Inertial manifolds for nonautonomous dynamical systems and for nonautonomous evolution equations
A limit set trichotomy for order-preserving systems on time scales.
-smoothness of invariant fiber bundles for dynamic equations on measure chains.
Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations
In this paper we summarize an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.
New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations
In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682. We describe the analysis of the proposed methods along with numerical experiments including comparison...
Maxwell’s equations revisited – mental imagery and mathematical symbols
Using Maxwell’s mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations , , , , which together with the constituting relations , , form what we call today Maxwell’s equations. Main tools are the divergence, curl and gradient integration theorems and a version of Poincare’s lemma formulated in vector calculus notation. Remarks on the history of the development of electrodynamic theory, quotations and references to original and secondary literature complement...
Page 1