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• ### Longest Common Factor Made Fully Dynamic(1804.08731)

April 23, 2018 cs.DS
In the longest common factor (LCF) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring in both $S$ and $T$. This is a classical and well-studied problem in computer science. The LCF length for two strings can vary greatly even when a single character is changed. A data structure that can be built in $\tilde{\mathcal{O}}(n)$ (The $\tilde{\mathcal{O}}$ notation suppresses $\log^{\mathcal{O}(1)} n$ factors.) time and can return an LCF of the two strings after a single edit operation (that is reverted afterwards) in $\tilde{\mathcal{O}}(1)$ time was very recently proposed as a first step towards the study of the fully dynamic LCF problem. In the fully dynamic version, edit operations are allowed in any of the two strings, and we are to report an LCF after each such operation. We present the first algorithm that requires strongly sublinear time per edit operation. In particular, we show how to return an LCF in $\tilde{\mathcal{O}}(n^{3/4})$ time after each operation using $\tilde{\mathcal{O}}(n)$ space. We also present an algorithm with $\tilde{\mathcal{O}}(\sqrt{n})$ query time for the restricted case where edits are allowed only in one of the two strings and faster algorithms for several restricted variants of dynamic and internal LCF problems (here `internal' means that we are to answer queries about LCF on multiple factors of a given text).
• ### Linear-Time Algorithm for Long LCF with $k$ Mismatches(1802.06369)

Feb. 18, 2018 cs.DS
In the Longest Common Factor with $k$ Mismatches (LCF$_k$) problem, we are given two strings $X$ and $Y$ of total length $n$, and we are asked to find a pair of maximal-length factors, one of $X$ and the other of $Y$, such that their Hamming distance is at most $k$. Thankachan et al. show that this problem can be solved in $\mathcal{O}(n \log^k n)$ time and $\mathcal{O}(n)$ space for constant $k$. We consider the LCF$_k$($\ell$) problem in which we assume that the sought factors have length at least $\ell$, and the LCF$_k$($\ell$) problem for $\ell=\Omega(\log^{2k+2} n)$, which we call the Long LCF$_k$ problem. We use difference covers to reduce the Long LCF$_k$ problem to a task involving $m=\mathcal{O}(n/\log^{k+1}n)$ synchronized factors. The latter can be solved in $\mathcal{O}(m \log^{k+1}m)$ time, which results in a linear-time algorithm for Long LCF$_k$. In general, our solution to LCF$_k$($\ell$) for arbitrary $\ell$ takes $\mathcal{O}(n + n \log^{k+1} n/\sqrt{\ell})$ time.
• ### Longest Common Prefixes with $k$-Errors and Applications(1801.04425)

Jan. 13, 2018 cs.DS
Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we study the problem of computing the longest prefix of each suffix of a given string of length $n$ over a constant-sized alphabet that occurs elsewhere in the string with $k$-errors. This problem has already been studied under the Hamming distance model. Our first result is an improvement upon the state-of-the-art average-case time complexity for non-constant $k$ and using only linear space under the Hamming distance model. Notably, we show that our technique can be extended to the edit distance model with the same time and space complexities. Specifically, our algorithms run in $\mathcal{O}(n \log^k n \log \log n)$ time on average using $\mathcal{O}(n)$ space. We show that our technique is applicable to several algorithmic problems in computational biology and elsewhere.
• ### How to answer a small batch of RMQs or LCA queries in practice(1705.04589)

May 12, 2017 cs.DS
In the Range Minimum Query (RMQ) problem, we are given an array $A$ of $n$ numbers and we are asked to answer queries of the following type: for indices $i$ and $j$ between $0$ and $n-1$, query $\text{RMQ}_A(i,j)$ returns the index of a minimum element in the subarray $A[i..j]$. Answering a small batch of RMQs is a core computational task in many real-world applications, in particular due to the connection with the Lowest Common Ancestor (LCA) problem. With small batch, we mean that the number $q$ of queries is $o(n)$ and we have them all at hand. It is therefore not relevant to build an $\Omega(n)$-sized data structure or spend $\Omega(n)$ time to build a more succinct one. It is well-known, among practitioners and elsewhere, that these data structures for online querying carry high constants in their pre-processing and querying time. We would thus like to answer this batch efficiently in practice. With efficiently in practice, we mean that we (ultimately) want to spend $n + \mathcal{O}(q)$ time and $\mathcal{O}(q)$ space. We write $n$ to stress that the number of operations per entry of $A$ should be a very small constant. Here we show how existing algorithms can be easily modified to satisfy these conditions. The presented experimental results highlight the practicality of this new scheme. The most significant improvement obtained is for answering a small batch of LCA queries. A library implementation of the presented algorithms is made available.
• ### Faster algorithms for 1-mappability of a sequence(1705.04022)

May 11, 2017 cs.DS
In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. The fastest known algorithm for k = 1 requires time O(mn log n/ log log n) and space O(n). We present two algorithms that require worst-case time O(mn) and O(n log^2 n), respectively, and space O(n), thus greatly improving the state of the art. Moreover, we present an algorithm that requires average-case time and space O(n) for integer alphabets if m = {\Omega}(log n/ log {\sigma}), where {\sigma} is the alphabet size.
• ### Optimal Computation of Overabundant Words(1705.03385)

