scholarly journals Applications of a general comparison theorem for convolution integrals

1983 ◽  
Vol 76 (3) ◽  
pp. 197-223
Author(s):  
Jürgen Löfström
Keyword(s):  
Comparison Theorem ◽  
Convolution Integrals

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.

scholarly journals A comparison theorem

1985 ◽  
Vol 106 (1) ◽  
pp. 188-195
Author(s):  
Walter Leighton
Keyword(s):  
Comparison Theorem

A systematic method for the analytical evaluation of convolution integrals

2002 ◽  
Vol 45 (1) ◽  
pp. 65-69 ◽  
Author(s):  
I.S. Goldberg ◽  
M.G. Block ◽  
R.E. Rojas
Keyword(s):  
Analytical Evaluation ◽  
Systematic Method ◽  
Convolution Integrals

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

scholarly journals Cohomological comparison theorem

2015 ◽  
Vol 219 (12) ◽  
pp. 5573-5589
Author(s):  
Edward L. Green ◽  
Dag Oskar Madsen ◽  
Eduardo Marcos
Keyword(s):  
Comparison Theorem

scholarly journals The twofold way of super holonomy

2016 ◽  
Vol 28 (6) ◽  
Author(s):  
Josua Groeger
Keyword(s):  
Comparison Theorem ◽  
Wilson Loops ◽  
Holonomy Algebra ◽  
Functorial Approach

AbstractThere are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops. Either theory comes with its own version of invariance of vectors and subspaces under holonomy. By our first main result, the Twofold Theorem, these definitions are equivalent. Our proof is based on the Comparison Theorem, our second main result, which characterises Galaev’s holonomy algebra as an algebra of coefficients, building on previous results. As an application, we generalise some of Galaev’s results to

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

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