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

Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

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...
Introduction to Polynomial Functions01:26

Introduction to Polynomial Functions

Polynomial functions are fundamental elements in algebra and calculus, defined by expressions that combine variables and constants through addition, subtraction, and multiplication, with the variable raised to nonnegative integer exponents. A general polynomial function of degree n is given byWhere an ≠ 0. The term anxn is the leading term, and an is the leading coefficient, while a0 is referred to as the constant term.Characteristics and ClassificationPolynomials are categorized by their...
Long Division of Polynomials01:26

Long Division of Polynomials

Polynomial division is an essential algebraic process to simplify expressions and solve equations. Just as numerical division separates a number into quotient and remainder, polynomial long division partitions a polynomial into simpler components; in this context, the dividend is the polynomial being divided, the divisor is the expression dividing it, and the result is expressed in terms of a quotient and a remainder.The division begins by arranging the dividend and divisor in standard...
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the Complete Factorization...
Binomial Expansion Using Pascal's Triangle01:30

Binomial Expansion Using Pascal's Triangle

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 gives the...
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is of the form p/q​,...

You might also read

Related Articles

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

Sort by
Same author

Finding Needles in a Haystack: Determining Key Molecular Descriptors Associated with the Blood-brain Barrier Entry of Chemical Compounds Using Machine Learning.

Molecular informatics·2019
Same author

Cube-Related Corner Coalesced Nets.

Molecules (Basel, Switzerland)·2019
Same author

Spongy Nanostructures.

Journal of nanoscience and nanotechnology·2018
Same author

Binding Site and Potency Prediction of Teixobactin and other Lipid II Ligands by Statistical Base Scoring of Conformational Space Maps.

Current computer-aided drug design·2017
Same author

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors.

International journal of molecular sciences·2017
Same author

Molecular Dynamic Studies of the Complex Polyethylenimine and Glucose Oxidase.

International journal of molecular sciences·2016

Related Experiment Video

Updated: May 7, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

Counting Polynomials in Tori T(4,4)S[c,n].

Mircea V Diudea

    Acta Chimica Slovenica
    |September 25, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces counting polynomials to describe graph properties using number sequences. Formulas for vertex and edge proximity polynomials in T(4,4)[c,n] tori were derived using a cutting procedure.

    More Related Videos

    Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
    09:32

    Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

    Published on: April 12, 2019

    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

    Related Experiment Videos

    Last Updated: May 7, 2026

    Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
    06:35

    Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

    Published on: February 15, 2016

    Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
    09:32

    Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

    Published on: April 12, 2019

    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

    Area of Science:

    • Graph theory
    • Combinatorics
    • Algebraic graph theory

    Background:

    • Counting polynomials offer a method to encode graph properties through numerical sequences.
    • Understanding graph partitions and their counts is crucial in various mathematical fields.
    • Existing literature lacks specific formulas for proximity polynomials in toroidal graphs.

    Purpose of the Study:

    • To define and explore counting polynomials, specifically vertex proximity and edge proximity polynomials.
    • To derive formulas for these polynomials in the context of T(4,4)[c,n] toroidal graphs.
    • To establish a computational method for analyzing graph properties in these specific graph structures.

    Main Methods:

    • Definition of counting polynomials based on graph partitions and their extents.
    • Introduction of vertex proximity and edge proximity polynomials.
    • Application of a cutting procedure to derive formulas for T(4,4)[c,n] tori.

    Main Results:

    • Formulas for calculating vertex proximity polynomials in T(4,4)[c,n] tori were successfully derived.
    • Formulas for calculating edge proximity polynomials in T(4,4)[c,n] tori were successfully derived.
    • The cutting procedure proved effective for computing these polynomials in toroidal graphs.

    Conclusions:

    • The study successfully defined and calculated counting polynomials for graph properties in specific toroidal graphs.
    • The derived formulas provide a new tool for analyzing graph structures and their partitions.
    • This work contributes to the field of algebraic graph theory by extending the application of counting polynomials.