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This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. ... Using the so-called L prandom calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. ... square solution of the Bessel random 216 differential equation (1) on the interval 0 < r 1 ≤ t ≤ r 2 < ∞. 217 Remark 4. ...doi:10.1016/j.cam.2016.01.034 fatcat:wz7p72qdvvb75hkspspvnykhou
Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. ... Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties, Advances in Difference Equations, 2018:392, 1--29 (2018)] ... Conflict of Interest Statement The authors declare that there is no conflict of interests regarding the publication of this article. ...arXiv:1811.07887v1 fatcat:4cc4sqf2ezh67jajcef6h5ca44
Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. ... We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. ... Conflicts of Interest: The authors declare no conflict of interest. ...doi:10.3390/mca23040076 fatcat:bisk6mmb2zdtvkn6jbvniskxzu
For integers k and n (0<k <n) and complex parameters v = (vy Von), consider the system of partial differential equations, denoted by (4%), for a holomorphic function f(Z) of n? ... Many integral representations and two contour integrals of Bessel polynomials of two variables are established with the help of known results. ...
Physics Letters B
We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative ... Similarities and differences of these solutions are also discussed. ... Equation (20) is a fourth order linear differential equation whose solutions can be written in the form of exponential functions e rv where r is the root of equation 2βr 4 − 3r 2 + 27ν 2 = 0, where r ...doi:10.1016/j.physletb.2007.06.015 fatcat:fgmekaj5xrb5fhbdcodkuu7qcm
While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate that there is a family of such solutions, which are exact, by employing a ... Such quantum states and beams, in contrast to the Bessel ones, may have an azimuthal-angle-dependent probability density and finite quantum uncertainty of the OAM, which is determined by the packet's width ... However similar to a "pure Bessel" state with OAM, which is (see e.g., Refs. [13, 29] ) (17) solution (16) is non-normalizable in infinite volume since Airy functions are not square integrable. ...doi:10.1103/physreva.91.013847 fatcat:jsyf5hiexzf4jptwbsi23s3prq
For differential equations representing laws of physics such a choice limits realizations of random fields to physically possible solutions. ... differential equation. ... This study is a contribution to the Reduced Complexity Models grant number ZT-I-0010 funded by the Helmholtz Association of German Research Centers. ...arXiv:1909.03447v1 fatcat:66embfn6wnet3nfrfr3p5swggi
For differential equations representing laws of physics such a choice limits realizations of random fields to physically possible solutions. ... differential equation. ... This study is a contribution to the Reduced Complexity Models grant number ZT-I-0010 funded by the Helmholtz Association of German Research Centers. ...doi:10.3390/proceedings2019033005 fatcat:5tue43dwangs3biduwh274grcy
In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. ... We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. ... Computations were performed at Brown's TCASCV and NCSA's (University of Illinois) facilities. ...doi:10.1016/s0045-7825(02)00421-8 fatcat:zi3fo5fejbb2to67vqdehycg3q
We also study the effects of GUP in quantized models through approximate analytical solutions of the Wheeler-DeWitt (WD) equation, in the limit of small scale factor for the universe, and compare the results ... with the ordinary quantum cosmology in each case. ... Acknowledgement The author would like to thank the research council of Azad University of Chalous for financial support. ...doi:10.1142/s0218271809014935 fatcat:4fepgwb7q5drnb5e5u3kg2zdni
Furthermore, the analytical solution of the diffusion-like equation describes water saturation profiles, which are in qualitatively agreement with results reported in the literature. ... Spontaneous imbibition of water into oil-saturated porous chalk having a cylindrical shape with the top and bottom faces closed for fluid exchange was modeled by solving a diffusion-like equation with ... Variation and uncertainty in experimental parameters may allow for variations of the CDCs used in the calculation of oil recovery vs. time for each Table 3 The first forty zeros of the Bessel-function ...doi:10.1016/j.petrol.2005.10.008 fatcat:affflpa6wvgcfkxfwzbje2ksfq
In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X_0 and X_1. ... Appl., 61(9), 2782--2792 (2011)], a mean square convergent power series solution on (-1/e,1/e) was constructed, under the assumptions of mean fourth integrability of X_0 and X_1, independence, and at most ... Conflict of Interest Statement The authors declare that there is no conflict of interests regarding the publication of this article. ...arXiv:1807.03141v1 fatcat:ppa5cg45mrevld3hqiebpwrezu
The price is derived by means of repeated use of Green’s function, which, in turn, is derived from a series solution of the partial differential equation to value a discount bond. ... Pathwise equivalence to a rescale time-changed Bessel square process also is established. ...
In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X0 and X1. ... Appl., 61(9), 2782-2792 (2011)], a mean square convergent power series solution on (−1/e, 1/e) was constructed, under the assumptions of mean fourth integrability of X0 and X1, independence, and at most ... Conflict of Interest Statement The authors declare that there is no conflict of interests regarding the publication of this article. ...doi:10.1007/s00009-019-1338-6 fatcat:nsxmgzbtp5exfa5ij724poj5ey
low-pass filters are formed on the basis of Intrinsic Mode Function (IMF), de-noising effect of signal with noise is analyzed, and the evaluation indicators of dynamic uncertainty and approximation are ... structure impulse response, designs the measuring circuit based on charge sensor, conducts detailed theoretical deduction on dynamic model of sensor, charge-amplifier, filter and single conversion differential ... dynamic root-mean-square error or effective value of dynamic error. ...doi:10.1109/access.2019.2958387 fatcat:bcyirkz3pfb4flzmdw5kb6hyny
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