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BIBO stability of continuous and discrete -time systems01:24

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Continuing care describes the variety of health, personal, and social services provided over a prolonged period. The need for continuing care is increasing because people are living longer. Many people do not have families or others to care for them. Continuing care is mainly for patients who are disabled, functionally dependent, or suffering from a terminal disease. It is available within institutional settings or in homes. Examples include nursing centers or facilities, assisted living,...
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A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either...
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Continuous in Situ Extraction toward Multiphase Complex Systems Based on Superwettable Membrane with

Zhe Xu1,2, Zhongpeng Zhu1,2, Ning Li1

  • 1Key Laboratory of Bio-Inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry , Chinese Academy of Sciences , Beijing 100190 , P. R. China.

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Summary

This study introduces continuous in situ extraction using superwettable membranes. This novel method efficiently separates multiphase systems in real-time, offering a superior alternative to traditional extraction processes.

Keywords:
extraction chemistryhydrophobicitymicroporous membranemultiphase complex systemnanostructureoleophilicity

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Area of Science:

  • Chemical Engineering
  • Materials Science

Background:

  • Liquid-phase extraction is crucial in the chemical industry but often involves lengthy, multi-step processes.
  • Traditional methods require significant space and time, limiting efficiency.

Purpose of the Study:

  • To develop a continuous in situ extraction method for multiphase complex systems.
  • To leverage superwettable materials for simultaneous solute extraction and solvent separation.

Main Methods:

  • Utilized a porous polytetrafluoroethylene (PTFE) membrane with nanostructure-induced superwettability.
  • Achieved real-time separation of immiscible solvents based on wetting differences.

Main Results:

  • Demonstrated rapid, selective, and efficient real-time removal of extracting agents.
  • Showcased significant improvements in operating time, liquid recovery, and procedural simplicity.
  • Confirmed high extracting performance and excellent membrane durability in harsh conditions.

Conclusions:

  • The developed superwettable membrane facilitates continuous in situ extraction, offering a more efficient process.
  • This technology presents a potential alternative for industrial extractions, improving time, recovery, and simplicity.