Dušan D. Repovš is a Slovenian mathematician from Ljubljana, Slovenia.
In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates several values of the same function. For example, the logarithm functions are essentially characterized by the logarithmic functional equation
In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form:
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
George Adomian was an American mathematician of Armenian descent who developed the Adomian decomposition method (ADM) for solving nonlinear differential equations, both ordinary and partial. The method is explained, among other places, in his book Solving Frontier Problems in Physics: The Decomposition Method. He was a faculty member at the University of Georgia (UGA) from 1966 through 1989. While at UGA, he started the Center for Applied Mathematics. Adomian was also an aerospace engineer.
Yurii Oleksiyovych Mitropolskiy was a renowned Soviet and Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. He was born in Poltava Governorate and died in Kyiv.
Anatoly Mykhailovych Samoilenko was a Ukrainian mathematician, an Academician of the National Academy of Sciences of Ukraine, the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary differential equations (ODEs) having a finite dimensional state vector. Four points may give a possible explanation of the popularity of DDEs:
- Aftereffect is an applied problem: it is well known that, together with the increasing expectations of dynamic performances, engineers need their models to behave more like the real process. Many processes include aftereffect phenomena in their inner dynamics. In addition, actuators, sensors, and communication networks that are now involved in feedback control loops introduce such delays. Finally, besides actual delays, time lags are frequently used to simplify very high order models. Then, the interest for DDEs keeps on growing in all scientific areas and, especially, in control engineering.
- Delay systems are still resistant to many classical controllers: one could think that the simplest approach would consist in replacing them by some finite-dimensional approximations. Unfortunately, ignoring effects which are adequately represented by DDEs is not a general alternative: in the best situation, it leads to the same degree of complexity in the control design. In worst cases, it is potentially disastrous in terms of stability and oscillations.
- Voluntary introduction of delays can benefit the control system.
- In spite of their complexity, DDEs often appear as simple infinite-dimensional models in the very complex area of partial differential equations (PDEs).
Projected dynamical systems is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of optimization and equilibrium problems and the dynamical world of ordinary differential equations. A projected dynamical system is given by the flow to the projected differential equation
A set-valued function is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory.
In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form
Themistocles M. Rassias is a Greek mathematician, and a professor at the National Technical University of Athens, Greece. He has published more than 300 papers, 10 research books and 45 edited volumes in research Mathematics as well as 4 textbooks in Mathematics for university students. His research work has received more than 19,000 citations according to Google Scholar and more than 5,800 citations according to MathSciNet. His h-index is 49. He serves as a member of the Editorial Board of several international mathematical journals.
Endre Pap was born 26 February 1947 in Mali Iđoš in Vojvodina, Serbia, to a Hungarian family. B.Sc. 1970. M.Sc. 1973. Ph.D. 1975. Full Professor since 1986 at the Faculty of Sciences of the university in Novi Sad. Director of the Institute of Mathematics 1979–1980. He is now the Rector and a Full Professor of the Singidunum University in Belgrade. He was a president of Academy of Sciences and Arts of Vojvodina (VANU). He is now a corresponding member of European Academy of Sciences (EAS). He is a member from the outside of the Public Organ of the Hungarian Academy of Sciences, since 2000. He is an honorary professor at Budapest Tech University since 2005, and a professor at the Obuda University in Budapest. He obtained in 2003 the October prize of the city Novi Sad for his scientific work. He was a member of the Accreditation Commission for High Education of Serbia since 2006, the president of Council for Natural Sciences, and a member of the Senat of the University of Novi Sad since 2007. He has been a member of the National Council for High Education since 2015. He was a long-time professor at the Singidunum University, Belgrade, rector and now he is a professor emeritus at the Singidunum University, Belgrade.
The stability problem of functional equations originated from a question of Stanisław Ulam, posed in 1940, concerning the stability of group homomorphisms. In the next year, Donald H. Hyers gave a partial affirmative answer to the question of Ulam in the context of Banach spaces in the case of additive mappings, that was the first significant breakthrough and a step toward more solutions in this area. Since then, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyers's theorem. In 1978, Themistocles M. Rassias succeeded in extending Hyers's theorem for mappings between Banach spaces by considering an unbounded Cauchy difference subject to a continuity condition upon the mapping. He was the first to prove the stability of the linear mapping. This result of Rassias attracted several mathematicians worldwide who began to be stimulated to investigate the stability problems of functional equations.
Advances in Difference Equations is a peer-reviewed mathematics journal covering research on difference equations, published by Springer Open.
A functional differential equation is a differential equation with deviating argument. That is, a functional differential equation is an equation that contains a function and some of its derivatives evaluated at different argument values.
Isaac Elishakoff is a Distinguished Research Professor in the Ocean and Mechanical Engineering Department in the Florida Atlantic University, Boca Raton, Florida. He is a figure in the area of mechanics. He has made several contributions in the areas of random vibrations, solid mechanics of composite material, semi-inverse problems of vibrations and stability, functionally graded material structures, and nanotechnology.
Klaus Schmitt is an American mathematician doing research in nonlinear differential equations, and nonlinear analysis.
