some TV, radio, print, took some nice photos, AND made some big rock in New England. . . . . . . . full day. . . . . . . .click on the photos and video above to get in on some of the days events. . . . . . .thanks to Boston for all of the love. . . . . see you this summer. . . . . . . . . . .

Today. . . . . on the road to ZOOTOPIA. . . . . .and a short set at GIANTS STADIUM !!!!!!!. . . . . . .we'll be ridin' over with a couple of winners from Z-100. . . . ..they'll be spendin' most of the day with us. . . . . . .photos for you tomorrow. . . . . . . . .and . . . . . . .idon't forget . . . . . . .tomorrow. . . . . . . .THE LATE SHOW WITH DAVID LETTERMAN. . . . . . . .all of you can get in on this one. . . . . . .CBS. . . . . . .check your local listings. . . . . . . . .

That does it for another GUTTERFLOWER TOUR DIARY. . . . . .oh, don't forget the GUTTERFLOWER disc has a special internet section which allows you access to GUTTERFLOWER TOUR tickets before the show goes on sale to the public. . . . . check the TOUR section of the site for details. . . . . . . . . .boom. . . . . . . .that's how this one ends. . . . . .see you tomorrow with Zootopia coverage. . . . . . . .til then. . . . .

be cool. . . . .

byebye

love

goo


text:
# [OS X TeX] FYI: BBEdit updated to 8.6, significant improvements in the TeX handling.

Gary L. Gray gray at engr.psu.edu
Wed Jan 10 20:23:09 EST 2007

```On Jan 10, 2007, at 5:19 PM, Maarten Sneep wrote:

> BBedit has been updated to version 8.6, and the TeX module received
> some (needed) attention. From the release notes:
>
> The TeX language module has been significantly enhanced, with
> folding support, improved section/subsection detection for the
> function menu, much more robust math-mode detection, and greatly
> enhanced LaTeX support. These changes resolve various reported
> bugs, as well.
>
> If you wish to place a "marker" in the function menu, you can write
> a comment of the following form:
>
> %: this is a mark
>
> This comment syntax matches that used by TeXShop.
>
> The new TeX module also includes some support for ConTeXt, in the
> form of recognition and generation of fold ranges for \startXXX...
> \stopXXX environments, and special-case support for the "mode"
> environment (we ignore the contents of the mode environment,
> because it often contains out-of-order environment start/stop
> commands which can confuse the parser).
>
> (end quote)
>
> There are more changes, but this is it for TeX. The update is free
> for 8.5 users.

I gave it a try and it really does look interesting. I just wish that
I could sync between BBEdit and the preview as I do in TeXShop. That
really is the deal breaker for me.

-- Gary


text:
Albert Cohen, Ingrid Daubechies, Gerlind Plonka
Regularity of refinable function vectors
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
MSC:
39B62 Systems of functional equations
42A05 Trigonometric polynomials, inequalities, extremal problems
Abstract: We study the existence and regularity of compactly supported
solutions $\phi = (\phi_{\nu})_{\nu=0}^{r-1}$ of vector
refinement equations.
The space spanned by the translates of $\phi_{\nu}$ can only
provide approximation order if the refinement mask
$\mbox{\boldmath$P$}$ has certain particular factorization
properties. We show, how the factorization of
$\mbox{\boldmath$P$}$ can lead to decay of
$|\hat{\phi}_{\nu}(u)|$ as $|u| \rightarrow \infty$.
The results on decay are used in order to prove uniqueness
of solutions and convergence of the cascade algorithm.


text:
# Egress Lighting

#### tdtastic

##### Active Member
Ummm, ok..... BEFORE I have to dive into the federal regulations to prove a point (not on here but to the uneducated powers-that-be who run my building) someone PLEASE back me up that I'm not on glue:

All public buildings (educational in this case) are required to have battery-powered emergency lighting and exit signage in ADDITION to any gasoline generator that might supply back-up power to said building. RIGHT???

We hosted an event in our space over the weekend where hundreds of people moved into and out of our auditorium and surrounding spaces. In the middle of one of the presentations, our building experienced a complete loss of power. After the usual "few seconds" our gasoline generator did NOT kick in, which would have at least powered my auditorium's house lighting and partial fluorescent lighting in the hallways. For nearly an hour, the whole building was plunged into total darkness. Our staff was totally at a loss of what to do. We got through it but not without many (and justifiable) complaints from the patrons and participants.

I was told that our generator has been on the fritz for a while and that the school is waiting on the funds to be approved in the state capital. Insert massive eye-roll.

