Cubic function
View article: Інтерполяційні кубічні многочлени на сітках золотого перерізу для оптимізації і розв’язування нелінійних рівнянь однієї змінної
Інтерполяційні кубічні многочлени на сітках золотого перерізу для оптимізації і розв’язування нелінійних рівнянь однієї змінної Open
Interpolation cubic polynomials constructed on golden section grids possess unique properties that form the basis of an algorithm for the approximate solution of nonlinear equations and the search for extremal points of continuous single-v…
View article: Discovery of a Universal Cubic Pattern for "Hard" Numbers and Complete Solution of the Three-Cube Representations for 33, 42, 114, 390, 627, 633, 921 and 975
Discovery of a Universal Cubic Pattern for "Hard" Numbers and Complete Solution of the Three-Cube Representations for 33, 42, 114, 390, 627, 633, 921 and 975 Open
For the first time, a universal cubic pattern is discovered that allows all known “hard”numbers in the range 1–1000 to be expressed as the sum of three integer cubes using the sametwin pair with difference 1: x = −80 538 738 812 075 974 y …
View article: Discovery of a Universal Cubic Pattern for "Hard" Numbers and Complete Solution of the Three-Cube Representations for 33, 42, 114, 390, 627, 633, 921 and 975
Discovery of a Universal Cubic Pattern for "Hard" Numbers and Complete Solution of the Three-Cube Representations for 33, 42, 114, 390, 627, 633, 921 and 975 Open
For the first time, a universal cubic pattern is discovered that allows all known “hard”numbers in the range 1–1000 to be expressed as the sum of three integer cubes using the sametwin pair with di…
View article: Zeros of cubic polynomials in zeon algebra
Zeros of cubic polynomials in zeon algebra Open
It is well known that every cubic polynomial with complex coefficients has three not necessarily distinct complex zeros. In this paper, zeros of cubic polynomials over complex zeons are considered. In particular, a monic cubic polynomial w…
View article: Predictive Modeling of Thermo Physical Properties in Deep Eutectic Solvent Systems Using Jouyban–Acree and Mcallister Correlations
Predictive Modeling of Thermo Physical Properties in Deep Eutectic Solvent Systems Using Jouyban–Acree and Mcallister Correlations Open
The present study investigates the excess viscosity behavior of binary mixtures of 2-propenol and benzyl alcohol over the entire composition range at temperatures 298.15, 308.15, and 318.15 K. Experimental viscosity values were measu…
View article: Predictive Modeling of Thermo Physical Properties in Deep Eutectic Solvent Systems Using Jouyban–Acree and Mcallister Correlations
Predictive Modeling of Thermo Physical Properties in Deep Eutectic Solvent Systems Using Jouyban–Acree and Mcallister Correlations Open
The present study investigates the excess viscosity behavior of binary mixtures of 2-propenol and benzyl alcohol over the entire composition range at temperatures 298.15, 308.15, and 318.15 K. Experimental viscosity values were measured an…
View article: Characterization of Hyperbolic Cubic CNS Polynomials
Characterization of Hyperbolic Cubic CNS Polynomials Open
We characterize monic cubic CNS polynomials with only real roots in terms of relations between the other coefficients.
View article: On cubic Blaschke products
On cubic Blaschke products Open
We show that every cubic Blaschke product has a unique hyperbolic inflection point in the unit disk and, moreover, this point lies at the hyperbolic midpoint of the two critical points. Using this structure result for cubic Blaschke produc…
View article: On cubic Blaschke products
On cubic Blaschke products Open
We show that every cubic Blaschke product has a unique hyperbolic inflection point in the unit disk and, moreover, this point lies at the hyperbolic midpoint of the two critical points. Using this structure result for cubic Blaschke produc…
View article: Cubic residuacity of real quadratic integers
Cubic residuacity of real quadratic integers Open
Given a real quadratic integer $u=A+B\sqrt{D}$ with cubic norm, we identify all the classes in a related form class group that represent primes $p$ for which $u$ is a cubic residue mod $p$. A special case of this result was conjectured in …
View article: Cubic residuacity of real quadratic integers
Cubic residuacity of real quadratic integers Open
Given a real quadratic integer $u=A+B\sqrt{D}$ with cubic norm, we identify all the classes in a related form class group that represent primes $p$ for which $u$ is a cubic residue mod $p$. A special case of this result was conjectured in …
View article: Fundamentals of cubic skein modules
Fundamentals of cubic skein modules Open
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathematics and physics, including algebraic geometry, hyperboli…
View article: The Tricomplex Polynomial and Its Root Structure
The Tricomplex Polynomial and Its Root Structure Open
This paper develops a systematic theory of Tricomplex Polynomials and their roots. It is proved that a polynomial of degree 𝑛 in ℂ3 possesses 𝑛4 roots, generalizing the classical fundamental theorem of algebra. The study further identifies…
View article: Fundamentals of cubic skein modules
Fundamentals of cubic skein modules Open
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathematics and physics, including algebraic geometry, hyperboli…
View article: Cubic points on dynamical modular curves
