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Topic review
Updated time: 01 Nov 2020
Definition: The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It was obtained a theoretical model of how oscillations patterns are originated and how time lengths have an important role over expenditures oscillations ergodicity and non-ergodicity.
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Topic review
Updated time: 26 Nov 2021
Submitted by: Praveen Agarwal
Definition: Many important functions in applied sciences are defined via improper integrals or series (or infinite products). Those functions are generally called special functions. Special functions contain a very old branch of mathematics. For example, trigonometric functions have been studied for over a thousand years, due mainly to their numerous applications in astronomy. Nonetheless, the origins of their unified and rather complete theory date back to the nineteenth century. From an application point of view, special functions such as important mathematical tools, due to their remarkable properties, are designated so based on their usefulness for the applied scientists and engineers—as Paul Tur´an once remarked, special functions would be more appropriately labeled useful functions. Various special functions, such as Bessel and all cylindrical functions; the Gauss, Kummer, confluent, and generalized hypergeometric functions; the classical orthogonal polynomials; the incomplete Gamma and Beta functions and error functions; the Airy, Whittaker functions; etc., will provide solutions to integer-order differential equations and systems, used as mathematical models. However, there has recently been an increasing interest in and widely extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena of physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Today, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to fractional-order (or multiorder) differential and integral equations.
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Topic review
Updated time: 21 Feb 2021
Submitted by: Diego Altafini
Definition: In mathematics, a homothetic behavior is characterized by a transformation of an affine space by a factor λ and results in an invariance of this space form or configuration, albeit its overall scale changes. In this sense, if two objects or parts of those objects have distinct sizes, but conserve the same appearance, they can be considered homothetic. In networks, the occurrence of homothetic behaviors would imply that a section of the network, when modelled independently, ought to retain a certain regularity in their distribution of centrality hierarchies (visual similitude) when compared to a larger section, independently modelled as well, that contains it. Hence, the smaller network maintains its overall proportions (configuration, hierarchies and values) across scales. This visual similitude was perceived while apposing several Normalized Angular Choice (NACH) models, a Space Syntax’ derivative from mathematical betweenness. Network homotheties, due to their invariability in form and value, can be used as an alternative to extensive network generalization for the construction of large spatial networks. Hence, data maps can be constructed sooner and more accurately as “pieces of a puzzle”, since each individual lesser scale graph possesses a faster processing time.
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Others
Updated time: 10 Dec 2020
Submitted by: Terry Moschandreou
Abstract: A closely related problem to The Clay Math Institute "Navier-Stokes, breakdown of smooth solutions here on an arbitrary cube subset of three dimensional space with periodic boundary conditions is examined. The incompressible Navier-Stokes Equations are presented in a new and conventionally different way here, by naturally reducing them to an operator form which is then further analyzed. It is shown that a reduction to a general 2D N-S system decoupled from a 1D non-linear partial differential equation is possible to obtain. This is executed using integration over n-dimensional compact intervals which allows decoupling. Here we extract the measure-zero points in the domain where singularities may occur and are left with a pde that exhibits finite time singularity. The operator form is considered in a physical geometric vorticity case, and a more general case. In the general case, the solution is revealed to have smooth solutions which exhibit finite-time blowup on a fine measure zero set and using the Gagliardo-Nirenberg inequalities it is shown that for any non zero measure set in the form of cube subset of 3D there is finite time blowup.
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Others
Updated time: 26 Sep 2021
Submitted by: Luna Shen
Abstract: Axioms (ISSN 2075-1680) is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. It's now indexed within SCIE (Web of Science), Scopus, dblp, and other databases.
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Biography
Updated time: 24 Sep 2020
Abstract: Mohammad Mehdi Rashidi is a professor of Mechanical Engineering, He works at Tongji University (Shanghai). He has published over 330 journal papers and 50 conference papers, his citations and h-index is 14550, 69 respectively. He is the editor of ten International Journals (ISI or Scopus indexed): Engineering Section Editor (managing 11 Associate editors) of Heliyon, (March 2019 – present). Editorial Advisory Board of International Journal of Numerical Methods for Heat & Fluid Flow (ISI, IF= 45) (May 2018 – present). Editorial Board Member of Neural Computing and Applications (ISI, IF= 4.213) (July 2017 – Nov 2018). Associate Editor of Journal of Thermal Analysis and Calorimetry (ISI, IF= 209) (Jan 2018 – present). Editorial Board of PLOS ONE (ISI, IF= 2.766) (Jan 2018 – present). Editorial Board of Heliyon (Elsevier) (March 2018 – present). Editorial Board Member of Tribology in Industry (ISI, IF= 1.32) (Sep 2017 – present). Honorary Editorial Advisory Board of Journal of Thermal Engineering (SCOPUS) (Sep 2014 – present). Editorial Board Member of Maejo International Journal of Science and Technology (ISI, IF= 0.312) (Sep 2015 – present). Deputy Section Editor of the Journal of Engineering (Web of Science), (Nov 2017 – Dec 2021).
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Biography
Updated time: 10 Nov 2020
Submitted by: Nikolay K Vitanov
Abstract: Short biography of Prof. Nikolay K. Vitanov, specialist in Applied Mathematics from Bulgaria.
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Videos
Updated time: 08 Nov 2021
Videos
Updated time: 29 Oct 2021
Others
Updated time: 06 Dec 2020
Submitted by: Gustave Udahemuka
Abstract: Detection of an active wildfire in a satellite image scene relies on an accurate estimation of the background temperature of the scene, which must be compared to the observed temperature, to decide on the presence of fire.The expected background temperature of a pixel is commonly derived based on spatial-contextual information. Multi-temporal information and multi-spectral information have also been exploited in estimation of the background temperature of a pixel. This review discusses different approaches of estimation of background temperature and highlights the potentiality of the estimation of the background temperature using the multi-temporal data for early fire detection and real-time fire monitoring. The perspectives of a proposed multi-temporal approach are also outlined.
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