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How do you compute the midpoint of an interval?
How do you compute the midpoint of an interval?

... The proof of Eq. (10) is easy: in the absence of underflow, the division by 2 is error-free since it amounts to decrementing the biased exponent by one; in case of underflow, the division by 2 is realized by shifting the fractional part one bit to the right (See Fig. 3), which can only introduce an ...
The maximum modulus of a trigonometric trinomial
The maximum modulus of a trigonometric trinomial

the linear difference-differential equation with linear coefficients
the linear difference-differential equation with linear coefficients

Sample_Chapter - McGraw Hill Higher Education
Sample_Chapter - McGraw Hill Higher Education

... will correspond to the parameters used to define the distribution. When we generate a value from a distribution, we call that value a random variate. Probability distributions from which we obtain random variates may be either discrete (they describe the likelihood of specific values occurring) or c ...
Compositions of n with parts in a set
Compositions of n with parts in a set

random number generation and its better technique
random number generation and its better technique

Recursive definitions A sequence is defined recursively if (B) some
Recursive definitions A sequence is defined recursively if (B) some

Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23
Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23

Tolerance Analysis of Flexible Assemblies Using Finite Element and
Tolerance Analysis of Flexible Assemblies Using Finite Element and

... Sheet metal and composite laminate parts are used often in the aerospace, automotive, and many other areas. For example, the skin of an aircraft wing typically is assembled from many smaller sheets of pre-formed sheet metal riveted together. Variations in the sheet metal parts result in residual as ...
Notes on Discrete Mathematics
Notes on Discrete Mathematics

... 11.3.5.1 Example: A Fibonacci-like recurrence . . . . 194 11.3.6 Recovering coefficients from generating functions . . . 194 11.3.6.1 Partial fraction expansion and Heaviside’s cover-up method . . . . . . . . . . . . . . . . 196 Example: A simple recurrence . . . . . . . . . . 196 Example: Coughing ...
PowerPoint
PowerPoint

Probability with Engineering Applications
Probability with Engineering Applications

Transcendence of Various Infinite Series Applications of Baker’s Theorem and
Transcendence of Various Infinite Series Applications of Baker’s Theorem and

... In chapter 5, we change things slightly by changing the summation from being over the natural numbers, to summation over the integers. This allows us to relax restrictions placed on B(x), while still yielding nice results. We are able to use elementary techniques to obtain closed forms for various s ...
4.1 Reduction theory
4.1 Reduction theory

... Proof. Just take the matrix discriminant of Equation (4.1) and use the fact that any element of GL2 (Z) has discriminant ±1. What this means then is that GL2 (Z) acts on the space F∆ of binary quadratic forms of discriminant ∆ for any ∆. The importance of equivalent forms is in the following. We say ...
cor. to 3 sig. fig
cor. to 3 sig. fig

... The important digits of a number are called significant figures. In most cases, the far left non-zero digit, having the largest place value in a number, is the first significant figure. This is also the most important figure. Subsequent important digits are called the second significant figure, the ...
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(pdf)

A Combinatorial Miscellany
A Combinatorial Miscellany

Lesson 11: The Decimal Expansion of Some Irrational Numbers
Lesson 11: The Decimal Expansion of Some Irrational Numbers

Lectures 1-31 - School of Mathematical Sciences
Lectures 1-31 - School of Mathematical Sciences

... was proved correct. He also conjectured that the answer is ‘no’ if six is replaced by 10, 14, or any number congruent to 2 mod 4. He was completely wrong about this, but this was not discovered until the 1960’s. Euler’s formations are known as mutually orthogonal latin squares; we will study them la ...
Nonnegative k-sums, fractional covers, and probability of small
Nonnegative k-sums, fractional covers, and probability of small

SCILAB IS NOT NAIVE
SCILAB IS NOT NAIVE

On the b-ary Expansion of an Algebraic Number.
On the b-ary Expansion of an Algebraic Number.

... and ak is non-zero for infinitely many indices k. The sequence (ak )k k0 is uniquely determined by u: it is its b-ary expansion. We then define the function nbdc, `number of digit changes', by nbdc(n; u; b) ˆ Cardf1  k  n : ak 6ˆ ak‡1 g; for any positive integer n. Apparently, this function has n ...
Mathematical Methods (CO-145)
Mathematical Methods (CO-145)

NBER WORKING PAPER SERIES Darrell Duffie
NBER WORKING PAPER SERIES Darrell Duffie

1 errors - New Age International
1 errors - New Age International

... The magnitude of the error in the value of the function due to cutting (truncation) of its series is equal to the sum of all the discarded terms. It may be large and may even exceed the sum of the terms retained, thus making the calculated result meaningless. (iii) Round-off Errors: When depicting e ...
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Karhunen–Loève theorem

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