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Multimachine Stability01:25

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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
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Simplified Synchronous Machine Model01:30

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The Synchronous Machine Model is a fundamental tool in analyzing and ensuring the transient stability of power systems. This model simplifies the representation of a synchronous machine under balanced three-phase positive-sequence conditions, assuming constant excitation and ignoring losses and saturation. The model is pivotal for understanding the behavior of synchronous generators connected to a power grid, particularly during transient events.
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Positive reinforcement is a powerful method for teaching new behaviors to both animals and humans. B.F. Skinner demonstrated this with his experiments using rats in a Skinner box. When a rat pressed a lever, it received a food pellet. This immediate reward encouraged the rat to repeat the behavior. This method, where a reward follows every instance of the behavior, is known as continuous reinforcement. It is highly effective for establishing new behaviors quickly.
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Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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A heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. Different types of heuristics are used in different types of situations, and the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
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Related Experiment Video

Updated: Nov 8, 2025

The Joint Effect of Social Comparison and Social Distance on Evaluation of Intertemporal Choice Outcomes in Event-related Potential Studies
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The Joint Effect of Social Comparison and Social Distance on Evaluation of Intertemporal Choice Outcomes in Event-related Potential Studies

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Single machine resource allocation scheduling problems with deterioration effect and general positional effect.

Chunlai Liu1, Chuanhui Xiong2

  • 1Management School, Hangzhou Dianzi University, China.

Mathematical Biosciences and Engineering : MBE
|April 24, 2021
PubMed
Summary

This study introduces unified models for single machine scheduling problems with time-dependent processing times. The research demonstrates these models efficiently solve complex scheduling challenges, optimizing resource allocation and meeting deadlines.

Keywords:
deterioration effectmachine schedulingpositional effectresource allocation

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Area of Science:

  • Operations Research
  • Computer Science
  • Applied Mathematics

Background:

  • Traditional scheduling models often assume fixed processing times.
  • Real-world job processing times can vary based on start time, position, and resource availability.
  • Optimizing resource allocation is crucial for efficient scheduling.

Purpose of the Study:

  • To develop unified models for single machine scheduling problems with time-dependent processing times.
  • To analyze scheduling criteria alongside total weighted resource consumption.
  • To adapt models for various due window assignment considerations.

Main Methods:

  • Development of two unified mathematical models for scheduling.
  • Bicriteria analysis incorporating general scheduling criteria and resource consumption.
  • Exploration of two distinct approaches for handling dual criteria.

Main Results:

  • The proposed unified models effectively handle time-dependent processing times.
  • The models are applicable to scheduling problems with diverse due window assignments.
  • Both problem versions were proven to be solvable within polynomial time.

Conclusions:

  • The developed models offer a flexible and efficient approach to complex scheduling scenarios.
  • Polynomial-time solvability indicates practical applicability for large-scale problems.
  • This research advances the field of scheduling by integrating dynamic processing times and resource management.