In this paper we continue our investigations. begun in the previous paper, of describing the solution sets of constrained extremum problems inf Au). l&l-‘(p) (*) where fand f are twice continuously differentiable functionals on a reflexive Banach space V, and r-‘(p) denotes the level set of the functional f with value p E R. Considering p as a parameter in (*) we obtain results concerning the c...

Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established: • There is a ball of local operations with shared randomness lying within the space spanned by the no-signalling operations and centred at the completely noisy channel. • The existence of the ball of local operations with shared randomness is emp...

This contribution gives a partial survey over the native spaces associated to (not necessarily radial) basis functions. Starting from reproducing kernel Hilbert spaces and invariance properties, the general construction of native spaces is carried out for both the unconditionally and the conditionally positive deenite case. The deenitions of the latter are based on nitely supported functionals ...

In the present investigation, the results of extensive benchmarking study of density functional theory (DFT) methods on some catalytically important metal dimers have been reported. The calculations were carried out on Al2, Ti2, V2, Cr2, Mn2, Fe2, Co2, Ni2, Cu2, and Zn2 using DFT functionals such as GGA, meta GGA, hybrid meta GGA along with recently developed Minnesota functionals. The bond len...

In this paper, the regularized estimation of the displacement vector field (DVF) of a dynamic image sequence is considered. A new class of non-quadratic convex regularization functionals is employed to estimate the motion field in the presence of motion discontinuities and occlusions. The derivation of the functionals is based on entropy considerations and do not require parameter tuning as in ...

We show that to every recursive total continuous functional Φ there is a representative Ψ of Φ in the hierearchy of partial continuous functionals such that Ψ is S1 − S9 computable over the hierarchy of partial continuous functionals. Equivalently, the representative Ψ will be PCF -definable over the partial continuous functionals, where PCF is Plotkin’s programming language for computable func...

HADWIGER INTEGRATION OF DEFINABLE FUNCTIONS Matthew L. Wright Robert Ghrist, Advisor This thesis defines and classifies valuations on definable functionals. The intrinsic volumes are valuations on “tame” subsets of R, and by easy extension, valuations on functionals on R with finitely many level sets, each a “tame” subset of R. We extend these valuations, which we call Hadwiger integrals, to de...

The current paper deals with the parametric modification of Bernstein operators which preserve constant and Korovkin?s other test functions in limit case. uniform convergence newly constructed is studied. Also, rate investigated by means modulus continuity, using belong to Lipschitz class help Peetre?s-K functionals. Finally, some numerical examples are given illustrate effectiveness defined fo...