May 9, 2017 cs.DS
The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word $w$ in a given sequence $x$ can be used for classifying $w$ as avoided or overabundant. The definitions used for the expectation and deviation of $w$ in this statistical model were described and biologically justified by Brendel et al. (J Biomol Struct Dyn 1986). We have very recently introduced a time-optimal algorithm for computing all avoided words of a given sequence over an integer alphabet (Algorithms Mol Biol 2017). In this article, we extend this study by presenting an $\mathcal{O}(n)$-time and $\mathcal{O}(n)$-space algorithm for computing all overabundant words in a sequence $x$ of length $n$ over an integer alphabet. Our main result is based on a new non-trivial combinatorial property of the suffix tree $\mathcal{T}$ of $x$: the number of distinct factors of $x$ whose longest infix is the label of an explicit node of $\mathcal{T}$ is no more than $3n-4$. We further show that the presented algorithm is time-optimal by proving that $\mathcal{O}(n)$ is a tight upper bound for the number of overabundant words. Finally, we present experimental results, using both synthetic and real data, which justify the effectiveness and efficiency of our approach in practical terms.
• ### Palindromic Decompositions with Gaps and Errors(1703.08931)

March 27, 2017 cs.DS
Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient algorithms for the factorization of sequences into palindromes and maximal palindromes have been devised in recent years. We extend these studies by allowing gaps in decompositions and errors in palindromes, and also imposing a lower bound to the length of acceptable palindromes. We first present an algorithm for obtaining a palindromic decomposition of a string of length n with the minimal total gap length in time O(n log n * g) and space O(n g), where g is the number of allowed gaps in the decomposition. We then consider a decomposition of the string in maximal \delta-palindromes (i.e. palindromes with \delta errors under the edit or Hamming distance) and g allowed gaps. We present an algorithm to obtain such a decomposition with the minimal total gap length in time O(n (g + \delta)) and space O(n g).
• ### Optimal Computation of Avoided Words(1604.08760)

April 29, 2016 cs.DS
The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of $w$, denoted by $std(w)$, effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word $w$ of length $k>2$ is a $\rho$-avoided word in $x$ if $std(w) \leq \rho$, for a given threshold $\rho < 0$. Notice that such a word may be completely absent from $x$. Hence computing all such words na\"{\i}vely can be a very time-consuming procedure, in particular for large $k$. In this article, we propose an $O(n)$-time and $O(n)$-space algorithm to compute all $\rho$-avoided words of length $k$ in a given sequence $x$ of length $n$ over a fixed-sized alphabet. We also present a time-optimal $O(\sigma n)$-time and $O(\sigma n)$-space algorithm to compute all $\rho$-avoided words (of any length) in a sequence of length $n$ over an alphabet of size $\sigma$. Furthermore, we provide a tight asymptotic upper bound for the number of $\rho$-avoided words and the expected length of the longest one. We make available an open-source implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation.


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# Thread: Solving Linear Trig Equations?

1. ## Solving Linear Trig Equations?

Hello again!

I need some help on solving linear trig equations!

1. 1 - tan (2x + pi/2) = 0 0 Θ ≤ 2 pi

I was told that there are 4 answers possible for this question. How is this possible?

2. Find all solutions of each equation.
a) cot x = 2.3 (I can find it with special angles, but not this)
b) 5 cos 3x = -3

3. c) 2sinx - 1 = -2

Thanks!

2. Originally Posted by finalfantasy
Hello again!

I need some help on solving linear trig equations!

1. 1 - tan (2x + pi/2) = 0 0 Θ ≤ 2 pi
So,
$\tan (2x+\pi/2) = - 1$.
But, $\tan (2x+\pi/2) = - \cot x$.
That means,
$-\cot 2x = - 1$.
Thus,
$\cot 2x = 1$.
I find it easier to think in tangents so take reciprocal of both sides,
$\tan 2x = 1$
Thus,
$2x = \frac{\pi}{4}+\pi n$ for interger $n$.
Thus,
$x = \frac{\pi}{8} + \frac{\pi}{2}n = \frac{5\pi}{8}n$.

3. 1) 1-tanx(2x + pi/2) = 0

-tan(2x + pi/2) = -1

tan(2x + pi/2) = 1

tan is positive in Quad 1 and 3, using the CAST rule.

(alpha) = pi/4 (using special triangles)
therefore (2x + pi/2) = pi/4
2x = pi/4 - pi/2
2x = -pi/4
x = -pi/8 + pi(n)

Quadrant 3: 2x + pi/2 = pi + pi/4 (to get to Quad 3 we must add pi to alpha)
2x = pi + pi/4 - pi/2
2x = 3pi/4
x = 3pi/8 + pi(n)

These answers are not between 0 and 2pi, therefore:

We can sub 0, 1, and 2 for n for both quadrants.

n= 0 : x = 3pi/8 (-pi/8 is NOT in domain)

n= 1 : x = -pi/8 + pi
= 7pi/8

x = 3pi/8 + pi
x = 11pi/8

n= 2 : x = -pi/8 + 2pi
x = 15pi/8

Those are your four solutions. Hope that helped.

4. Quadrant 3: 2x + pi/2 = pi + pi/4 (to get to Quad 3 we must add pi to alpha)
2x = pi + pi/4 - pi/2
2x = 3pi/4
x = 3pi/8 + pi(n)

Thank you all!

It makes sense now, but how is 3pi/8 not between 0 and 2 pi? Does not it equal 67.5 deg?

5. Originally Posted by finalfantasy
Quadrant 3: 2x + pi/2 = pi + pi/4 (to get to Quad 3 we must add pi to alpha)
2x = pi + pi/4 - pi/2
2x = 3pi/4
x = 3pi/8 + pi(n)

Thank you all!

It makes sense now, but how is 3pi/8 not between 0 and 2 pi? Does not it equal 67.5 deg?
You're right, it actually is. I just worded what I meant wrong. I meant to say that not both solutions are between 0 and 2pi. That's why i did use 3pi/8 when subbing in n. Im glad that helped though! Its the unit we're doing right now as well.

6. ^ when do you know you should sub n in for 0, 1 or 2 if the angle is in between 0 and 2 pi?

