Discontinuous solutions of neutral functional differential equations

The fundamental theory of existence, uniqueness and continuous differentiability of Lp-solutions for Neutral Functional Differential Equations is presented. Also, the spectrum of the solution operator of general autonomous linear NFDEs is described. Finally, an extension of Hartman Grobman Theorem on local conjugacy near a hyperbolic equilibrium is proved

Discontinuous solutions of neutral functional differential equations

The fundamental theory of existence, uniqueness and continuous differentiability of Lp-solutions for Neutral Functional Differential Equations is presented. Also, the spectrum of the solution operator of general autonomous linear NFDEs is described. Finally, an extension of Hartman Grobman Theorem on local conjugacy near a hyperbolic equilibrium is proved

Alfred Russel Wallace: Self-educated genius and polymath

Alfred Russel Wallace was a Colossus: courageous, heroic, radical, modest, and above all, a man of insatiable curiosity. One hundred years on one can propose that his prescience anticipated many modern scientific developments and that despite relative neglect his far-ranging insight continues to inspire even now. His earliest memories take us to Usk in South Wales, where he was born in 1823, and many experiences there are fondly recounted as formative influences. Adolescent interest in natural history during apprenticeship to his elder brother, a land-surveyor at the dawn of the railway era in Mid Wales and the Neath valley, blossomed into a lifelong fascination with the living world. The depth and reach of his thinking on the diversity and distribution of species outpaced his contemporaries, and he became the undisputed father of biogeography. Interaction with the ‘poor farmers’ of South Wales and exposure to their humble conditions inculcated a concern for the deprivation of the underclasses, and were influential in the shaping of his societal concerns and later activism. After proposing the basic principles of speciation and of selection and arriving at a novel and original concept of evolutionary mechanisms, Wallace daringly pursued several non-scientific interests: phrenology, mesmerism, spiritualism, and the great question of whether we are alone in the cosmos. Honoured late in a long life, Wallace became regarded as one of the greatest scientists in the world, despite his enthusiasms for supernatural phenomena. Eclipsed after his passing in 1913, a gradual realisation of the depth of his mainstream science as well as premature dismissal of some of his more arcane insights continues beyond his centenary year