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

Convergence of Fourier Series01:21

Convergence of Fourier Series

128
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
128
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

1.5K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.5K
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

490
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
490
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

196
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
196
Region of Convergence01:17

Region of Convergence

385
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
385
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

348
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.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
348

You might also read

Related Articles

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

Sort by
Same author

Incidence and clinical outcomes of extended duration support in patients with Impella 5.5 - Analysis from the LOQI Registry.

JHLT open·2026
Same author

Rumor and counter-rumor dynamics in a stochastic delay-fractional framework: a GL-NSFD approach.

Scientific reports·2026
Same author

Reply: Importance of clinical context in choice of analytical method.

The Journal of thoracic and cardiovascular surgery·2026
Same author

Applications of Lucas sequences in convergence and signal processing.

Scientific reports·2026
Same author

Dynamic behavior of a stochastic epidemic model for skin sores: theoretical and computational perspectives.

Scientific reports·2026
Same author

Stability analysis of discrete delta fractional models under summation multipoint constraints for robust engineering systems.

Scientific reports·2026

Related Experiment Video

Updated: Jun 7, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K

Bessel statistical convergence: New concepts and applications in sequence theory.

Ibrahim S Ibrahim1, Majeed A Yousif1, Pshtiwan Othman Mohammed2

  • 1Department of Mathematics, College of Education, University of Zakho, Zakho, Iraq.

Plos One
|November 14, 2024
PubMed
Summary

This study introduces Bessel statistical convergence and related sequence concepts. These novel ideas extend approximation theorems, enhancing mathematical analysis with practical applications.

More Related Videos

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

21.7K

Related Experiment Videos

Last Updated: Jun 7, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

21.7K

Area of Science:

  • Mathematical Analysis
  • Sequence Theory

Background:

  • Existing sequence theories lack comprehensive frameworks for certain convergence behaviors.
  • Approximation theorems require updated methodologies for broader applicability.

Purpose of the Study:

  • Introduce novel concepts: Bessel convergence, Bessel boundedness, Bessel statistical convergence, and Bessel statistical Cauchy sequences.
  • Extend Korovkin-type approximation theorems using Bessel statistical convergence.
  • Demonstrate practical implications through established operators.

Main Methods:

  • Development of new definitions and inclusion relations in sequence theory.
  • Extension of classical Korovkin-type approximation theorems.
  • Application of theorems to Bernstein and Fejér convolution operators.

Main Results:

  • Established new inclusion relations and properties for Bessel statistical sequences.
  • Successfully extended the first and second Korovkin-type approximation theorems.
  • Demonstrated the utility of the extended theorems with concrete examples.

Conclusions:

  • The novel Bessel statistical convergence concepts provide a robust framework for sequence analysis.
  • Extended approximation theorems offer enhanced analytical capabilities.
  • Findings have potential applications in various scientific disciplines requiring sequence analysis.