We consider the second order Cauchy problem u +m(|Au|)Au = 0, u(0) = u0, u(0) = u1, where m : [0,+∞) → [0,+∞) is a continuous function, and A is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that u0 and u1 are regular enough, depending on the continuity modulus of m, and on the strict/weak hyp...

Ce sites may play an important role in defining active sites in ceria-based catalysis. Yet, though present at the catalyst surface, their positions have not been experimentally observed. Recently, it has been argued that Ce sites are the preferred location for the binding of Au− species on a highly reduced CeO2(111) surface with subsurface oxygen defects. Hence, Au atoms have been proposed as t...

Let F denote an algebraically closed field with characteristic 0 and let V denote a vector space over F with finite positive dimension. Let A,A denote a tridiagonal pair on V with diameter d. We say that A,A has Krawtchouk type whenever the sequence {d − 2i}i=0 is a standard ordering of the eigenvalues of A and a standard ordering of the eigenvalues of A. Assume A,A has Krawtchouk type. We show...

In this paper, we study the regularity of mild solution for the following fractional abstract Cauchy problem ( ) ( ) ( ), (0, ] t D u t Au t f t t T α = + ∈ (0) u = 0 x on a Banach space X with order (0,1) α ∈ , where the fractional derivative is understood in the sense of Caputo fractional derivatives. We show that if A generates an analytic α-times resolvent family on X and ([0, ]; ) p f L T ...

In this paper, one–dimensional (1D) wave equation with a general nonlinearity utt−uxx +mu+f(u)= 0, m > 0 under Dirichlet boundary conditions is considered; the nonlinearity f is a real analytic, odd function and f(u)= au+ ∑ k≥r̄+1 f2k+1u , a 6=0 and r̄∈N. It is proved that for almost all m > 0 in Lebesgue measure sense, the above equation admits smallamplitude quasi-periodic solutions correspondi...