Bio 5.2 makkelijk

Reguläre Ausdrücke (Regular Expressions)

• A regular expression (Regex or RE) constitutes a sequence of characters that specifies a set of matching strings according to a defined syntax.
• Text editors and utilities commonly use regular expressions for searching and manipulating text.
• Numerous programming languages offer support for regular expressions in string-based operations.

History

• Regular expressions originated from automata theory, the theory of formal languages, and Turing machine theory.
• These theories developed models to describe and analyze discrete systems.
• Stephen Kleene introduced the concept of regular languages in 1956.
• Regular expressions were first used by Ken Thompson in the QED text editor in the 1960s.
• In the 1970s, Thompson integrated regular expressions into the Unix editor ed, which later influenced their use in the grep search tool.
• Regular expressions have since been adopted in a wide array of programming languages, text editors, and other tools.

Basic Concepts

Literals

• The most basic regular expression is a literal character, such as a, which matches only the character a.

Metacharacters

• Metacharacters are special characters that carry specific meanings in regular expressions.
• Common metacharacters include:
  • . Matches any single character except a newline.
  • * Matches zero or more occurrences of the preceding character.
  • + Matches one or more occurrences of the preceding character.
  • ? Matches zero or one occurrence of the preceding character.
  • [] Defines a character class, matching any single character within the brackets.
  • () Defines a group, which can be referenced later.
  • ^ Matches the beginning of a line.
  • $ Matches the end of a line.
  • \ Escapes a metacharacter, treating it as a literal.

Character Classes

• A character class, enclosed in square brackets, represents a set of characters to match.
• [abc] matches a, b, or c.

Quantifiers

• Quantifiers specify the frequency of a preceding character or group within a string.
• Common quantifiers are:
  • * Matches zero or more occurrences.
  • + Matches one or more occurrences.
  • ? Matches zero or one occurrence.
  • {n} Matches exactly n occurrences.
  • {n,} Matches n or more occurrences.
  • {n,m} Matches between n and m occurrences.

Groups

• Groups, defined by parentheses, organize sections of a regular expression.
• (ab)+ groups the characters ab and matches one or more occurrences of ab.

Examples

• . Matches any single character except a newline.
• a* Matches zero or more occurrences of a.
• a+ Matches one or more occurrences of a.
• a? Matches zero or one occurrence of a.
• [abc] Matches a, b, or c.
• (abc) Matches abc.
• ^abc$ Matches a line that begins and ends with abc.

Applications in Computer Science

• Regular expressions serve many purposes in computer science:
  • Text Search: Used to find specific patterns within text bodies.
  • Text Replacement: Can replace text bodies with other strings.
  • Validation: Used to verify if a string adheres to a specific format.
  • Lexical Analysis: Can break down source code into tokens.

Tools

• Numerous tools support the use of regular expressions:
  • Text Editors: Many text editors support regular expressions for searching and replacing text.
  • Command-Line Tools: Command-line tools like grep, sed, and awk support regular expressions.
  • Programming Languages: Most programming languages provide regular expression support.

Advantages

• Powerful tool for text manipulation.
• Can perform complex tasks such as text search, replacement, and validation.
• Available in many text editors, command-line tools, and programming languages.

Disadvantages

• Can be difficult to learn and use effectively.
• Regular expressions can be hard to read and debug.
• Inefficient if not used carefully.

Física (Physics)

Vectores (Vectors)

Suma de Vectores (Vector Addition)

Método Analítico (Analytical Method)

• Vector components are calculated as follows:
  • $\qquad A_x = A \cos \theta$
  • $\qquad A_y = A \sin \theta$
• Example:
  • $\vec{A} = 25u \ 30^\circ$
  • $\vec{B} = 40u \ 130^\circ$
• Component calculation:
  • $\qquad A_x = (25u) \cos(30^\circ) = 21.65u$
  • $\qquad A_y = (25u) \sin(30^\circ) = 12.5u$
  • $\qquad B_x = (40u) \cos(130^\circ) = -25.71u$
  • $\qquad B_y = (40u) \sin(130^\circ) = 30.64u$
• Sum of components:
  • $\qquad R_x = A_x + B_x = 21.65u - 25.71u = -4.06u$
  • $\qquad R_y = A_y + B_y = 12.5u + 30.64u = 43.14u$
• Resultant vector (R):
  • $\qquad R = \sqrt{R_x^2 + R_y^2} = \sqrt{(-4.06u)^2 + (43.14u)^2} = 43.33u$
• Direction:
  • $\qquad \theta = \tan^{-1} \left( \frac{R_y}{R_x} \right) = \tan^{-1} \left( \frac{43.14u}{-4.06u} \right) = -84.63^\circ$
• Because $R_x$ is negative and $R_y$ is positive, the angle is in the second quadrant.
  • $\qquad \theta = -84.63^\circ + 180^\circ = 95.37^\circ$

Producto Escalar (Dot Product)

• $\qquad \vec{A} \cdot \vec{B} = |\vec{A}| \cdot |\vec{B}| \cos \theta$
• $\qquad \vec{A} \cdot \vec{B} = (A_x \cdot B_x) + (A_y \cdot B_y) + (A_z \cdot B_z)$
• Example:
  • $\vec{A} = 4\hat{i} - 3\hat{j}$
  • $\vec{B} = 6\hat{i} + 8\hat{j}$
• $\qquad \vec{A} \cdot \vec{B} = (4)(6) + (-3)(8) = 24 - 24 = 0$
• Because the dot product equals zero, the vectors are perpendicular.

Producto Vectorial (Cross Product)

• $\qquad \vec{A} \times \vec{B} = |\vec{A}| \cdot |\vec{B}| \sin \theta \hat{n}$
  • $\hat{n}$ is a unit vector perpendicular to the plane containing $\vec{A}$ and $\vec{B}$.
• $\qquad \vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ A_x & A_y & A_z \ B_x & B_y & B_z \end{vmatrix}$
• Example:
  • $\vec{A} = 4\hat{i} - 3\hat{j}$
  • $\vec{B} = 6\hat{i} + 8\hat{j}$
• $\qquad \vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 4 & -3 & 0 \ 6 & 8 & 0 \end{vmatrix} = \hat{i}(0 - 0) - \hat{j}(0 - 0) + \hat{k}(32 - (-18)) = 50\hat{k}$