This document discusses the magnetic force on current-carrying conductors in several situations:
1) It explains Ampere's force law and how magnetic fields exert forces on currents. Magnetic fields inside and outside a current element are the same.
2) It shows examples of calculating the magnetic force on a finite wire, half-circle wire, and rectangular current loop using the right hand rule and Ampere's force law.
3) It discusses how no force is exerted between a straight wire passing through the center of a circular loop, both carrying current, due to the magnetic fields canceling out.
El documento habla sobre la tercera semana. En pocas palabras, el texto se refiere a eventos ocurridos durante la tercera semana de algún período de tiempo no especificado.
The document summarizes key concepts about solenoids and magnetic fields:
1) The magnetic field inside a solenoid is strong and uniform, while the field outside is weaker. The field lines inside a real solenoid of finite length are concentrated but more diffuse externally.
2) Magnetic fields are produced by electric currents. The field due to a current-carrying loop or solenoid can be calculated through integration.
3) Charged particles moving in a magnetic field experience a Lorentz force and exhibit circular or helical motion depending on their initial velocity relative to the field lines. This leads to phenomena like magnetic mirrors and focusing.
This document summarizes Faraday's law of induction and Lenz's law. It describes four key experiments conducted by Faraday that demonstrated induction of electric currents. The magnitude of the induced electromotive force (emf) in a loop is equal to the rate of change of the magnetic flux through the loop over time. Lenz's law states that the direction of the induced current will be such that its magnetic field opposes the original change in magnetic field that caused it.
This document discusses the magnetic force on current-carrying conductors in several situations:
1) It explains Ampere's force law and how magnetic fields exert forces on currents. Magnetic fields inside and outside a current element are the same.
2) It shows examples of calculating the magnetic force on a finite wire, half-circle wire, and rectangular current loop using the right hand rule and Ampere's force law.
3) It discusses how no force is exerted between a straight wire passing through the center of a circular loop, both carrying current, due to the magnetic fields canceling out.
El documento habla sobre la tercera semana. En pocas palabras, el texto se refiere a eventos ocurridos durante la tercera semana de algún período de tiempo no especificado.
The document summarizes key concepts about solenoids and magnetic fields:
1) The magnetic field inside a solenoid is strong and uniform, while the field outside is weaker. The field lines inside a real solenoid of finite length are concentrated but more diffuse externally.
2) Magnetic fields are produced by electric currents. The field due to a current-carrying loop or solenoid can be calculated through integration.
3) Charged particles moving in a magnetic field experience a Lorentz force and exhibit circular or helical motion depending on their initial velocity relative to the field lines. This leads to phenomena like magnetic mirrors and focusing.
This document summarizes Faraday's law of induction and Lenz's law. It describes four key experiments conducted by Faraday that demonstrated induction of electric currents. The magnitude of the induced electromotive force (emf) in a loop is equal to the rate of change of the magnetic flux through the loop over time. Lenz's law states that the direction of the induced current will be such that its magnetic field opposes the original change in magnetic field that caused it.
This document discusses Ampère's circuital theorem in electromagnetism. It begins by introducing Ampère and his circuital theorem, which states that the integral of magnetic field B around any closed path L is equal to the permeability times the total current enclosed by the path. It then provides examples of applying the right hand rule to determine the direction of the magnetic field from an enclosed current. Finally, it presents the theorem in differential form using Stokes' theorem, relating the integral of the magnetic field to the curl of the current density.
The document discusses various concepts in entity-relationship (E-R) modeling including: weak entity sets and how their primary keys are formed; reducing E-R diagrams to relational schemas; extended E-R features like specialization, generalization, and aggregation; and differences between E-R diagrams and UML class diagrams. Key symbols used in E-R notation are also summarized.
This document provides an overview of relational database design and normalization. It discusses the goals of database design as generating schemas without unnecessary redundancy and allowing easy data retrieval. Normalization aims to design schemas in a desirable normal form, such as Boyce-Codd normal form (BCNF) or third normal form (3NF). The document introduces key concepts like functional dependencies, normal forms, decomposition, and closure of functional dependencies, which are used to determine if a schema is properly normalized and how to decompose schemas if necessary.
This document provides an overview of relational database design concepts including normal forms and decomposition. It begins with an outline of topics to be covered such as algorithms for functional dependencies, decomposition using multi-valued dependencies, normal forms, and modeling temporal data. The document then reviews Boyce-Codd normal form and provides examples of testing for and decomposing relations into BCNF. It also introduces third normal form and covers testing for and decomposing relations into 3NF. Finally, it briefly discusses multi-valued dependencies and compares BCNF and 3NF.
This document provides an overview of resolution in propositional logic. It introduces resolution as a new rule of inference that allows inferring a resolvent clause from two clauses. It describes how to convert arbitrary well-formed formulas into conjunctions of clauses to use with resolution. Resolution refutations are discussed as a way to decide logical entailments by attempting to derive the empty clause. Various strategies for conducting resolution refutation searches more efficiently are also covered, including ordering strategies and refinement strategies. Finally, the document defines Horn clauses and their special properties that allow for linear-time deduction algorithms.
This document provides an overview of the Propositional Calculus. It discusses:
- The language of propositional calculus using atoms, connectives, and well-formed formulas
- Rules of inference like modus ponens, conjunction introduction, and disjunction introduction
- Defining proofs and theorems based on applying rules of inference
- Semantics by associating logical elements with truth values under interpretations
- Important concepts like validity, equivalence, entailment, and the soundness and completeness of rules of inference.
- The propositional satisfiability (PSAT) problem and solving techniques like exhaustive search and GSAT.
