The Undecidability of the Existence of Zeros of Real Elementary Functions

1974 ◽  
Vol 21 (4) ◽  
pp. 586-589 ◽  
Author(s):  
Paul S. Wang
Keyword(s):  
Elementary Functions ◽  
Existence Of Zeros

Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences

2020 ◽  
Vol 108 (5-6) ◽  
pp. 802-813
Author(s):  
Yu. N. Zakharyan ◽  
T. N. Fomenko
Keyword(s):  
Existence Of Zeros

scholarly journals Second-order integrable Lagrangians and WDVV equations

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue
Keyword(s):  
Lagrangian Density ◽  
Theta Functions ◽  
Second Order ◽  
Elementary Functions ◽  
Lagrange Equations ◽  
Wdvv Equations ◽  
Integrability Conditions ◽  
Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

Introduction to the Elementary Functions

1971 ◽  
Vol 55 (391) ◽  
pp. 103
Author(s):  
G. Merlane ◽  
R. A. Knight ◽  
W. E. Hoff
Keyword(s):  
Elementary Functions

Front instability in a condensed phase combustion model

2015 ◽  
Vol 4 (3) ◽  
pp. 153-176 ◽  
Author(s):  
Alexis Bonnet ◽  
Fathi Dkhil ◽  
Elisabeth Logak
Keyword(s):  
Activation Energy ◽  
Condensed Phase ◽  
Linear Instability ◽  
Combustion Model ◽  
Energy Limit ◽  
High Activation ◽  
Front Solution ◽  
High Activation Energy ◽  
Linearized Problem ◽  
Existence Of Zeros

AbstractWe consider a condensed phase (or solid) combustion model and its linearization around the travelling front solution. We construct an Evans function to characterize the eigenvalues of the linearized problem. We estimate this functional in the high activation energy limit. We deduce the existence of zeros with nonnegative real part for high activation energy, which proves the linear instability of the travelling front solution.

Highly accurate tables for elementary functions

1995 ◽  
Vol 35 (3) ◽  
pp. 352-360
Author(s):  
Wolfram Luther
Keyword(s):  
Elementary Functions
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