I'm livid because we have been allowed to put on shows here when the generator-powered egress lighting and signage has NOT been functional. I was told we no longer have a battery backup system; I was here to witness their removal years ago. This sounds like total crap to me - am I wrong?!? Our campus looses power at least ten times a year -- it's something systemic in the grid where we are. I'm PISSED because someone here has known of the faulty generator and lack up backup for months but has done nothing to help us implement some temporary precautions until our generator is replaced!!! Aside from the flashlight in my pocket I have NO way to light our auditorium in the event of a power loss. I will be stuck with six hundred people freaking out in the dark with no way to address them over a mic and no way to light their way. What can I do in the meantime!?

I have events in here all this week and I honestly fear, knowing what I know now about our egress lighting, that I could be considered complicit if there was an emergency when I knowing let people assemble here when we aren't in compliance with federal egress regulations.

Do I need to calm down about this?! Is this something any of you have experienced? Before I go citing NFPA or OSHA standards I just need assurance that my gut instinct is correct: that regardless of specific regulations, it is completely UNACCEPTABLE that our ENTIRE building be plunged into abject darkness for an indefinite amount of time whenever our building experiences a total power loss. Am I crazy? Am I?

#### chausman

##### Chase
Fight Leukemia
https://nationalfireinc.com/inspection-testing/emergency-exit-light.html

Section 5-9.1.2 gives you 10 seconds from power failure to when the alternative source should supply power to emergency lighting.

I will say personally that it's unacceptable to continue to operate without a working generator and automatic transfer switch, and no battery backed system in place. I'm sure that the local AHJ would have similar feelings.

The only possible comfort is that for the most part, nearly everyone in the room will have a flashlight in their pocked (cell phone). Not ideal at all, and not something that should be relied on. But something to think about if a situation were to occur.

#### RonHebbard

##### Well-Known Member
Ummm, ok..... BEFORE I have to dive into the federal regulations to prove a point (not on here but to the uneducated powers-that-be who run my building) someone PLEASE back me up that I'm not on glue:

All public buildings (educational in this case) are required to have battery-powered emergency lighting and exit signage in ADDITION to any gasoline generator that might supply back-up power to said building. RIGHT???

We hosted an event in our space over the weekend where hundreds of people moved into and out of our auditorium and surrounding spaces. In the middle of one of the presentations, our building experienced a complete loss of power. After the usual "few seconds" our gasoline generator did NOT kick in, which would have at least powered my auditorium's house lighting and partial fluorescent lighting in the hallways. For nearly an hour, the whole building was plunged into total darkness. Our staff was totally at a loss of what to do. We got through it but not without many (and justifiable) complaints from the patrons and participants.

I was told that our generator has been on the fritz for a while and that the school is waiting on the funds to be approved in the state capital. Insert massive eye-roll.

I'm livid because we have been allowed to put on shows here when the generator-powered egress lighting and signage has NOT been functional. I was told we no longer have a battery backup system; I was here to witness their removal years ago. This sounds like total crap to me - am I wrong?!? Our campus looses power at least ten times a year -- it's something systemic in the grid where we are. I'm PISSED because someone here has known of the faulty generator and lack up backup for months but has done nothing to help us implement some temporary precautions until our generator is replaced!!! Aside from the flashlight in my pocket I have NO way to light our auditorium in the event of a power loss. I will be stuck with six hundred people freaking out in the dark with no way to address them over a mic and no way to light their way. What can I do in the meantime!?

I have events in here all this week and I honestly fear, knowing what I know now about our egress lighting, that I could be considered complicit if there was an emergency when I knowing let people assemble here when we aren't in compliance with federal egress regulations.

Do I need to calm down about this?! Is this something any of you have experienced? Before I go citing NFPA or OSHA standards I just need assurance that my gut instinct is correct: that regardless of specific regulations, it is completely UNACCEPTABLE that our ENTIRE building be plunged into abject darkness for an indefinite amount of time whenever our building experiences a total power loss. Am I crazy? Am I?
@tdtastic If / when you install a UPS to carry your LX and audio boards through brief outages, consider having your production intercom system and "God mic" on the UPS as well so you can coordinate with your SM and crew as well as give instructions to your patrons. As to assessing your state of craziness, that's beyond my scope.
Toodleoo!
Ron Hebbard

Ben Stiegler

#### MNicolai

##### Well-Known Member
Fight Leukemia
All public buildings (educational in this case) are required to have battery-powered emergency lighting and exit signage in ADDITION to any gasoline generator that might supply back-up power to said building. RIGHT???