This document discusses adversarial search techniques for two-agent games with perfect information. It introduces the minimax procedure and how it recursively assigns values to nodes in a game tree by maximizing the value for the maximizing agent and minimizing for the minimizing agent. The alpha-beta pruning technique is described which improves search efficiency by pruning subtrees that cannot alter the minimax value of the root. Examples of applying minimax and alpha-beta to tic-tac-toe are provided. The document also discusses handling games of chance using expectimax search and learning effective evaluation functions from self-play.
This document discusses different approaches to solving constraint satisfaction problems including assignment problems. It provides examples of the eight queens problem and constraint propagation techniques. Constructive methods start with no assignments and add values satisfying constraints, while heuristic repair starts with a proposed solution and changes it to violate fewer constraints. Function optimization techniques like hill climbing and simulated annealing are also discussed.
The document discusses different methods for reinforcement learning, including learning heuristic functions from experiences, learning in explicit and implicit graphs, using rewards instead of goals for tasks, and different algorithms like temporal difference learning and value iteration that help agents learn optimal policies by assigning credit to relevant state-action pairs.
The document describes planning techniques in artificial intelligence, including STRIPS planning systems, forward and backward search methods, and partial-order planning. It discusses how STRIPS uses operators to describe state changes and searches for a sequence of actions to reach a goal state. Backward search methods work by regressing goals through operators to produce subgoals. Partial-order planning searches a plan space by transforming incomplete plans into more articulated plans until finding an executable plan.
This document provides an overview of the Situation Calculus, a formal logic framework for representing states, actions, and how actions transform states. It describes key components of the Situation Calculus including: (1) representing states as constants and using predicates to describe state properties, (2) representing actions and how they change state properties using effect axioms, (3) using frame axioms to represent properties that don't change with actions, and (4) generating plans by proving the existence of goal states and extracting the actions. Challenges with the approach include dealing with ramifications of actions and specifying all relevant preconditions and qualifications.
The document provides an overview of learning Bayes networks from data. It discusses learning the structure and conditional probability tables (CPTs) of a Bayes network given training data. When the network structure is known, the CPTs can be directly estimated from sample statistics in the training data, handling both cases of complete and missing data using techniques like expectation-maximization. When the structure is unknown, scoring metrics like minimum description length are used to search the space of possible structures to find the best fitting network. Dynamic decision networks extend this framework to model sequential decision making problems.
This document outlines probabilistic inference in Bayes networks. It begins with a review of probability theory concepts like joint probability, marginal probability, conditional probability, and Bayes' rule. It then discusses probabilistic inference in Bayes networks, including causal/top-down inference using evidence to determine probabilities, diagnostic/bottom-up inference using effects to determine causes, and "explaining away" where additional evidence makes other probabilities less certain. The document also covers uncertain evidence, D-separation to determine conditional independence, and inference techniques in polytrees.
This document discusses representing commonsense knowledge. It describes commonsense knowledge as everyday facts that most people understand, like objects falling when dropped or fish needing water. Representing all commonsense knowledge is difficult as there are no defined boundaries and some concepts cannot be described with sentences alone. The document outlines research areas in representing objects, materials, space, time, and physical processes. It also discusses knowledge representation using semantic networks and frames to organize taxonomic hierarchies and relationships between objects, properties, and categories in a graph structure. Nonmonotonic reasoning is also discussed for handling exceptions to default inferences.
Rule-based expert systems use facts and rules to achieve expert-level competence in solving problems. They consist of a knowledge base containing facts and rules, an inference engine that manipulates the knowledge base to deduce information, and an explanation subsystem. Rule-based systems apply logical rules to the known facts to determine unknown information. Inductive logic programming learns rules by generalizing from examples to cover positive instances while avoiding negative ones.
The document discusses knowledge-based systems and their ability to reason over extensive knowledge bases. It addresses the theoretical problems of soundness, completeness, and tractability when using logical reasoning systems. Horn clauses and PROLOG are introduced as more efficient ways to perform inference compared to full predicate calculus. Different methods for reasoning including forward chaining and truth and assumption-based maintenance are also summarized.
This document discusses resolution in predicate calculus. It covers topics like unification, predicate calculus resolution, converting well-formed formulas to clause form, using resolution to prove theorems, and answer extraction. It also discusses the equality predicate and paramodulation inference rule. The document provides examples to illustrate various concepts and techniques in resolution-based automated theorem proving in first-order logic.
This document provides an outline and overview of key concepts in resolution in predicate calculus, including:
- Unification, which allows resolving clauses that have matching but complementary literals
- Converting formulas to clause form by eliminating quantifiers and connectives
- Using resolution to prove theorems by deriving the empty clause
- The equality predicate and paramodulation, an inference rule used with resolution when equality is present
The document describes these concepts over multiple sections and provides examples to illustrate predicate calculus resolution.
The document discusses the predicate calculus and its use for representing knowledge. It introduces the motivation and basic components of the predicate calculus language, including terms, well-formed formulas, and quantifiers. It explains the semantics of the language including interpretations, models, and the semantics of quantifiers. Finally, it provides examples of how predicate calculus can be used to conceptualize and represent knowledge about the world.
This document discusses various heuristic search algorithms including A*, iterative-deepening A*, and recursive best-first search. It begins by introducing the concept of using evaluation functions to guide best-first search and preferentially expand nodes with lower heuristic values. It then presents the general graph search algorithm and describes how A* specifically reorders nodes using an evaluation function that considers path cost and estimated cost to the goal. Consistency conditions for the heuristic function are discussed which guarantee A* finds optimal solutions.
This document discusses uninformed search algorithms. It outlines breadth-first search, depth-first search, and iterative deepening search. Breadth-first search finds the shortest path but uses exponential memory. Depth-first search uses linear memory but may explore large parts of the search space without finding the goal. Iterative deepening search combines the benefits of depth-first search and guarantees of finding the shortest solution like breadth-first search.
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