Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Multimachine Stability01:25

Multimachine Stability

698
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.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
698
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

438
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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
438
Simplified Synchronous Machine Model01:30

Simplified Synchronous Machine Model

1.0K
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.
In this model, each generator is connected to a...
1.0K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

460
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
460
Optimization Problems01:26

Optimization Problems

220
Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...
220
Linearization and Approximation01:26

Linearization and Approximation

233
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
233

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

The Eco-Friendly Preparation of Se, Zn, and Ag MONPs and Their Current Medical Applications and Drug Delivery for AD Diseases.

TheScientificWorldJournal·2026
Same journal

Fear of COVID-19: A Comparative Study Among University Students in Peru.

TheScientificWorldJournal·2026
Same journal

Opportunities and Challenges of Integrating Ethiopian Traditional Medicine System Into Modern Medicine: A Narrative Review.

TheScientificWorldJournal·2026
Same journal

Exploring the Antiparasitic Activity of the Sea Cucumber Isostichopus sp. aff. badionotus From the Northern Coast of Colombia Against Trypanosoma cruzi.

TheScientificWorldJournal·2026
Same journal

Kalanchoe ceratophylla (Crassulaceae): The True Identity of Sidingin, a Medicinal Plant From Sumatra, Based on Morphological and Molecular Evidence.

TheScientificWorldJournal·2026
Same journal

Genetic Variation of Chicken Growth Differentiation Factor-9 Gene and Association With Egg Characteristics: A Systematic Review.

TheScientificWorldJournal·2026
See all related articles

Related Experiment Videos

Best possible approximation algorithms for single machine scheduling with increasing linear maintenance durations.

Xuefei Shi1, Dehua Xu1

  • 1School of Science, East China Institute of Technology, Nanchang, Jiangxi 330013, China.

Thescientificworldjournal
|April 5, 2014
PubMed
Summary
This summary is machine-generated.

Researchers developed the FFD-LS2I algorithm for single machine scheduling with linear maintenance durations. This algorithm achieves an optimal worst-case bound of 2, proving its efficiency for specific problem parameters.

Related Experiment Videos

Area of Science:

  • Operations Research
  • Computer Science
  • Algorithm Design

Background:

  • Single machine scheduling problems are crucial in optimizing production processes.
  • Maintenance activities significantly impact scheduling efficiency and machine availability.
  • Linear maintenance duration functions (f(t) = a+bt) are common in real-world scenarios.

Purpose of the Study:

  • To develop an efficient approximation algorithm for single machine scheduling with multiple linear maintenance activities.
  • To analyze the worst-case performance bound of the proposed algorithm.
  • To establish the theoretical limits of approximation algorithms for this scheduling problem.

Main Methods:

  • Proposing the FFD-LS2I approximation algorithm.
  • Analyzing the algorithm's worst-case performance bound.
  • Proving the NP-hardness of achieving a better approximation ratio for the problem.

Main Results:

  • The FFD-LS2I algorithm achieves a worst-case bound of 2.
  • It is demonstrated that no polynomial-time approximation algorithm can achieve a bound less than 2 for b ≥ 0 (unless P=NP).
  • The FFD-LS2I algorithm is optimal for b > 1, and the existing FFD-LS algorithm is optimal for b ≤ 1.

Conclusions:

  • The FFD-LS2I algorithm provides an optimal worst-case performance for single machine scheduling with linear maintenance durations when b > 1.
  • The established theoretical bound highlights the inherent complexity of the problem.
  • The findings guide the selection of the most efficient algorithm based on the maintenance duration parameter 'b'.