If one out of the 2 answers from that angle is in between that interval, you would sub in n for that? as seen when you added 3pi /8? I'm terribly slow at getting this, but what does that do? Give you the ... coterminal, related angle ? :S

And can you help me with this one too ^.^

2. Find all solutions of each equation.
a) cot x = 2.3 (I can find it with special angles, but not this)
b) 5 cos 3x = -3

3. c) 2sinx - 1 = -2

You people here are very kind! Thanks!

7. Originally Posted by finalfantasy
^ when do you know you should sub n in for 0, 1 or 2 if the angle is in between 0 and 2 pi?

If one out of the 2 answers from that angle is in between that interval, you would sub in n for that? as seen when you added 3pi /8? I'm terribly slow at getting this, but what does that do? Give you the ... coterminal, related angle ? :S

And can you help me with this one too ^.^

2. Find all solutions of each equation.
a) cot x = 2.3 (I can find it with special angles, but not this)
b) 5 cos 3x = -3

3. c) 2sinx - 1 = -2

You people here are very kind! Thanks!
Well, basically, when the question just asks to solve, then your domain is not restricted and you can do it for all numbers, thus putting the " + pi(n) " in there. Like I did here:

x = -pi/8 + pi(n)
x = 3pi/8 + pi(n)

That means that it could go on for infinity, since the sine or cos curve keeps going, it never stops. UNLESS, there was a domain restriction. Then that tells you that you must only find the solutions on the curve between, say, 0 and 2pi. To do so, you sub in 0 for n giving you 0pi, 1 for n giving you pi, and 2 for in giving you 2pi. Those are the values between 0 and 2pi. And that's how you get your solutions. Hope that helps a little bit.

And for those other questions, I would love to help you, but seeing as I really dont have time right now, I can't. But an alternative to the special triangles is just doing a quick sketch of the curve. That helps you see where the points are exactly. I have to go study for my math test tomorrow, hope that helps!

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# How do you simplify (5x^-7y^-3)/(30y^9x^-4)?

May 16, 2018

$= \frac{1}{6 {x}^{3} {y}^{12}}$

#### Explanation:

Recall the law of indices concerning negative indices:

${x}^{-} m = \frac{1}{x} ^ m \text{ } \mathmr{and} \frac{1}{x} ^ - m = {x}^{m}$

Apply these laws to the highlighted indices below

$\frac{5 \textcolor{b l u e}{{x}^{-} 7} \textcolor{m a \ge n t a}{{y}^{-} 3}}{30 {y}^{9} \textcolor{g r e e n}{{x}^{-} 4}}$

=(cancel5color(green)(x^4))/(cancel30_6 y^9color(blue)(x^7)color(magenta)(y^3)

$= \frac{1}{6 {x}^{3} {y}^{12}}$

May 16, 2018

$\frac{1}{6 {y}^{12} {x}^{3}}$
The reason is because negative exponents in the numerator go to the denominator and is the same concept for negative exponents in the denominator. then you divide the remaining exponents (aka subtract the exponents) for example ${x}^{4} / {x}^{7} = \frac{1}{x} ^ 3$


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# Adjusted R Squared Calculator for Multiple Regression

Instructions: Use this calculator to compute the adjusted R-Squared coefficient for a multiple linear regression. Please input the data for the independent variables $$(X_i's)$$ and the dependent variable ($$Y$$), in form below:

Dependent variable sample data ($$Y$$, comma or space separated) =
X values (comma or space separated, press '\' for a new variable)
Independent variable Names (Comma separated. Optional) =
Dependent variable Name (optional) =

## Adjusted R Squared for Multiple Linear Regression Calculator

The Adjusted R Squared coefficient is a correction to the common R-Squared coefficient (also know as coefficient of determination), which is particularly useful in the case of multiple regression with many predictors, because in that case, the estimated explained variation is overstated/overestimated by R-Squared. The Adjusted R Squared coefficient is computed using the following formula:

$\text{Adj. } R^2 = \displaystyle 1 - \frac{(1-R^2)(n-1)}{n-k-1}$

where $$n$$ is the sample size, $$k$$ is the number of predictors (excluding the constant).

This solver is for a multiple linear regression. If you want to compute the Adjusted R Squared coefficient for a simple regression model, please use this adjusted R-Squared calculator for simple regression models calculator instead. Or, if you already know the value of the coefficient of determination $$R^2$$, the use this R Squared to Adjusted R Squared calculator. Also, if you need to estimate the regression model, use this multiple linear regression calculator.

### What is a Good Adjusted r-Squared for a Linear Regression Model?

The closer to 1, the better. In real life, getting an adjusted R-Squared coefficient very close to 1 is not that easy, as it would imply having some kind of a "perfect model", which is rare to find in real life.


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Thread: proportion of numbers that contain a 3

1. proportion of numbers that contain a 3

1. How many natural numbers less than 100 contain a 3? (Note that 13, 35 and 73 all contain a 3 but 42, 65 and 88 do not). What proportion is this?

2. Approximately what proportion of numbers less than 1000 contain a 3?

3. Explain why almost all million-digit numbers contain at least one 3.

P.S. I know that there are 19 numbers less than 100 that contain 3 but I found that by counting to 100. Then how do I find the proportions?

2. Originally Posted by demode
1. How many natural numbers less than 100 contain a 3? (Note that 13, 35 and 73 all contain a 3 but 42, 65 and 88 do not). What proportion is this?

2. Approximately what proportion of numbers less than 1000 contain a 3?

3. Explain why almost all million-digit numbers contain at least one 3.

P.S. I know that there are 19 numbers less than 100 that contain 3 but I found that by counting to 100. Then how do I find the proportions?
Q1.

Ten numbers from 10 to 99 start with 3..... 30, 31, 32, 33, 34...
one number from 0 to 9 is 3,
nine numbers from 10 to 99 end with 3..... 13, 23, 33, 43....

33 is double counted.

Alternatively,
3 occurs in the 10's position 10 times......30, 31 to 39

and 3 occurs in the units position 10 times.....3, 13, 23, 33, 43...

