We undertake the construction of quadratic parity-violating terms involving curvature in four-dimensional metric-affine gravity. demonstrate that there are only 12 linearly independent scalars, plus an additional one can be removed by using Pontryagin invariant. Several convenient bases for this sector provided both components and differential form notation. also particularize our general findi...

In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. particular, discuss specific features spectrum and, finally, give further details associated quadratic form (and domain).

From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian Maxwell electrodynamics or the non-abelian Yang-Mills theory. On the other hand the quadratic law demands spacetime metric as its potential which is equivale...

Similarity join in distance spaces constrained by the metric postulates is the necessary complement of more famous similarity range and the nearest neighbor search primitives. However, the quadratic computational complexity of similarity joins prevents from applications on large data collections. We present the eD-Index, an extension of D-index, and we study an application of the eDIndex to imp...

We study large scale extended trust region subproblems (eTRS) i.e., the minimization of a general quadratic function subject to a norm constraint, known as the trust region subproblem (TRS) but with an additional linear inequality constraint. It is well known that strong duality holds for the TRS and that there are efficient algorithms for solving large scale TRS problems. It is also known that...

The paper contains a description of an efficient algorithm for linearly constrained nonlinear minimax approximation. This algorithm uses an elimination of constraints together with the product-form variable metric updates. The main advantage of the new algorithm consists in a simple determination of the direction vector. No quadratic programming subproblem has to be solved. The efficiency of th...

We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with non-polynomial interactions. The metric in the Einstein version is a highly nonlinear function of the metric in the quadratic version. Both massive excitations are ...

We consider the problem of placing n points, each one inside its own, prespecified disk, with the objective of maximizing the distance between the closest pair of them. The disks can overlap and have different sizes. The problem is NP-hard and does not admit a PTAS. In the L∞ metric, we give a 2-approximation algorithm running in O(n √ n log n) time. In the L2 metric, we give a quadratic time a...

One of the most classical and successful software testing strategies is that of testing boundary values in the input domain (Reid 1997). In this paper we introduce a notion of boundary values for a finite subset of a metric space. Boundary values are distinguished between nucleus (central elements) and perimeter ( peripheral elements). Nucleus (resp. perimeter) elements are those objects whose ...

We present a class of static supersymmetric multi-center black hole solutions arising in four-dimensional N = 2 supergravity theories with terms quadratic in the Weyl tensor. We also comment on possible corrections to the metric on the moduli space of these black holes solutions.