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Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

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Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Binomial Expansion Using Pascal's Triangle01:30

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Expanding a binomial expression such as (a + b)n results in a predictable sequence of terms that can be systematically derived using Pascal’s Triangle. This triangular array of numbers plays a central role in understanding and computing the coefficients of binomial expansions.Pascal’s Triangle is constructed such that each row corresponds to the coefficients of a binomial raised to a power. The topmost row, known as the zeroth row, corresponds to (a + b)0, and each successive row...
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Related Experiment Video

Updated: Mar 16, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

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Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding.

Hong Lai1, Jun Zhang2, Ming-Xing Luo3

  • 1School of Computer and Information Science, Southwest University, Chongqing 400715, China.

Scientific Reports
|August 13, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a hybrid quantum secret sharing scheme using m-bonacci sequences and Lagrange polynomials. It offers eavesdropping detection and adaptable sharing for classical participants with lower bandwidth.

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Last Updated: Mar 16, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

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Area of Science:

  • Quantum Information Science
  • Cryptography
  • Computer Science

Background:

  • Secure communication is challenged by prevalent attacks.
  • Integrating quantum solutions with classical secret sharing requires low computational cost.
  • Existing quantum secret sharing schemes lack adaptability to dynamic changes.

Purpose of the Study:

  • To propose a novel hybrid threshold adaptable quantum secret sharing scheme.
  • To enable eavesdropping detection without joint quantum operations.
  • To allow secret sharing for a flexible number of participants with reduced bandwidth.

Main Methods:

  • Utilizing m-bonacci orbital angular momentum (OAM) pump for entangled states.
  • Employing Lagrange interpolation polynomials for share generation.
  • Implementing reverse Huffman-Fibonacci-tree coding for encoding.

Main Results:

  • The scheme effectively detects eavesdropping using m-bonacci sequences.
  • Secret shares are generated with Lagrange interpolation polynomials and Huffman-Fibonacci coding.
  • The scheme supports an arbitrary number of participants above a threshold.
  • Lower bandwidth requirements compared to existing schemes.

Conclusions:

  • The proposed scheme is robust against eavesdropping and adaptable to dynamic network changes.
  • It offers a practical solution for secure communication in real-world applications.
  • Demonstrates advantages in bandwidth efficiency and dynamic participant management.