33 is in both groups.

3. Originally Posted by demode

2. Approximately what proportion of numbers less than 1000 contain a 3?

P.S. I know that there are 19 numbers less than 100 that contain 3 but I found that by counting to 100. Then how do I find the proportions?
If you take 0 as a natural number, then the proportion for Q1 is $\frac{19}{100}$

Q2.

3 can appear in the units, tens and hundreds positions.
You can avoid double-counting as follows

03XX occurs $10^2$ times, since X can be 3.

0Y3X occurs $9(10)$ times, where Y cannot equal 3 to avoid double-counting.

Y can be 0, 1, 2, 4, 5, 6, 7, 8, 9.

0YY3 occurs $9^2$ times

There are $10^3$ numbers from 0 to 999.

Then you can express the proportion as a fraction.

4. Originally Posted by demode
1. How many natural numbers less than 100 contain a 3? (Note that 13, 35 and 73 all contain a 3 but 42, 65 and 88 do not). What proportion is this?

2. Approximately what proportion of numbers less than 1000 contain a 3?

3. Explain why almost all million-digit numbers contain at least one 3.

P.S. I know that there are 19 numbers less than 100 that contain 3 but I found that by counting to 100. Then how do I find the proportions?
Quite possibly, due to the term "approximation",
these questions may be in the context of calculating the probability of having a 3.

Hence, for Q3...

the probability of a million digit number not containing a 3 is

$\frac{8}{9}\left(\frac{9}{10}\right)^{999,999}$

which is pretty small.

Then the probability of a million digit number containing at least one 3 is

$1-\frac{8}{9}\left(0.9\right)^{999,999}$

which is practically indistinguishable from 1.

,

,

what proportion of the first 10000 natural

Click on a term to search for related topics.


