Related papers: Laplace transformation updated
A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex…
Let $K$ be a number field, and let $K(x_1,...,x_d)$ be the field of rational fractions in the variables $x_1,...,x_d$. In this paper, we introduce two kinds of Laplace transform adapted to solutions of the differential…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Understanding the transition to turbulence has been impeded by a modeling oversight
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
The complete Lipschitz-Hankel integrals (LHIs) include the Laplace transforms of the Bessel functions, multiplied by powers. Such Laplace transforms can be evaluated using associated Legendre functions. It is noted that there are errors in…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
Let $\mathcal{L}\{f(t)\} = \int_{0}^{\infty}e^{-st}f(t)dt$ denote the Laplace transform of $f$. It is well-known that if $f(t)$ is a piecewise continuous function on the interval $t:[0,\infty)$ and of exponential order for $t > N$; then…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
The harmonic chain is a classical many-particle system which can be solved exactly for arbitrary number of particles (at least in simple cases, such as equal masses and spring constants). A nice feature of the harmonic chain is that the…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
The functional relation coming from the $x-y$ symplectic transformation of Topological Recursion has a lot of applications, for instance it is the higher order moment-cumulant relation in free probability or can be used to compute…
The author's method (math-ph/9804010) that uses the Laplace transform to find exact values for a large class of convergent series is extended to trigonometric series.
Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are…
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving…
After introducing the concept of null functions, we shall present a uniqueness result in the sense of the null functions for the Laplace transform on time scales with arbitrary graininess. The result can be regarded as a dynamic extension…
Some reasons are given to suggest that the interpretation of the Lorentz' transformations as if they referred to coordinates instead of to intervals could be incorrect. Besides, the usual form of such transformations, by using variables…
In this paper we examine the existence of bicomplexied inverse Laplacetransform as an extension of its complexied inverse version within theregion of convergence of bicomplex Laplace transform. In this course weuse the idempotent…