Higher Geometry - Mathematical & Statistical Sciences

Three Point Geometry Axioms for the Three Point Geometry: 1. There exist exactly 3 points in this geometry. 2. Two distinct points are on exactly one line. 3. Not all the points of the geometry …

  Geometry

Geometric Constructions - UC Denver

Philosophy of Constructions Constructions using compass and straightedge have a long history in Euclidean geometry. Their use reflects the basic axioms of this system.

  Basics, Geometry

The Chinese Remainder Theorem - UC Denver

by 3, and remainder 3 when divided by 7. We are looking for a number which satisfies the congruences, x ≡ 2 mod 3, x ≡ 3 mod 7, x ≡ 0 mod 2 and x ≡ 0 mod 5.

  Chinese, Theorem, Remainder, Chinese remainder theorem

Proof Methods - Mathematical and Statistical Sciences

Writing mathematical proofs is therefore an art form (the art of convincing) and a social process since it is directed at people (the readers). A mathematical proof of a statement strongly depends on who the proof is written for. Proofs for a research audience are quite different from those found in textbooks. And even textbook proofs look ...

  Writing, Proof, Mathematical, Writing mathematical proofs, Mathematical proof

Equivalence Relations - Mathematical and Statistical Sciences

1) a is an upper bound for B, and 2) a R x for every upper bound x for B. Example: Reals with the usual ordering. B = {x | 5 < x < 7 } 8, 7.5, 11, 7.00001 are all upper bounds of B. 7 is also an upper bound, and 7 ≤ any of the upper bounds, so 7 …

  Bound, Upper, Upper bounds

Chapter 10 Error Detection and Correction

The Hamming distance between two word i th b f diffds is the number of differences between corresponding bits. 10.25. Example 10.4 Let us find the Hamming distance between two pairs of words. 1. The Hamming distance d(000, 011) is2because 2. The HiHamming distance d(10101, 11110) is 3 because

  Distance, Hamming, Hamming distance

Tutorial: Checksum and CRC Data Integrity Techniques for ...

– Hamming Distance 2 (HD=2); some two-bit errors are undetected. 18 Fletcher Checksum • Use two running one’s complement checksums – For fair comparison, each running sum is half width – E.g., 16-bit Fletcher Checksum is two 8-bit running sums – Initialize: A = 0; B = 0;

  Distance, Hamming, Hamming distance

A Neural Probabilistic Language Model - Journal of Machine ...

objects are almost maximally far from each other in hamming distance. A useful way to visualize how different learning algorithms generalize, inspired from the view of ... 1. n-grams withn up to 5 (i.e. 4 words of context) have been reported, though, but due to data scarcity, most predictions

  Distance, Probabilistic, Hamming, Hamming distance

Metric Spaces - UiO

distance we get when we stop at a third pont z along the way, i.e. d(x,y) ≤ d(x,z)+d(z,x) It turns out that these conditions are the only ones we need, and we sum them up in a formal definition. Definition 1.1.1 A metric space (X,d) consists of a non-empty set X and a function d : …

  Distance

3F3 5 Design of FIR Filters - Vyssotski

10 (1+δ p) dB, or peak-to-peak passband ripple ≅ 20 log 10 (1+2δ p) dB; minimum stopband attenuation = -20 log 10 (δ s) dB. Example: δ p= 6% peak-to-peak passband ripple ≅ 20 log 10 (1+2δ p) = 1dB; δ s = 0.01 minimum stopband attenuation = -20 log 10 (δ s) = 40dB. The band-edge frequencies ω s and ω p are often called corner ...