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# Column Size For 30m Span

span* spans a number of those 12 columns, and should always add up to 12 for each row (or the number of columns in the parent). Note: The use of different definitions and the span tag is a powerful feature - allowing a consistent look n feel on all pages. 央视网络春晚 - 网易新闻. リビング・居室の増改築｜茨城県水戸市周辺･福島県いわき市周辺のリフォーム・増改築の相談ならお任せください. has-border { border-top:1px solid #ffffff; } #animated-columns-5db97947113f2. By default, each cell will take up the width of one column. How do I set the width of columns in my tables? Timothee Timothee Dec 19, 2011. Sadly there is a strange thing in the radGridView1. now please advice can i build. for two - way slab along the longer span shall be placed below 1. If more than one are marked, it uses the last one in the stack. I’m having a go at CSS Grids at the moment and the gutters were the thing I’ve been finding the most troublesome. 9”x9” columns are to be used for a single storey structure with M15 grade of concrete. The span of a beam is dependent on a few variables. CEO Dennis Alter’s 70-acre estate, which sports a 20,000 square-foot “playhouse,” is still on the block for $30 million, the Philadelphia Inquirer reports. * In this example, “Bold Headline text” was selected. In these situations we can use Colspan or Rowspan attributes. div(column, column, column). 21 hours ago · Global Backend as a Service market sizes from 2015 to 2024, along with CAGR for 2018-2024 Market size comparison for 2017 vs 2024, with actual data for 2017, estimates for 2018 and forecast from. What size steel beam do i need to span 7 meters for a pergola - Answered by a verified Expert We use cookies to give you the best possible experience on our website. The first column got a width of 25 percent and columns 2 and 3 were deleted now that they. 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Under "Width and Spacing" section enter the column width and spacing value or just click the tiny arrows right to the value to increase or decrease the value, this will change the columns width and spacing with equal value of all columns. Why You Ought To Prepare With Your Cannabis There are numerous methods to consume marijuana that is medical will offer you the most health advantages minus the harmful unwanted effects that smoking may bring. Normally, the double decker tent has no poles in the interior of. span Centre of interior span Interior span Moment -0. Site Error Email about the topic was sent to Josef :-) Back. 70+ channels, unlimited DVR storage space, & 6 accounts for your home all in one great price. Set the Button control's ColumnSpan property to 2. We create the dot leaders with a ‘:before’ pseudo-element attached to the LI elements. feet ) of workshop area. Think of column-width as a minimum width suggestion for the browser. This site uses cookies for analytics, personalized content and ads. In a villa construction with load bearing wall having a room size 4. Basically, a small extension that acts as a screen scraper and lets your easily scrape data from a website. Steel Construction – Rules of Thumb Floors (Beams and Girders) To calculate the necessary depth of a beam, divide the span (in inches) by 20. As you can see, a control can span either extra columns, extra rows or in the case of button 4: both. In case, 9"x9" column size is to be used for 1 and half storey structure, then it is advised to use M20 grade concrete. First of all , the question is which type of column you are using timber , concrete etc. This site uses cookies for analytics, personalized content and ads. If a beam having long span (e. in details the spacing of the bars at the column strips can bars near the support unless otherwise indicated or shown those along the longer span at center and over the longer span 2. Ever created an Excel worksheet and wish that one or more of your cells could span across two or more columns? Excel 2016 and previous recent versions have a "merge" feature which lets you span a. For example, three equal columns would use three. The column-width property specifies the column width. Those standard HTML elements are not accepted even in their HTML or. The Bare Bones Guide to HTML lists all the tags that current browsers are likely to recognize. \begin{figure} and \begin{table} span only one column. The economical span lengths of the pitched roof trusses, excluding the Mansard trusses, range from 6 m to 12 m. Description - German Designed and manufactured, the Clearspan Tent is the leader in tenting solutions - Ideal for both short term and long term installations. 0 and I lost my wiki markup editor :. I assumed that the horizontal forces due to wind are taken by the holding bolts thus got 30mm dim bolts. Tottenham want to snatch £30m midfielder from Everton's grasp – report Everton could lose out on Barcelona loanee Andre Gomes, as Spurs eye £30m swoop in the summer. 25 μm; find Supelco-24107 MSDS, related peer-reviewed papers, technical documents, similar products & more at Sigma-Aldrich. When the SfDataGrid. One can use beams of size 9″ X 12″ (225 MM x 300MM) with a slab thickness of 5″ (125 MM) cast in M20 concrete for spans up to 5m. Limited | Boxspan® Roof Member Span Tables. Note: This attribute will overwrite any width set in the element. Given a design span of 15 feet 1 inch and a 16 inch joist spacing, first determine which size lumber will work. How to span multiple rows. 【薬用入浴剤 招福の湯 付き】接着用品 接着テープ 事務用品 まとめお得セット。生活用品・インテリア・雑貨 (業務用100セット) スリーエム 3M メンディングテープ 810-1-12D 12mm×30m 【×100セット】. If this width is smaller than the combined MinimumWidth values of all fill-mode columns, the horizontal scroll bar is displayed, all fill-mode columns are shown with their minimum widths, and user column-resizing is disabled. construction. span_1_of_3. The LayoutColumn has span attribute that sets the size (or width) of a column (measured in grid units). The element only serves to provide information about columns: it isn't the column itself. Tienda de farmacia de Canadá, farmacias en línea con receta y sin receta canadienses. Concast have invested heavily over the last five years in a state of the art precast bridge beam facility. Please enable. The is one column wide, like normal, but the Design Traps cell spans two columns and the Improve Hideout cell takes three, which totals six columns wide. Credit Crisis 1: per Downsize DC: Many sources but the Fed. Let's say we want the first column to be 40% of the table and the two remaning columns to be 30% (as 40% + 30% +30% = 100%). A single-span symmetrical portal frame (as illustrated in the figure below) is typically of the following proportions: A span between 15 m and 50 m (25 m to 35 m is the most efficient). If I just try to set the figure's size to 0. That way the heading would span across both columns of the 2-column text frame. Is that possible ?. Viagra-Cialis-Levitra genérico y de marca en línea sin receta. Net MVC Razor using jQuery AJAX. #animated-columns-5db97947113f2. Paramore Ecuador. Remove existing Contents pages for Volume 2. 特長 ·各種食品、飲料水等のデリバリー用ホース。·食品衛生法に適合し油脂食品に強く長寿命で、安全性に十分配慮して. The Col lets you specify column widths across 5 breakpoint sizes (xs, sm, md, large, and xl). (The DEFINE statement designates characteristics such as formats and customized column headings. This is because failure of column would cause progressive collapse in buildings whereas such event would not occur when other members fail. or 2x12s at 24" O. LastColumnFill. You could consider using classic experience. 00 feet Distribution Factor for Moment Distribution Factor, DFM = W / E = 0. This is working fine till here. The third row contains only one datacell. Structural design is never done on assumptions. column-width is a flexible property. The introduction of ‘column-gap’ and ‘row-gap’ will make things so much nicer. اللهم صلي وسلم على نبينا محمد. Add(control, pos, span, flags, border) The following table lists the methods of GridBagSizer class −. Net MVC Razor using jQuery AJAX. Rangel Pestana 1580 Brás São Paulo SP | +55 11 3385-3310 | @wiler-k. The number of cells to the right this cell should span. Bulma is a free, open source CSS framework based on Flexbox and built with Sass. Instant access to millions of Study Resources, Course Notes, Test Prep, 24/7 Homework Help, Tutors, and more. As the world's largest manufacturer of capillary columns for gas chromatography (GC), Agilent stands for more than 40 years of experience and the highest quality in manufacturing. 