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Mean square solution of Bessel differential equation with uncertainties

2017
*
Journal of Computational and Applied Mathematics
*

This paper deals

doi:10.1016/j.cam.2016.01.034
fatcat:wz7p72qdvvb75hkspspvnykhou
*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. ...##
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Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling
[article]

2018
*
arXiv
*
pre-print

Another novelty is that we tackle the non-homogeneous

arXiv:1811.07887v1
fatcat:4cc4sqf2ezh67jajcef6h5ca44
*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. ...##
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Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling

2018
*
Mathematical and Computational Applications
*

Another novelty is that we tackle the non-homogeneous

doi:10.3390/mca23040076
fatcat:bisk6mmb2zdtvkn6jbvniskxzu
*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. ...##
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Page 232 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

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. ...##
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Generalized uncertainty principle in Bianchi type I quantum cosmology

2007
*
Physics Letters B
*

We present approximate analytical

doi:10.1016/j.physletb.2007.06.015
fatcat:fgmekaj5xrb5fhbdcodkuu7qcm
*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 ...##
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Gaussian and Airy wave packets of massive particles with orbital angular momentum

2015
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

While wave-packet

doi:10.1103/physreva.91.013847
fatcat:jsyf5hiexzf4jptwbsi23s3prq
*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. ...##
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Gaussian processes for data fulfilling linear differential equations

2019
*
arXiv
*
pre-print

For

arXiv:1909.03447v1
fatcat:66embfn6wnet3nfrfr3p5swggi
*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. ...##
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Gaussian Processes for Data Fulfilling Linear Differential Equations

2019
*
Proceedings (MDPI)
*

For

doi:10.3390/proceedings2019033005
fatcat:5tue43dwangs3biduwh274grcy
*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. ...##
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Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

2002
*
Computer Methods in Applied Mechanics and Engineering
*

In particular, we focus on the

doi:10.1016/s0045-7825(02)00421-8
fatcat:zi3fo5fejbb2to67vqdehycg3q
*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. ...##
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COSMOLOGY WITH MINIMAL LENGTH UNCERTAINTY RELATIONS

2009
*
International Journal of Modern Physics D
*

We also study the effects

doi:10.1142/s0218271809014935
fatcat:4fepgwb7q5drnb5e5u3kg2zdni
*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. ...##
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Spontaneous imbibition of water into cylindrical cores with high aspect ratio: Numerical and experimental results

2006
*
Journal of Petroleum Science and Engineering
*

Furthermore, the analytical

doi:10.1016/j.petrol.2005.10.008
fatcat:affflpa6wvgcfkxfwzbje2ksfq
*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 ...##
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Improving the approximation of the first and second order statistics of the response process to the random Legendre differential equation
[article]

2018
*
arXiv
*
pre-print

In this paper, we deal

arXiv:1807.03141v1
fatcat:ppa5cg45mrevld3hqiebpwrezu
*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. ...##
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Page 7145 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

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. ...##
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Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation

2019
*
Mediterranean Journal of Mathematics
*

In this paper, we deal

doi:10.1007/s00009-019-1338-6
fatcat:nsxmgzbtp5exfa5ij724poj5ey
*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. ...##
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Signal Measurement of Projectile Penetration Overload Based on Charge Sensor

2019
*
IEEE Access
*

low-pass filters are formed on the basis

doi:10.1109/access.2019.2958387
fatcat:bcyirkz3pfb4flzmdw5kb6hyny
*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. ...
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