We study the asymptotic behaviour of radially symmetric solutions of the nonlocal equation In a bounded spherically symmetric domain ft C R"f where A,(<) m 1 fftW(<p) «fcr, with a Neumann boundary condition. The analysis is based on "energy methods combined with some a-priori estimates, the latter being used to approximate the sohtion by the first two terms of an asymptotic expansionWe only nee...

For any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consist entirely of bounded elements. It is not too stringent, and is satisfied, for instance, by rings of ...

We consider in dimension four weakly convergent sequences of approximate biharmonic maps into sphere with bi-tension fields bounded in L for some p > 1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on R.

We present an approximate logarithmic multiplier with two-stage operand trimming, which prioritises area and energy consumption while retains acceptable accuracy. The trims the least significant parts of input operands in first stage mantissas obtained operands' approximations second stage. evaluated multiplier's efficiency terms error, energy, utilisation using NanGate 45nm. experimental resul...

In this paper, we consider various extension problems associated with elements in the the closure with respect to either the multiplier norm or the completely bounded multiplier norm of the Fourier algebra of a locally compact group. In particular, we show that it is not always possible to extend an element in the closure with respect to the multiplier norm of the Fourier algebra of the free gr...

Abstract In this paper we consider a problem, called convex projection, of projecting set onto subspace. We will show that to projection one can assign particular multi-objective optimization such the solution problem also solves (and vice versa), which is analogous result in polyhedral case considered Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016). practice, however, only comput...