06 ctw white diamond solitaire bezeled in 14k gold. - Amy_MSFT Jan 26 '18 at 7:42. Not that anything other than a string value will need to be bound (i. Deflection And Precambering Of Steel Beams 131 Fig. 25 mm, df 0. There are two types of Lists in HTML. q 070024 Undersized column (See Column Table) q 070024 Substantially damaged, bowed, rotted or over -notched (more than 1/3 rd width of column) Railings-Railings, also known as guards, are required whenever the deck is two feet or more above grade. It is very nice that we can use a grid layout with a css standard these days. Design the slab system shown in Figure 1 for an intermediate floor where the story height = 12 ft, column cross-sectional dimensions = 18 in. By default, a browser will adjust table columns to fit the contents of the table. You can see it back in a lot of frameworks in all sorts of ways. column-rule-width column-rule-style column-rule-color All three properties above can be set using the shorthand 'column-rule' property. What structural system can give me a big distance between columns? the columns for the nicer aesthetic I found that the distance between the columns is more than 16 m. Column and beam construction is common in most homes. Allows a single table cell to span the width of more than one cell or column. 特長 ·各種食品、飲料水等のデリバリー用ホース。·食品衛生法に適合し油脂食品に強く長寿命で、安全性に十分配慮して. In a villa construction with load bearing wall having a room size 4. For the efficient design of composite beams, the ratio of span to beam depth is in the range 22 to 25, and so a composite beam is 25 to 30% shallower than a steel beam, and up to 30 to 40% lighter in steel weight. Standard “Retirement” Standard Proposed Date New Standard 24’ Rdwy, Ty IV Jan 2009 Oct 2009 Oct 2011 Tx46 all all Ty A, B, C Tx28 and Tx34 other other Ty IVIV Tx54. CRUD operation in simple terms means Select, Insert, Edit, Update and Delete operations. This brings us to an important limitation. Colspan and Rowspan. Two-Way Concrete Floor Slab with Beams Design and Detailing. The problem which i am facing is, when i show all columns every column will have some calculated width e. I could have had it spanning only two of the columns and had another cell at the top, if that's what I wanted. ENGINEERED WOOD PRODUCTS (EWP) LVL SPAN AND SIZE CHARTS. Column Spanning. In some situations we need the Table Cells span across (or merged) more than one column or row. The concrete slab roof is cantilevered out by 1. For example, three equal columns would use three. The support columns are placed in each 4 corners and they are 300mm x 300mm size. Esperanda La Felicidad Cap铆tulo 3,Video, CCTV-E, canal español, CCTV, Noticia china, Programaci贸n, China, Televisi贸n. Set the table column width constant regardless of the amount of text in its cells? 499. It is assumed to be the most crucial structural member of a building because the safety of a building rest on the column strength. with fixed width columns either side and a center. MultiColumnText is great for creating columns without too much code, but it lacks an element of control. Look up to the top row to see the width of steel I-beam, or size, that you need for your project to support the KIPS that will bear down upon it. If more than 12 columns are placed within a single row, each group of extra columns will, as one unit, wrap onto a new line. Beam Size is Governed by 2 criterias * Serviceability * Loading Column Size is mainly governed by loading provided it complies with some specifications mentioned in IS 456, IS 13920 etc. Add or change the space inside the table. Reinforcement ratio (steel area / gross column area) must be between 1% and 8%; column analysis (method "A") also checks bar fit based on assumptions about aggregate size and tie or spiral diameter, and assuming 1-1/2 in. Viagra O Cialis. Minimum size of the column should not be less than 9”x9”. 0 Members and 5 Guests are viewing this topic. Has anyone done this before?. Status and trends in the health of land, water, air, biodiversity and urban environments in NSW. Select how many columns to span, and set the spacing above and below the span, if desired. Remove existing Contents pages for Volume 2. Change column width. Introduction In Part 1 we examined the elementary basics of the DataGrid, an ASP. What should be the size of column for a 9m span? What size timbers do i need for a lean to roof on a extension with a span of 3. Highcharts - Interactive JavaScript charts for your web pages. 21 hours ago · Landscape Arch has a span of 290 feet base to base and is only 6 feet thick at its center, very thin for its length. Then find the required Fb value at the bottom of the column. Macro variable ull is to produce a black line under span header. 316/0001-07 Todos Av. However, if you need support for IE10 and down, you should use float. The support columns are placed in each 4 corners and they are 300mm x 300mm size. a popular approach to ingestion is utilizing a vaporizer, but getting increasingly popular for most clients is cooking with cannabis. For end spans. row and add the appropriate number of. Porch Construction Drawings (may be used in conjunction with site plan for permit submittal) Rafter size and spacing: _____ Beam Size_____ Footing Size _____ Table A: Porch Depth Footing Size Beam Size Max Beam Span Rafter Size Post Size 10ft 18” sq x 1’ D 4x8 10ft 2x6 @ 24” o. Lucks Food Decorating company is the premier source for all your wholesale icing decoration needs. If the 4th column end up being zero it is in the span (and you may find which by doing the inverse of the column reductions). ; 40 Prepare Column 6 and record the type of span construction. Sudan Vision Turkey’s investment footprint in Sudan has become quite visible. You can see it back in a lot of frameworks in all sorts of ways. Instead of showing the text “Hello World” when people view your application, what we want to do is to show a place for user to save data to the database. Design the slab system shown in Figure 1 for an intermediate floor where the story height = 12 ft, column cross-sectional dimensions = 18 in. As shown above, each col element refers to one table row but you can also use the span attribute to make it span more than one column (don’t confuse this with the span tag as they have nothing in common). DPW Urban Forestry - 2010 Spring Planting List/title. I don't even get close to what a span table would indicate you could for reasons mentioned in earlier post here ervn though I do use a #grade. In this example we're defining a grouped column with IT Skills having two child columns Skills and Proficiency. Free and easy to use online HTML Tables generator -- enter the table data and just copy and paste the generated table code into your website. Column Sizer in Xamarin DataGrid (SfDataGrid). Okay, without understanding the underlying data, and what your use case is, your code doesn't make a lot of sense to me. GtkComboBox:column-span-column "column-span-column" gint: Read / Write If this is set to a non-negative value, it must be the index of a column of type G_TYPE_INT in the model. Unfortunately if your theme doesn’t give you the tools to build one, you might be feeling like it’s time to upgrade your theme. Please note that the knee braces will cause reverse bending in the beam and so if the bottom flange is not braced (which is most common) it will reduce the allowable stress. * In this example, “Bold Headline text” was selected. Each span has three css classes: webix_table_checkbox – adds the checkbox functionality to a span. How can I specify the widths of columns in a table having a specified width and using fixed table layout when a cell in the first row spans multiple columns? Using the following code, the first column gets the desired width of 100px. photo gallery flexible width span 5 columns. Column classes indicate the number of columns you’d like to use out of the possible 12 per row. First of all , the question is which type of column you are using timber , concrete etc. Maximum floor joist span for No. ii) Maximum bending stress if the beam carries a central load of 40KN. In colspec or spanspec, it applies on to the cells in that column or span. Why is the length of RC beam limited? It depends on the height of the beam but on the other hand you need to increase the width (for slenderness prevention). A concrete column reinforced with vertical bars and individual lateral ties. I’m having a go at CSS Grids at the moment and the gutters were the thing I’ve been finding the most troublesome. The default is false. If I just try to set the figure's size to 0. rfa) before. Ordene Viagra en línea ahora. Once you have determined the load characteristics of your raised deck and the number of deck support columns required you can determine the design and size of the deck support columns. GrungeAmadeus. span Centre of interior span Interior span Moment -0. Note there are three cells (columns) that are being spanned by that command. Refer to the numbers in (Table 052-196-3008-02), and the. CSS Grid Layout: The Span Keyword If you're placing items onto their parent grid with grid-column or grid-row , you can use the span keyword to avoid specifying end lines when items should span more than one column or row. How to Create a Header in Excel to Span Across the Top of the Page Reduce a Worksheet Size in Excel 2007. 