We consider gravitational self interaction in the lowest approximation and assume that graviton interacts with gravitational energy-momentum tensor in the same way as it interacts with particles. We show that, using gravitational vertex with a preferred gravitational energy-momentum tensor, it is possible to obtain a metric necessary for explaining perihelion precession. The preferred gravitati...

In the period 1914–1922, a significant amount of work on logic was carried out in Göttingen. Beginning in 1914, Hilbert and his students, in particular Heinrich Behmann, were studying Whitehead and Russell’s Principia Mathematica, which resulted in Behmann’s dissertation (1918, see Mancosu 1999). In the Fall of 1917, Paul Bernays joined Hilbert in Göttingen and from then on worked as his assist...

The Isomorphism of Polynomials (IP) [28], which is the main concern of this paper, originally corresponds to the problem of recovering the secret key of a C∗ scheme [26]. Besides, the security of various other schemes (signature, authentication [28], traitor tracing [5], . . . ) also depends on the practical hardness of IP. Due to its numerous applications, the Isomorphism of Polynomials is thu...

Rapid Communications are intended for important new results which deserve accelerated publication, and are therefore given priority in editorial processing and production AR.apid Communication in Physical Review D should be no longer than jk~e printed pages and must be accompanied by an abstract Page .proofs are sent to authors, but because of the accelerated schedule, publication is generally ...

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...

We propose an algorithm for approximately solving the mixed packing and covering problem; given a convex compact set ∅ = B ⊆ RN , either compute x ∈ B such that f (x) ≤ (1 + )a and g(x) ≥ (1 − )b or decide that {x ∈ B | f (x) ≤ a, g(x) ≥ b} = ∅. Here f, g : B → RM + are vectors whose components are M non-negative convex and concave functions, respectively, and a, b ∈ RM ++ are constant positive...

In the Covering Steiner problem, we are given an undirected graph with edgecosts, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the required number of vertices from every group. The Covering Steiner problem is a common generalization of the k-M...