No. Unless required by local ordinances, NFPA says you need one or the other, per NFPA 101. There are some exceptions, such as that you must have battery lighting in the generator room in case you need to diagnose an issue during a power loss event.

Do I need to calm down about this?! Is this something any of you have experienced? Before I go citing NFPA or OSHA standards I just need assurance that my gut instinct is correct: that regardless of specific regulations, it is completely UNACCEPTABLE that our ENTIRE building be plunged into abject darkness for an indefinite amount of time whenever our building experiences a total power loss. Am I crazy? Am I?
Your system fails the requirement in NFPA 101 to transition from normal power to emergency power within 10 seconds. This would be readily apparent and well known if the code minimum requirement for regular testing of life safety backup systems was performed. With some exceptions, this is every 3-5 weeks per NFPA 101.

------

I happen to have Florida Building Code handy, which is generally fairly consistent with International Building Code's model code. Under Means of Egress, FBC 2014 says the following:

1006.3 Emergency power for illumination.
The power supply for means of egress illumination shall normally be provided by the premises’ electrical supply.

In the event of power supply failure, an emergency electrical system shall automatically illuminate all of the following areas:

1. Aisles and unenclosed egress stairways in rooms and spaces that require two or more means of egress.

2. Corridors, interior exit stairways and ramps and exit passageways in buildings required to have two or more exits.

3. Exterior egress components at other than their levels of exit discharge until exit discharge is accomplished for buildings required to have two or more exits.

4. Interior exit discharge elements, as permitted in Section 1027.1, in buildings required to have two or more exits.

5. Exterior landings as required by Section 1008.1.6 for exit discharge doorways in buildings required to have two or more exits.

The emergency power system shall provide power for a duration of not less than 90 minutes and shall consist of storage batteries, unit equipment or an on-site generator. The installation of the emergency power system shall be in accordance with Section 2702.
Get facilities on the horn. If facilities won't do something, escalate to higher levels in the school system. If in doubt, ask your AHJ for direction, in which case they will gladly shut you down and cite your employer until they are compliant.

#### Ben Stiegler

##### Well-Known Member
proud of you for speaking up! Its often unpopular to be the safety person doing the right thing.

#### Amiers

##### Renting to Corporate One Fixture at a Time.
Go buy yourself a megaphone and some really good flash lights in the mean time. If you don’t get yourself crap down before hand.

Removing the battery lights is just silly I agree with you there. When I ran facilities in WI. I met with our fire guy every 6 months to replace extinguishers and the batteries in all the signage that had them. He is an ex fire chief and kept up with all the new laws. My goto when the actual fire marshal came around and started rattling off opinions versus code I was ready with proper retorts.

Definitely go through proper channels before you go and nark on yourself though. No ultimatums. Just say calmly and collected this needs to be done ASAP not when the money comes in.

Give it a few weeks and if they sit on their hands pull your trigger ideally a few weeks before you have a big show so it can get fixed in time.

#### RickR

##### Well-Known Member
I strongly advise that you use your best diplomatic voice. Schools are typically large employers and can have enormous political and moral power.

Gather evidence, allies and focus on facts along with those code citations. Maintain a professional stance and calm exterior.

#### MNicolai

##### Well-Known Member
Fight Leukemia
Removing the battery lights is just silly I agree with you there.
It’s not uncommon. Batteries are expensive to maintain. They corrode in place, have to be manually tested and inspected and replaced, one at a time.

In newer all LED venues it’s a little less unusual to see batteries, just because a single 550W inverter can do a whole venue’s worth egress lighting and you can remote the battery somewhere accessible instead of sending someone around a building with a ladder and screwdriver. It’s much more of a maintenance nightmare when you have the batteries all over the place, both in labor and in parts.

Most new construction schools I work on have life safety standby generators and have foregone all battery powered backup lighting. Just have to keep up on the maintenance and regular testing. With all the required lighting control panels to comply with energy code, it’s actually pretty economical on a campus of any moderate size to set up your LCP panels on normal/emergency power, and to do load shedding and lighting dimming during power loss events to get as much runtime on the gen as is possible.

With all of the energy code requirements for scheduling, daylight harvesting, receptacle controls, local dimming, variable CCT control, and occupancy detection, the days of architectural light fixtures being wired directly to line voltage switches and back to dumb circuit breakers are coming to an end.

As for generators, I just did a noise impact study on a building with 3 2M gens. They use 2 for the full building loads and the third is a redundant spare. On another campus our client is running one 2M gen to keep the campus online long enough for them to roll portable gen trucks in to tie into their ATS, which minimizes their install and maintenance costs of having multiple generators to keep the buildings online for x number of days when they go into hurricane command and control mode. Also just did a library where they have an 750kW generator to keep all the building’s HVAC online so they keep the paper products in a humidity controlled environment throughout the full duration of an outage. Can’t do HVAC off of batteries.

