ARTICLE | doi:10.20944/preprints201711.0164.v2
Subject: Mathematics & Computer Science, Analysis Keywords: Fractional Calculus; Bessel-Struve Function; Fractional Kinetic Equations; Sumudu Transforms
Online: 27 November 2017 (05:23:54 CET)
In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.
ARTICLE | doi:10.20944/preprints202212.0264.v1
Subject: Physical Sciences, Optics Keywords: Bessel beams; paraxial equation; paraxial Bessel beams; scale propagation beams
Online: 15 December 2022 (04:09:28 CET)
We present a new family of Bessel solutions of the paraxial equation. Such solutions keep their form during propagation due to a quadratic phase factor that makes them scaled propagation invariant fields. The Bessel beams we introduce have the particularity that the topological phase is twice the order of the Bessel function and the argument varies quadratically with the radius
ARTICLE | doi:10.20944/preprints202207.0421.v1
Subject: Physical Sciences, Optics Keywords: Bessel beams; Speckles; Imaging; Holography; Incoherent optics
Online: 27 July 2022 (10:38:52 CEST)
Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as an unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging, holography and sensing technologies. In the recent years, artificial speckle patterns have been generated with spatially incoherent sources using static and dynamic optical modulators for advanced imaging applications. In this report, a fundamental study has been carried out with Bessel distribution as the fundamental building block of the speckle pattern: speckle patterns formed by randomly interfering Bessel beams. Indirect computational imaging framework has been applied to study the imaging characteristics. In general, Bessel beams have a long focal depth, which in this scenario is counteracted by the increase in randomness enabling tunability of the axial resolution between the limits of Bessel beam and a Gaussian beam. Three-dimensional computational imaging has been synthetically demonstrated. The presented study will lead to a new generation of incoherent imaging technologies.
ARTICLE | doi:10.20944/preprints202012.0673.v2
Subject: Engineering, Automotive Engineering Keywords: biofilm; Miller recurrent algorithm; Bessel functions; differential-difference master equations
Online: 1 March 2021 (13:13:47 CET)
A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.
ARTICLE | doi:10.20944/preprints201711.0076.v1
Subject: Mathematics & Computer Science, Analysis Keywords: fractional calculus; k-bessel function; fractional kinetic equations; laplace transforms
Online: 13 November 2017 (03:45:49 CET)
Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal . In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.
ARTICLE | doi:10.20944/preprints201801.0143.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: current-quark masses; Helmholtz equation; roots of Bessel and Neumann functions
Online: 16 January 2018 (13:20:36 CET)
Current-quark masses are compared to the rest masses allowed by the Helmholtz equation in a polar model. Within the uncertainty of the current u quark mass determination, the current quark mass coincides with the rest mass allowed by the Helmholtz equation in the polar model in accordance with the second root of the zero Neumann function. Current d quark mass coincides with the rest mass calculated in accordance with the third root of the Bessel zero function. On the basis of a comparison of these results with the results obtained earlier for ordinary real particles u and d quarks stability is discussed.
ARTICLE | doi:10.20944/preprints201703.0119.v1
Subject: Mathematics & Computer Science, Analysis Keywords: Lévy–Khintchine representation; integral representation; Bernstein function; Stieltjes function; Toader–Qi mean; weighted geometric mean; Bessel function of the first kind; probabilistic interpretation; probabilistic interpretation; application in engineering; inequality
Online: 16 March 2017 (11:31:31 CET)
In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.