This paper proves sufficient conditions under which a completely separable order on non-convex sets can be represented by an additively separable function. The two major requirements are that indifference curves are connected and that intersections of the domain of the order with parallel-to-the-axes hyperplanes are connected. Jourrzal of Economic Literature Classification Numbers: 020, 022. c ...

We consider regularization of nonlinear ill-posed problems with constraints which are non-convex. As a special case we consider separable constraints, i.e. the regularization takes place in a sequence space and the constraint acts on each sequence element with a possibly non-convex function. We derive conditions under which such a constraint provides a regularization. Moreover, we derive estima...

This paper describes improved piecewise cubic convolution for two-dimensional image reconstruction. Piecewise cubic convolution is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a onedimensional derivation. The traditional approach is suboptimal for the usual case of non-separable scenes...

Using Toruńczyk’s charaterization theorem, we show that the space CB(X,Y ) of bounded continuous mappings from X into Y is a topological manifold modelled on the Hilbert space of weight 20 , with respect to the topology of uniform convergence, under the following three assumptions: (1) X is a noncompact, separable and metrizable space, (2) Y is a complete metric space which is an ANRU (ANR in u...

When a one-atom maser is operated in the standard way — excited, resonant two-level atoms traverse the resonator at random times — the emerging atoms are entangled with the cavity field. As a consequence, the results of measurements on different atoms tend to be correlated. We show that truly non-classical correlations can be found between two successive atoms by studying the properties of the ...

This paper considers the distributed optimization of a sum of locally observable, nonconvex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An asynchronous and distributed alternating directions method of multipliers (ADMM) method that allows the nodes to defer or skip the computation and transmissi...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

We study new separable orthogonally transitive abelian G2 on S2 models with two mutually orthogonal integrable Killing vector fields. For this purpose we consider separability of the metric functions in a coordinate system in which the velocity vector field of the perfect fluid does not take its canonical form, providing thereby solutions which are non-separable in comoving coordinates in gener...