Special Issue "Advances on Uncertainty Quantification: Theory and Modelling"
Deadline for manuscript submissions: 30 September 2020.
Interests: differential equations with randomness; mathematical modelling
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Interests: uncertainty quantification; mathematical epidemiology
Numerous physical, chemical, and biological phenomena, which are very important for scientistic and technological progress, have been traditionally formulated through mathematical models based on ordinary or partial differential equations, where the data (initial/boundary conditions, source term, and/or coefficients) are expressed by means of numerical values or deterministic functions. Nevertheless, scientists really fix these data from measurements, which are always subject to error. How satisfactory the results obtained from the model will be depends on the quality of these measurements (which can frequently take a lot of time and incur high costs). In addition to measurement errors, we must consider the random character of complex external factors that can affect the system, such as pressure, temperature, and humidity in Meteorology; the composition of the land in Seismology; investor tendency and economical policy of countries and companies in Finance; the environmental and genetical factors in Epidemiology; etc. These circumstances make it more advisable to consider the data as random magnitudes; if what is to be measured is a magnitude functionally independent of others values, it would be better to consider it as a random variable; when a dependency exists with respect to other magnitudes, such as time, space, etc., it would be more advisable to interpret it not as a function but as a stochastic process. The consideration of these facts leads to the reformulation of traditional deterministic models, which, in order to improve them, must be replaced by random models. Thus, this is the main purpose of this Special Issue: to gather contributions addressing new analytic and numerical methods and their applications to nontrivial problems to solve, simulate, and approximate random and stochastic equations in a wide sense (algebraic, difference, differential, integral, etc.). Applications of these equations in the settting of applications are particularly welcome.
Prof. Dr. Juan Carlos Cortés López
Prof. Dr. Rafael Villanueva Micó
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.
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- Random and stochastic equations (algebraic, difference, differential, integral, etc.)
- Random numerics
- Optimization under uncertainty techniques and modeling
- Parameters estimation techniques for random and stochastic equations
- Nonlinear systems with random excitation and perturbation and linearization techniques
- Control theory with randomness
- Spectral expansions for random and stochastic equations
- Random fields and applications
- Approximation of probability densities for random and stochastic equations
- Efficient simulation techniques for random and stochastic equations
- Models with uncertainty in biology, physics, chemistry, economics, and engineering