Weakly Hausdorff spaces and the cardinality of topological spaces
Weighted estimates for classical integral operators
Weighted estimates for classical operators
Weighted inequalities in Fourier analysis
Weighted norm inequalities for integral operators and related topics
Weights, one-sided operators, singular integrals and ergodic theorems
Weyl algebra and a realization of the unitary symmetry
In the paper the origins of the intrinsic unitary symmetry encountered in the study of bosonic systems with finite degrees of freedom and its relations with the Weyl algebra (1979, Jacobson) generated by the quantum canonical commutation relations are presented. An analytical representation of the Weyl algebra formulated in terms of partial differential operators with polynomial coefficients is studied in detail. As a basic example, the symmetry properties of the -dimensional quantum harmonic oscillator...
Why quintic polynomial equations are not solvable in radicals
We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations , and . Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.
Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations
A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a comprehensive...