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

Introduction to Differential Equations01:20

Introduction to Differential Equations

220
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
220
Separable Differential Equations01:20

Separable Differential Equations

198
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
198
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

602
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
602
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1.1K
Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

171
An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
171
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

109
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
109

You might also read

Related Articles

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

Sort by
Same author

Model Validation Pipeline Against Longitudinal Alzheimer's Biomarker Data.

Neuroinformatics·2026
Same author

Analysing DCE-MRI scans using hybrid techniques for early detection of prostate cancer based on fusion features of handcrafted and deep learning features.

Journal of medical engineering & technology·2026
Same author

Grapevine disease detection using (q,τ)-nabla calculus quantum deformation with deep learning features.

MethodsX·2025
Same author

The social organization of the Asian weaver ant colonies: A natural enemy novel sub-castes worker's functional activity findings.

PloS one·2025
Same author

Analytic study and statistical enforcement of extended beta functions imposed by Mittag-Leffler and Hurwitz-Lerch Zeta functions.

MethodsX·2025
Same author

Retraction Note: Partial differential equations of entropy analysis on ternary hybridity nanofluid flow model via rotating disk with hall current and electromagnetic radiative influences.

Scientific reports·2025

Related Experiment Video

Updated: Mar 22, 2026

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

12.0K

Differential inequalities imposed by the extended hypergeometric function.

Rabha W Ibrahim1, M Z Ahmad2, Hiba F Al-Janaby2

  • 1Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia.

Springerplus
|April 12, 2016
PubMed
Summary
This summary is machine-generated.

Researchers extended the generalized hypergeometric function using the Beta function, creating a new operator. This operator is used to investigate subordination and superordination properties of analytic functions, generalizing previous findings.

Keywords:
Analytic functionHypergeometric functionIntegral operatorSubordinationSuperordinationUnit diskUnivalent function

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.5K

Related Experiment Videos

Last Updated: Mar 22, 2026

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

12.0K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.5K

Area of Science:

  • Complex Analysis
  • Analytic Number Theory

Background:

  • The generalized hypergeometric function is a fundamental object in mathematical analysis.
  • The Beta function plays a crucial role in various areas of mathematics and statistics.
  • Operators are essential tools for studying the properties of analytic functions.

Purpose of the Study:

  • To introduce a new operator based on the generalized hypergeometric function and the Beta function.
  • To investigate subordination and superordination properties of analytic functions under this new operator.
  • To generalize and improve existing results in the field.

Main Methods:

  • Extension of the generalized hypergeometric function using the Beta function.
  • Definition and application of a new integral operator in the open unit disk.
  • Utilizing subordination and superordination principles for analytic functions.

Main Results:

  • Established new subordination and superordination results for normalized analytic functions.
  • Demonstrated the effectiveness of the newly introduced generalized Noor integral operator.
  • Provided generalizations and improvements upon previously known outcomes in geometric function theory.

Conclusions:

  • The study successfully introduced a novel operator with significant implications for geometric function theory.
  • The findings contribute to a deeper understanding of subordination and superordination phenomena.
  • The results offer a foundation for future research in related areas of complex analysis.