Cubic points on dynamical modular curves Open
We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use this to prove a classification statement on preperiodic poin…
View article: Cubic points on dynamical modular curves
Cubic points on dynamical modular curves Open
We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use this to prove a classification statement on preperiodic poin…
View article: Approximation of piecewise smooth functions by nonuniform nonlinear quadratic and cubic spline quasi-interpolants
Approximation of piecewise smooth functions by nonuniform nonlinear quadratic and cubic spline quasi-interpolants Open
View article: Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field
Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field Open
A famous conjecture of Keating and Snaith asserts that central values of $L$-functions in a given family admit a log-normal distribution with a prescribed mean and variance depending on the symmetry type of the family. Based on a recent wo…
View article: Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field
Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field Open
A famous conjecture of Keating and Snaith asserts that central values of $L$-functions in a given family admit a log-normal distribution with a prescribed mean and variance depending on the symmetry type of the family. Based on a recent wo…
View article: Determination of the parameters of a variable speed pump by nonlinear regression
Determination of the parameters of a variable speed pump by nonlinear regression Open
Centrifugal pumps are widely used in water supply systems and account for more than 90% of the electricity consumption of water pumping stations. Studies that seek to generalize the characterization of performance curves of centrifugal pum…
View article: Application of Cubic B-Spline Functions in Galerkin Finite Element Method for SolvingSecond Order Sub-Diffusion Equation
Application of Cubic B-Spline Functions in Galerkin Finite Element Method for SolvingSecond Order Sub-Diffusion Equation Open
In this study, the Galerkin finite element method (FEM) is applied to find the numerical solutions of the second-order sub-diffusion equation. The proposed approach employs cubic B-spline functions as both the trial and test functions. The…
View article: Cubic Oscillator: Geometric Approach and Zeros of Eigenfunctions
Cubic Oscillator: Geometric Approach and Zeros of Eigenfunctions Open
In this paper, we give a geometric approach to the cubic oscillator with three distinct turning points based on the $\mathcal{D\diagup SG}$\emph{\ correspondence }introduced in \cite{Thabet+al}. The existence of quantization conditions, de…
View article: Cubic Oscillator: Geometric Approach and Zeros of Eigenfunctions
Cubic Oscillator: Geometric Approach and Zeros of Eigenfunctions Open
In this paper, we give a geometric approach to the cubic oscillator with three distinct turning points based on the $\mathcal{D\diagup SG}$\emph{\ correspondence }introduced in \cite{Thabet+al}. The existence of quantization conditions, de…
View article: Analysis of Cardano’s Formula to Solved Cubic Equation
Analysis of Cardano’s Formula to Solved Cubic Equation Open
Cubic equation in complex is equation with the form az3 + bz2 + cz + d = 0, . The equation has solution that is often referred to as the root of the equation. In the method commonly is used to find the root of the equation is usually obtai…
View article: Closed-form answer to the molar volume of cubic equation of state
Closed-form answer to the molar volume of cubic equation of state Open
View article: Global solutions for 1D cubic dispersive equations, part III: the quasilinear Schrödinger flow
Global solutions for 1D cubic dispersive equations, part III: the quasilinear Schrödinger flow Open
The first target of this article is the local well-posedness question for 1D quasilinear Schrödinger equations with cubic nonlinearities. The study of this class of problems, in all dimensions, was initiated in pioneering work of Kenig-Pon…
View article: On the cubic-quintic Schrödinger equation
On the cubic-quintic Schrödinger equation Open
This paper explores the cubic-quintic Schrödinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the extensivel…
View article: A Cubic Spline Numerical Method for a Singularly Perturbed Two-Parameter Ordinary Differential Equation
A Cubic Spline Numerical Method for a Singularly Perturbed Two-Parameter Ordinary Differential Equation Open
This paper presents a uniformly convergent cubic spline numerical method for a singularly perturbed two-perturbation parameter ordinary differential equation. The considered differential equation is discretized using the cubic spline numer…
View article: Evaluating Cubic Equations of State with Various α Functions for Viscosity Predictions of 124 Industrial Important Fluids Based on Residual Entropy Scaling
Evaluating Cubic Equations of State with Various α Functions for Viscosity Predictions of 124 Industrial Important Fluids Based on Residual Entropy Scaling Open
Accurate prediction of viscosity remains a challenge in industry due to the lack of reliable simple universal models. This work investigates the accuracy of four cubic equations of state (EOS) with different α functions for pure fluid visc…
View article: Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM Open