特長 ·各種食品、飲料水等のデリバリー用ホース。·食品衛生法に適合し油脂食品に強く長寿命で、安全性に十分配慮して. This post also applies another way to define span header. Here is a grid of the CSS3 Multi-column Layout Module, all the properties, values and current browser support. Single Column. Introduction The System of Columns and Beams have been used in Construction since Ancient Egypt (Which lasted from about 3100BC until it was finally absorbed in to the Roman Empire in 30 BC) Ancient Greece and Ancient Rome. As you can see, we have used spans instead of real inputs. 3 F is the total design ultimate load on the strip of slab between adjacent columns. In colspec or spanspec, it applies on to the cells in that column or span. However, since precast is a cast material, essentially any shape can be manufactured to meet a project's needs. Is that possible ?. You can span columns by using the span field in the TableRow. In this gridview I have Textboxes and a add button in footer to add the records. You can change this behaviour to allow cells to span multiple columns. thu vien chau duc Thứ Năm, 20 tháng 2, 2014. 830px section --> Latest tour --> Blog News Film & TV. Why use colspan= or rowspan=? Sometimes it makes sense for a cell to span multiple columns or multiple rows. 146) of the span length will result in the maximum moment in any span being equal to 1/16 wL2. Normally, a element takes up the space it needs to display the content. I have tried to do it with a script but it doesn’t work. Rex Swain's KEDIT/KEXX Summary (KEDIT for Windows, Version 1. You might use this when working with media queries to tell the spanning element to stop spanning. Considering main reinforcement dia. This guide was created as a resource to help you better understand and learn Grid, and was organized in a way I thought made the most sense when learning it. Should I replace a carport post as it was originally built or with an upgraded column?. GridbagSizer(). 019 clear minimum from top concrete slab and bottom of slab. The computational limitations restrict the grid size used in GCM models, and for many cloud types they are too large when compared to the scale of the cloud formation processes. Is that possible ?. 70+ channels, unlimited DVR storage space, & 6 accounts for your home all in one great price. Add(control, pos, span, flags, border) The following table lists the methods of GridBagSizer class −. DPW Urban Forestry - 2010 Spring Planting List/title. 4m Rubb rapid deployed military aircraft hangar was the first of the EFASS aircraft hangar range of soft walled temporary buildings to be specifically designed to comply with a very stringent military compliance matrix from the Royal Air Force. span* columns. Be sure that the column you use is suitable for water injections. width=" percentage or pixels " ~ Using the width attribute, you can explicitly set the width of your table. The items in the grid can change their size or keep the default size, when the window is resized. Column classes indicate the number of columns you’d like to use out of the possible 12 per row. cliui({wrap: boolean}) Enable or disable the wrapping of text in a column. The number of columns will be the minimum number of columns needed to show all the content across the element. 5 meters (m) long and out‐to‐out width of 27. We use cookies for various purposes including analytics. Select how many columns to span, and set the spacing above and below the span, if desired. Don't guess sizes. Clout Fitness Quick Release Pair of Locking 2" Olympic Size Barbell Clamp Collar Great for Pro Training$9. And your carry beam (which the joists sit on) - to span 20 feet or so forget it, you are talking a major structural beam - way beyond a 6x12 in wood, into a custom size natural wood beam like maybe a 6x18 or 8x14 or a manufactured beam (bad for outdoor use) or a good sized steel beam, and beyond about a 10-12' span you would be heavier than 6x6 posts too. Most of these will fall into categories of beams, columns, or walls. An Engineer’s Guide to: Openings in Concrete Floor Slabs BUILDINGS If you took an advanced concrete design course, you probably had a good introduction to the design of two-way slabs. Table headers will set the width on your td's automatically. Be sure that the column you use is suitable for water injections. If the span classes are not set, mdc-layout-grid__cell will fallback to a default span size of 4 columns. Set up column width in an APEX report (for Firefox) Von Tobias Arnhold → 2. 1: Design an interior panel of a flat slab of size 5 m ´ 5 m without providing drop and column head. 2 Parallel Chord Trusses The parallel chord trusses are used to support North Light roof trusses in industrial buildings as well as in intermediate span bridges. GtkComboBox:column-span-column "column-span-column" gint: Read / Write If this is set to a non-negative value, it must be the index of a column of type G_TYPE_INT in the model. LONG SPAN STRUCTURE’S Structures with span larger than 15-20 meters are regarded to as Long Span Structures. At widths of 100' feet or more, it is more economical to use a modular span steel building system with interior columns. So for instance if your RecyclerView is 320dp wide and you use a column width of 72dp , a span count of 4 ( 320dp / 72dp = 4. Ok, look into the first cell — it has colspan="3" in it, and so spans the three columns below it. There are two types of Lists in HTML. That means the width of Column0 is 1/4th, the width of column1 is 1/4th and the width of column2 is 2/4th of the grid. Serra Fita: a melhor seleção de Buscapé, esta domingo, ao melhor preço !Encontre aqui 1312 ofertas, marcas, produtos em promoção e estoque pronto para ser enviado de forma rápida e segura em sua casa. Generally long spans result in flexible, column-free internal spaces, reduce substructure costs, and reduce steel erection times. with fixed width columns either side and a center. Set the Button control's ColumnSpan property to 2. The column alignment specifier is formatted like: [][. 中国青年网：网民上网习惯调查. column-rule-width column-rule-style column-rule-color All three properties above can be set using the shorthand 'column-rule' property. Click on the Sign Up box below to ensure that you receive the latest span calculator updates!!. THE ENGINEER’S TOOLBOX Materials Densities 1 t/m 3 = 10 kN/m Water 1 t/m3 Concrete 2. Concast have invested heavily over the last five years in a state of the art precast bridge beam facility. Use column-width to declare the width of the columns. List and Library Column Widths In document libraries and in the List View it would be great if the column widths and text size could be adjustable. habbonext aaaaaaaaaaaaaaaa. How to create a 5x4 (5 rows, 4 columns) table with one of rows having a column span set to 4 (colspan="4")?. A column chart is a vertical bar chart rendered in the browser using SVG or VML, whichever is appropriate for the user's browser. If a beam having long span (e. Steel portal frames are widely used because they combine structural efficiency with functional form. For every breakpoint, you can specify the amount of columns to span, or set the prop to for auto layout widths. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to$585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over$1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported:


