nonlinear differential equation sentence in Hindi
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- Later studies, also on the topic of nonlinear differential equations, were carried out by George David Birkhoff, Andrey Nikolaevich Kolmogorov, Mary Lucy Cartwright and John Edensor Littlewood, and Stephen Smale.
- "' Thomas Brooke Benjamin "', English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations.
- In May 1690 in a paper published in " Acta Eruditorum ", Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation.
- As the field generated by quasimodular forms of some level has transcendence degree 3 over "'C "', this implies that any quasimodular form satisfies some nonlinear differential equation of order 3.
- His research interests are concentrated in computer algebra, symbolic and algebraic computations, algebraic and numerical analysis of nonlinear differential equations, polynomial equations, applications to mathematics and physics, and quantum computation with over 210 published articles.
- In 2015 he was awarded the SIAM-ETH Henrici prize for 3 original, broad and fundamental contributions to the applied and numerical analysis of nonlinear differential equations and their applications in areas such as fluid dynamics, image processing and social dynamics ".
- In continuous time, when you've got a bunch of nonlinear differential equations strung together, and you model them using, say, RungeKutta45, how many dimensions can you keep adding before the computational rounding-error and noise will take over?
- In 2006 he received with Martin Kruskal, Robert M . Miura, and John M . Greene the Leroy P . Steele Prize for their work on the inverse scattering transformation method for the solution of nonlinear differential equations ( special soliton modeling equations similar to the Korteweg de Vries equation ).
- His dissertation " Qualitative Problems for Nonlinear Differential Equations of Accretive Type in Banach Spaces " included original results published in top-ranked journals ( " Atti della Accademia Nazionale dei Lincei, Journal of Differential Equations, Journal of Mathematical Analysis and Applications, Nonlinear Analysis, Numerical Functional Analysis and Optimization " ).
- When attempting to look for'good'nonlinear differential equations it is this property of linear equations that one would like to see : asking for no movable singularities is often too stringent, instead one often asks for the so-called Painlev?property :'any movable singularity should be a pole', first used by Sofia Kovalevskaya.
- With his Ph . D . thesis " " Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen " " ( Boundary-value problem methods for parameter estimation in systems of nonlinear differential equations ) completed under the supervision of Jens Frehse and Roland Z . Bulirsch, he received a Ph . D . in applied mathematics from the University of Bonn in 1986.
- He is best known for his work in chemical engineering and hydrodynamics including the approximate methods for solving nonlinear differential equations of mass, heat, and momentum transfer; mathematical modeling of chemical reactor processes and catalytic distillation; heat, mass, and momentum transfer in turbulent flow; fluid dynamics in granular beds; surface convection ( Marangoni instability ), absorption, and molecular convection.
- When he was exposed there to classical human and animal data about learning, the philosophical paradoxes that were implicit in these data triggered an intellectual inquiry that led him to introduce, during his freshman year, the modern paradigm of using nonlinear differential equations with which to describe neural networks that model brain dynamics, as well as the basic equations that many scientists use for this purpose today ( see Research ).
- To find the minimums a variational method is used, resulting in a set of nonlinear differential equations, called " Brown's equations " after William Fuller Brown Jr . Although in principle these equations can be solved for the stable domain configurations " "'M " "'( " "'X " "'), in practice only the simplest examples can be solved.
- Where \ textstyle a : = \ frac { k _ f } { k _ i } is the ratio of post-yield \ textstyle k _ f to pre-yield ( elastic ) \ textstyle k _ i : = \ frac { F _ y } { u _ y } stiffness, \ textstyle F _ y is the yield force, \ textstyle u _ y the yield displacement, and \ textstyle z ( t ) a non-observable hysteretic parameter ( usually called the " hysteretic displacement " ) that obeys the following nonlinear differential equation with zero initial condition ( \ textstyle z ( 0 ) = 0 ), and that has dimensions of length:
- In 1986, Kruskal and Zabusky shared the Howard N . Potts Gold Medal from the Franklin Institute " for contributions to mathematical physics and early creative combinations of analysis and computation, but most especially for seminal work in the properties of solitons . " In awarding the 2006 Steele Prize to Gardner, Greene, Kruskal, and Miura, the American Mathematical Society stated that before their work " there was no general theory for the exact solution of any important class of nonlinear differential equations . " The AMS added, " In applications of mathematics, solitons and their descendants ( kinks, anti-kinks, instantons, and breathers ) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences.
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