'Scalar multiplication' diaporamas de présentation

PROGRAMME 5

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Coloured Petri Nets Modelling and Validation of Concurrent Systems

Syntax. CPN = (P, T, A, ? , V, C, G, E, I). Semantics. ++ ? E(p,t)<b> <<= M(p) for all p ? P (t,b) ? Y. MS. Chapter 4: Formal Definition of CP-nets. Coloured Petri Nets Modelling and Validation of Concurrent Systems. Kurt Jensen & Lars Michael Kristensen

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Section 7.4 Matrix Algebra

Section 7.4 Matrix Algebra.

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CS361

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Vectors

Vectors. Lesson 4.3. Terminal point. Initial point. What is a Vector?. A quantity that has both Size Direction Examples Wind Boat or aircraft travel Forces in physics Geometrically A directed line segment. Vector Notation. Given by Angle brackets <a, b> a vector with

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Divide-and-Conquer

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Simple Affine Extractors using Dimension Expansion .

Simple Affine Extractors using Dimension Expansion . Matt DeVos and Ariel Gabizon. Pseudorandomness. Vague Definition: A pseudorandom object(e.g. graph, function) has some nice property a random object would have with high probability . For example:

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TRIGONOMETRY

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CS361

Week 5 - Monday. CS361. Last time. What did we talk about last time? Trigonometry Transforms Affine transforms Rotation Scaling Shearing Concatenation of transforms. Questions?. Assignment 2. Project 2. Student Lecture: Normal Transforms and the Euler Transform . Normal transforms.

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Lesson 12.2

Lesson 12.2. Matrix Multiplication. Row and Column Order. The rows in a matrix are usually indexed 1 to m from top to bottom. The columns are usually indexed 1 to n from left to right. Elements are indexed by row, then column. Scalar Multiplication of Matrices.

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On the Efficient Generation of Elliptic Curves Over Prime Fields

CHES 2002, San Francisco. On the Efficient Generation of Elliptic Curves Over Prime Fields. E. Konstantinou, Y.C. Stamatiou,and C. Zaroliagis Department of Computer Engineering and Informatics, University of Patras, Greece & Computer Technology Institute, Patras, Greece. Elliptic Curves.

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Lesson 9-6

Lesson 9-6. Vectors . Transparency 9-6. 5-Minute Check on Lesson 9-5. Determine whether the dilation is an enlargement , a reduction or a congruence transformation based on the given scaling factor. r = ? 2. r = - 4 3. r = 1

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Orthogonal Functions and Fourier Series

Orthogonal Functions and Fourier Series. Vector Spaces. Set of vectors Closed under the following operations Vector addition: v 1 + v 2 = v 3 Scalar multiplication: s v 1 = v 2 Linear combinations: Scalars come from some field F e.g. real or complex numbers Linear independence

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CEE 451G ENVIRONMENTAL FLUID MECHANICS

CEE 451G ENVIRONMENTAL FLUID MECHANICS. LECTURE 1: SCALARS, VECTORS AND TENSORS. A scalar has magnitude but no direction. An example is pressure p. The coordinates x, y and z of Cartesian space are scalars. A vector has both magnitude and direction

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Vector Components

Vector Components. y. x. Coordinates. Vectors can be described in terms of coordinates. 6.0 km east and 3.4 km south 1 m forward, 2 m left, 2 m up Coordinates are associated with axes in a graph. x = 6.0 m. y = -3.4 m. Ordered Set.

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EXAMPLE 4

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Matrices and Determinants

An matrix is a rectangular array of numbers with m rows and n columns. is a matrix. . Matrices and Determinants. Matrices. Matrices and Determinants. Matrices.

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