text:
# help! z-2/x^2+4z+4+5/4z^2-16-z+2/2x^2-4z

#### susan pearson

##### New member
This problem has me stumped. I need to find the LCD and I can't seem to go any farther than what I've listed.

z-2 + 5 - z + 2
------------- ------------- -------------
x^2 + 4z + 4 4z^2 - 16 2x^2 - 4z

x^2 + 4z + 4 (2z + 4)(2z - 4) 2(x^2 - 2z)

Where am I going wrong or is this really as far as I can factor these and I need to find the LCD from these?

#### galactus

##### Super Moderator
Staff member

$$\displaystyle \L\\\frac{z-2}{x^{2}+2z+4}+\frac{5-z}{4z^{2}-16}+\frac{2}{2x^{2}-4z}$$

#### Denis

##### Senior Member
Re: help!

Susan, I suggest you experiment with the "code" button; to get something like this:
Code:
     z-2               5                z + 2
------------   +   ---------    -     ---------
x^2 + 4z + 4       4z^2 - 16          2x^2 - 4z
I have a feeling the 2 x's that appear should be z's: please check...

#### susan pearson

##### New member
YOU'RE RIGHT

galactus said:

$$\displaystyle \L\\\frac{z-2}{x^{2}+2z+4}+\frac{5-z}{4z^{2}-16}+\frac{2}{2x^{2}-4z}$$
You're right: I don't what I'm doing! you interpreted my scribble with everything correct but the 5 - z. The z should actually be z + 2 on the last fraction.

#### Denis

##### Senior Member
Re: help!

So, if z is the only variable, your expression is:

(z-2) / (z^2+4z+4) + 5 / (4z^2-16) - (z+2) / (2z^2-4z)

factoring a bit:
(z-2) / (z+2)(z+2) + 5 / 4(z-2)(z+2) - (z+2) / 2z(z-2)

to keep it manageable, let x = z-2 and y = z+2; then:
x / y^2 + 5 / 4xy - y / 2zx

applying the lcd 8zx^2y^3 leads to:
(4zx^2 + 5zy - 2y^3) / (4zxy^2)


text:
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http://iet.metastore.ingenta.com
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Energy has always been the driving force in the technological and economic development of societies. The consumption of a significant amount of energy is required to provide basic living conditions of developed countries (heating, transportation, lighting, etc.). Today's energy supply has a considerable impact on the environment, since it is fuelled by the burning of fossil fuels. In addition to this, the fossil fuel reserves are decreasing while the demand for energy is rapidly rising. Climate change, the depletion and geographical segregation of fossil fuel resources, health related issues as well as energy poverty constitute the driving forces towards the pursuit of alternative energy sources. In addition, countries with no access to oil reserves are being dependent from other countries for their energy supply, with a strong impact on politics and financial issues. But apart from occasional financial recessions, the long-term need for increasing amounts of energy as countries develop will become a major rate limiting step in the growth of the world economy [1]. The last years there is an on-going research on alternative fuels in order to overcome the fossil energy dependence and to provide a sustainable growth of economies and societies.

Chapter Contents:

• 1.1 Towards a hydrogen economy
• 1.2 Hydrogen - Thermo-physical properties
• 1.3 Hydrogen storage
• 1.3.1 Compressed hydrogen gas (CGH2)
• 1.3.2 Liquid hydrogen (LH2)
• 1.3.3 Solid storage of hydrogen (SSH2)
• 1.3.3.1 AB-type TiFe intermetallic compounds
• 1.3.3.2 AB2 Laves Phases Zr-based intermetallic compounds
• 1.4 Hydrogen compressors
• 1.4.1 Mechanical compressors
• 1.4.2 Non-mechanical compressors
• Acknowledgements
• References

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Hydrogen storage and compression, Page 1 of 2

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# Problem with integrating sine function

I have a problem solving an integration. This is my approach: \begin{align*} u &= \frac{1}{T}\cdot\intop_{0}^{T}(U_{0}+\hat{u}\cdot \sin(\omega t))dt\qquad\text{with }\omega=\frac{2\pi}{T}\\ u &= \frac{1}{T}\cdot\intop_{0}^{T}(U_{0}+\hat{u}\cdot \sin(\frac{2\pi}{T}\cdot t))dt\\ u &= \frac{1}{T}\cdot\left[U_{0}t-\hat{u}\cdot\frac{T}{2\pi}\cdot\cos\frac{2\pi}{T}\cdot t\right]_{0}^{T}\\ u &= \frac{U_{0}T}{T}-\hat{u}\cdot\frac{T}{2\pi\cdot T}\cdot\cos\frac{2\pi\cdot T}{T}\\ u &= U_{0}-\hat{u}\cdot\frac{1}{2\pi}\cdot\cos2\pi\\ u &= U_{0}-\frac{\hat{u}}{2\pi}. \end{align*}

But the solution should be ${u = U_{0}}$. Where is my mistake?

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It's $\cos 0=1$, not $\cos 0=0$.
What do you mean? I only have $\cos(2\pi)=1$ – Sven Walter Feb 12 '11 at 14:02
You are missing the term that comes from inserting the lower limit $t=0$ into the antiderivative. That term will cancel the one coming from $t=T$, since $\cos 2\pi$ and $\cos 0$ are both 1. – Hans Lundmark Feb 12 '11 at 14:11