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Numerical solution of random differential models
2011
Mathematical and computer modelling
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This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. Conditions for the mean square convergence of the proposed method are established. Finally, an illustrative example is included in which the main statistics properties such as the mean and the variance of the stochastic approximation solution process are given.
doi:10.1016/j.mcm.2010.12.037
fatcat:zk2pfyyme5hatovm2kklswl2em
Random differential operational calculus: Theory and applications
2010
Computers and Mathematics with Applications
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Note that 0 ≤ |E [X n Y m Z k W l − XYZW ]| = |E [X n Y m Z k W l − XYZW + XY m Z k W l − XY m Z k W l + XYZ k W l − XYZ k W l + XYZW l − XYZW l ]| = |E [(X n − X ) Y m Z k W l ] + E [X (Y m − Y ) Z k ...
W l ] + E [XY (Z k − Z ) W l ] + E [XYZ (W l − W )]| ≤ E [|(X n − X ) Y m Z k W l |] + E [|X (Y m − Y ) Z k W l |] + E [|XY (Z k − Z ) W l |] + E [|XYZ (W l − W )|] . (3.2) Applying twice the Schwarz inequality ...
doi:10.1016/j.camwa.2009.08.061
fatcat:prw3lc2m5rh7ldkdnon556wjui
Solving Riccati time-dependent models with random quadratic coefficients
2011
Applied Mathematics Letters
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As usual, in L p spaces, p-mean convergence is referred to as the corresponding p-norm; when p = 2, it is called m.s. convergence, for p = 4, m.f. convergence and so on. ...
Two important features related to L p spaces and p-mean convergence are that every p 2 -r.v. is a p 1 -r.v. and, p 2 -mean convergence entails p 1 -convergence, whenever p 2 > p 1 . ...
doi:10.1016/j.aml.2011.06.024
fatcat:p7gmylrw65g6di6cwb2fdnbrhy
A random differential transform method: Theory and applications
2012
Applied Mathematics Letters
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The space L 2 of all the 2-r.v.' ...
Like in L 2 , one introduces the concepts of 4-s.p. and mean fourth (m.f.) convergence in L 4 (see [4] ). ...
doi:10.1016/j.aml.2011.12.033
fatcat:yo5j6rutkvaqdknn7amfatgkli
Overwhelming hypercalcaemia in mandibular ameloblastoma
2014
BMJ Case Reports
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Diagnostic test
Normal values
Result
Interpretation
Complete blood count
WCC→4.5-11.0×10 9 /L
Haemoglobin→120-180 g/L
Platelet→150-450×10 9 /L
20.69
145
313
Leukocytosis→on-going infection ...
of malignancy
Serum magnesium
0.70-1.0 mmol/L
0.72
Normal
Serum phosphorus
0.81-1.49 mmol/L
0.53
Hypophosphataemia
Albumin
35-48 g/L
25
Hypoalbuminaemia→malnutrition from poor oral intake ...
doi:10.1136/bcr-2014-205491
pmid:25326561
pmcid:PMC4202038
fatcat:u7tomvvpnngnlhglqzjpycgnby
On the random gamma function: Theory and computing
2018
Journal of Computational and Applied Mathematics
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.; Villafuerte, L. (2018). On the random Gamma function: theory and computing. Journal of Computational and Applied Mathematics. 335:142-155. https://doi. ...
The study is based on the L p stochastic calculus with p = 2 and 4, usually referred to as mean square and mean fourth stochastic calculus, respectively. ...
In fact, for instance the following L 2 -operational basic property A ∈ L 2 , {X n : n ≥ 0} ⊂ L 2 : X n m.s. − −− → n→∞ X ∈ L 2 , ⇒ AX n m.s. − −− → n→∞ AX, (12) does not hold, in general, as ...
doi:10.1016/j.cam.2017.11.045
fatcat:enujzpcopzda3awltxiuvtqoqu
Mean square solution of Bessel differential equation with uncertainties
2017
Journal of Computational and Applied Mathematics
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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. ...
2 (t) ∈ L 8 (Ω) if X 0 ∈ L 16 (Ω). ...
Preliminaries on L p -random calculus
L q (Ω) ⊂ L p (Ω) for q > p ≥ 1, [16, p.13]. ...
doi:10.1016/j.cam.2016.01.034
fatcat:wz7p72qdvvb75hkspspvnykhou
Mean square numerical solution of random differential equations: Facts and possibilities
2007
Computers and Mathematics with Applications
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k+1 (1 + ha(t l )) cov[b(t i ), b(t k )]. ...