Increasing number of reasons to prefer a generator over scattered batteries. In my hurricane territory as well, schools often double as hurricane shelters so these systems are already being installed might as well get the most bang for the buck out of them.

Doesn’t change the fact the the OP’s generator is non-compliant, but you will see far fewer batteries in exit signage and egress lighting in years to come.

#### Amiers

##### Renting to Corporate One Fixture at a Time.
It’s not uncommon. Batteries are expensive to maintain. They corrode in place, have to be manually tested and inspected and replaced, one at a time.

In newer all LED venues it’s a little less unusual to see batteries, just because a single 550W inverter can do a whole venue’s worth egress lighting and you can remote the battery somewhere accessible instead of sending someone around a building with a ladder and screwdriver. It’s much more of a maintenance nightmare when you have the batteries all over the place, both in labor and in parts.

Most new construction schools I work on have life safety standby generators and have foregone all battery powered backup lighting. Just have to keep up on the maintenance and regular testing. With all the required lighting control panels to comply with energy code, it’s actually pretty economical on a campus of any moderate size to set up your LCP panels on normal/emergency power, and to do load shedding and lighting dimming during power loss events to get as much runtime on the gen as is possible.

With all of the energy code requirements for scheduling, daylight harvesting, receptacle controls, local dimming, variable CCT control, and occupancy detection, the days of architectural light fixtures being wired directly to line voltage switches and back to dumb circuit breakers are coming to an end.

As for generators, I just did a noise impact study on a building with 3 2M gens. They use 2 for the full building loads and the third is a redundant spare. On another campus our client is running one 2M gen to keep the campus online long enough for them to roll portable gen trucks in to tie into their ATS, which minimizes their install and maintenance costs of having multiple generators to keep the buildings online for x number of days when they go into hurricane command and control mode. Also just did a library where they have an 750kW generator to keep all the building’s HVAC online so they keep the paper products in a humidity controlled environment throughout the full duration of an outage. Can’t do HVAC off of batteries.

Increasing number of reasons to prefer a generator over scattered batteries. In my hurricane territory as well, schools often double as hurricane shelters so these systems are already being installed might as well get the most bang for the buck out of them.

Doesn’t change the fact the the OP’s generator is non-compliant, but you will see far fewer batteries in exit signage and egress lighting in years to come.
Insurance claims are quite a bit more expensive if something happens.

They took it out then they should of replaced it with something newer. Or at the least condensed if they were having cost issues.

Yes there was a Geni but it doesn’t sound like it’s been kept up with at all or it has been “looked” at by in house Operations and not real technicians.

#### BillConnerFASTC

##### Well-Known Member
For illuminated exit signs, go tritium. Up to at least 20 years, no wire, battery, generator.

#### FMEng

##### Well-Known Member
Fight Leukemia
This type of exit light isn't expensive, and a few can a cover a fairly large area.
https://www.homedepot.com/p/Lithoni...Emergency-Light-Combo-LHQM-LED-G-M6/202671798

https://www.homedepot.com/p/Lithoni...ed-LED-Emergency-Light-ELM2-LED-M12/202514328
It doesn't take much light to safely get a crowd out of the building. Having mothered many generators, I can honestly say changing batteries in a half dozen lights every 5 years is preferable to the maintenance rituals of a generator. The generator service truck costs a lot more per hour than the building custodian or district electrician.

#### BillConnerFASTC

##### Well-Known Member
This type of exit light isn't expensive, and a few can a cover a fairly large area.
https://www.homedepot.com/p/Lithoni...Emergency-Light-Combo-LHQM-LED-G-M6/202671798

https://www.homedepot.com/p/Lithoni...ed-LED-Emergency-Light-ELM2-LED-M12/202514328
It doesn't take much light to safely get a crowd out of the building. Having mothered many generators, I can honestly say changing batteries in a half dozen lights every 5 years is preferable to the maintenance rituals of a generator. The generator service truck costs a lot more per hour than the building custodian or district electrician.
Neither of those links worked for me. Are they both battery powered?

While an exit light over a door or opening is indeed easy to get to, the pendant cylinder or wall mounted bug eyes over fixed seating on tiered risers us not so easy. And not just batteries in 5 or 10 years but pressing the test button periodically. Code requires minumum 0.2 fc over all aisles, cross aisles, etc, in assemby seating, and thats very hard to get in midfle of many auditoriums. With LEDs, I'm a fan of central inverters. The one downside is when that battery has to be replaced in 5 or 10 years, its several thousand dollars. In a typical new hs theatre, i may have 20-30 fixtures designated for emergency. True that if not a normal light that bypasses or transfers for em, maybe 2/3 or half, but still discouraging to get to all for testing. (Once a year?) Plus i like to include step and aisle lights - hard to see the steps in dim light when the aisles are crowded and blocking light to floor - and that's tnverter or generator for large numbers.

CORRECTION: emergency i more than 0.2, which is required when occupied. Its more like 1 fc for em with a minimum level and maximum contrast ratio. Ill look it up when at my desk and will post.

Last edited:

#### BillConnerFASTC

##### Well-Known Member
As promised, from the 2015 Life Safety Code. I believe that IBC is pretty similar:

7.9.2 Performance of System.
7.9.2.1 Emergency illumination shall be provided for a minimum of 11⁄2 hours in the event of failure of normal lighting.
7.9.2.1.1 Emergency lighting facilities shall be arranged to provide initial illumination that is not less than an average of 1 ft-candle (10.8 lux) and, at any point, not less than 0.1 ft-candle (1.1 lux), measured along the path of egress at floor level.
7.9.2.1.2 Illumination levels shall be permitted to decline to not less than an average of 0.6 ft-candle (6.5 lux) and, at any point, not less than 0.06 ft-candle (0.65 lux) at the end of 1 1⁄2 hours.
7.9.2.1.3 The maximum-to-minimum illumination shall not exceed a ratio of 40 to 1.

Note also - summarizing -a monthly 30 second test of all emergency lighting is required and an annual 90 minute test is required. There is a half page of code on this testing, allowing self tests, computer testing, reporting, etc.

#### FMEng

##### Well-Known Member
Fight Leukemia
Neither of those links worked for me. Are they both battery powered?

While an exit light over a door or opening is indeed easy to get to, the pendant cylinder or wall mounted bug eyes over fixed seating on tiered risers us not so easy. And not just batteries in 5 or 10 years but pressing the test button periodically. Code requires minumum 0.2 fc over all aisles, cross aisles, etc, in assemby seating, and thats very hard to get in midfle of many auditoriums. With LEDs, I'm a fan of central inverters. The one downside is when that battery has to be replaced in 5 or 10 years, its several thousand dollars. In a typical new hs theatre, i may have 20-30 fixtures designated for emergency. True that if not a normal light that bypasses or transfers for em, maybe 2/3 or half, but still discouraging to get to all for testing. (Once a year?) Plus i like to include step and aisle lights - hard to see the steps in dim light when the aisles are crowded and blocking light to floor - and that's tnverter or generator for large numbers.

CORRECTION: emergency i more than 0.2, which is required when occupied. Its more like 1 fc for em with a minimum level and maximum contrast ratio. Ill look it up when at my desk and will post.
What I was suggesting is a few of a sub $100 item. Replacement batteries are like$20. I see this solution used in performance venues all the time in my part of the world. All placed within a step ladder's reach.

#### BillConnerFASTC

##### Well-Known Member
I just wonder how well these light an aisle in the middle. Better than nothing - sure - but it seems too often as an industry we settle for just-get-by or almost-get-by solutions. In this case - obviously lots of places do not meet code. What you propose may remedy that but just keep in mind that just meeting code is a D-- passing - and can't we aspire to at least a B average design?

And I'll never claim I have not fallen to the same trap - that doing something for less doesn't have its appeal - but dangerous to aspire to as good.

#### FMEng

##### Well-Known Member
Fight Leukemia
I've seen them in new facilities. I wonder if a design factor is a whether the aisles are flat or gently raked versus having steps? It seems to me that steps would require a higher and more evenly distributed light level to prevent accidents.

#### BillConnerFASTC

##### Well-Known Member
No codes I'm aware of distinguishes between level aisles, aisle ramps, and aisle stairs for illumination.

Last edited:
RonHebbard

#### tjrobb

##### Well-Known Member
PAR36 lamps are still used for emergency lighting, and can cover the center of an auditorium. No LED, though.
Also, NYC and Chi have additional requirements for em lighting.
As for testing, all equipment each month, including a run test of the generator. Can't recall if a load test is required for the genny, and if so how often. Transfer switches also need checked but that takes a specialist.

#### BillConnerFASTC

##### Well-Known Member
Luckily UL924 bypass systems and the incredibly small loads of LED have just about eliminated the need for transfer switches.