Let ω ∈ Ω be a fixed event, and let us consider the deterministic differential equation (H 1 ) f : S × T → L 2 , S ⊂ L 2 is a function of the 2-r.v. γ , continuous in both variables (X, t). ...
doi:10.1016/j.camwa.2006.05.030
fatcat:ziixx5t5pnf5hdrcntjykr5pa4
Random Airy type differential equations: Mean square exact and numerical solutions
2010
Computers and Mathematics with Applications
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One can demonstrate that L 2 endowed with the so-called 2-norm X 2 = E X 2 1/2 , (2) has a Banach space structure. ...
s {X n : n ≥ 0} is mean square (m.s.) convergent to X ∈ L 2 if lim n→∞ X n − X 2 = lim n→∞ E (X n − X ) 2 1/2 = 0. ...
doi:10.1016/j.camwa.2010.05.046
fatcat:vl7zy3wuhvc6ng4ph7w6p2evqy
Confocal Imaging Of Extracellular pH With Fluorescein Derivatives
2009
Biophysical Journal
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Villafuerte, Adrian L. Harris, Richard D. Vaughan-Jones. Oxford University, Oxford, United Kingdom. ...
doi:10.1016/j.bpj.2008.12.1481
fatcat:7nks7ngkpbaq7fq2he7zp4hzdy
A mean square chain rule and its applications in solving the random Chebyschev differential equation
[article]
2016
arXiv
pre-print
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Notice that (29) can equivalently be written in the following form (A 2 ) n 4 ≤ L × L n−1 , L = H 2 . Therefore, property (24) holds for κ = 0 and M = L > 0. ...
s in L 2 (Ω) that m.s. converges to the r.v. ...
arXiv:1612.08639v1
fatcat:am2wx7v23jg3vn4azvdk2cl2du
Marked Differences in the Splanchnometry of Farm-Bred and Wild Red-Legged Partridges (Alectoris rufa L.)
2001
Poultry Science
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Relative weights of heart, spleen, pancreas, and liver and the relative lengths of the small intestine and the cecum were taken from 40 farm-bred and 43 wild juvenile red-legged partridges (Alectoris rufa Linnaeus) in central Spain. Expressed as a ratio to head and body length, farm-bred partridges had lighter hearts (17% lighter), spleens (78%), and livers (29%) and shorter small intestines (15%) and cecae (20%), than wild birds of the (Key words: Alectoris rufa, gamebird-breeding, red-legged
doi:10.1093/ps/80.7.972
pmid:11469664
fatcat:dhddorjiqbdxbhc2xknt4b24ai
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... artridge, Spain, splanchnometry) 2001 Poultry Science 80:972-975
σ-Stabilization of a Flexible Joint Robotic Arm via Delayed Controllers
2019
Complexity
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zx _ x � L f h(x) + L g h(x) � x 2 + x 4 , (36) and computing the higher order derivative of h(x), € h(x) � L 2 f h(x), h (3) (x) � L 3 f h(x), h (4) (x) � L 4 f h(x) + VL g L 3 f h(x), (37) where L 2 ...
Now, let us define the state transformation z 1 � h(x), z 2 � _ h(x), z 3 � h (2) (x), and z 4 � h (3) (x), then it follows that _ z 1 � L f h(x), _ z 2 � L 2 f h(x), _ z 3 � L 3 f h(x), _ z 4 � L 4 ...
doi:10.1155/2019/7289689
fatcat:nb2sbvjgujft7chsjyiedjlbze
The Expanding Value Footprint of Oncology Treatments
2014
Value in Health
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all of whom provided helpful feedback on our interim analyses and earlier drafts of this report. • We also wish to thank Phill O'Neill for his contributions to the analysis of the IMS data; and to Lesley Cockroft for her review of the earlier draft. • We are grateful to IMS Health for allowing us access to the IMS database. Any errors in analysis remain the responsibility of the authors.
doi:10.1016/j.jval.2014.08.2386
pmid:27202367
fatcat:qcrd7cpcmbgd3f4m5o46sdracy
Using Network Density as a New Parameter to Estimate Distance
2008
Seventh International Conference on Networking (icn 2008)
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A wireless sensor network consists of a large quantity of small, low-cost sensor nodes that are limited in terms of memory, available energy and processing capacity. Generally, these sensor nodes are distributed in space to obtain physical parameters such as temperature, humidity, vibration or light conditions, and transmit the measured values to a central entity. The measurements are tagged with the corresponding location of the nodes in the network and the time of sampling, to enable a view
doi:10.1109/icn.2008.57
dblp:conf/icn/VillafuerteTS08
fatcat:ed2sfrhnlzho3keavcuy5cbbyy
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... the value distribution in space and time later on. Positioning of wireless sensor nodes without dedicated hardware is an open research question. Especially in the domain of embedded networked sensors, many applications rely on spatial information to relate collected data to the location of its origin. As a first step towards localization, an estimation of the distance between two nodes is often carried out to determine their positions. So far, the majority of approaches therefore explore physical properties of radio signals such as the strength of a received signal or its trip time. However, this is problematic since either the complexity on the software or on the hardware side is not adequate for embedded systems, or the approaches lack the required accuracy. In this paper we present the WDNI algorithm (Weighted Density of Node Intersection) to determine the distance between two nodes, relying solely on the investigation of local node densities. To evaluate the accuracy of this algorithm, we ran extensive simulations and experimented with different testbed setups using real sensor nodes, and finally compared WDNI to a range-free distance estimation algorithm based the analysis of RSSI values.
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