There has been increasing interest in investigating the possible parity violating features gravity theory and on cosmological scales. In this work, we consider a class of scalar-nonmetricity theory, which Lagrangian is polynomial built nonmetricity tensor scalar field. The coupled with field through its first order derivative. Besides monomials that are quadratic tensor, also construct cubic bo...

We present generic form of the covariant nonlocal action for infrared modifications of Einstein theory recently suggested within the weak-field curvature expansion. In the lowest order it is determined by two nonlocal operators — kernels of Ricci tensor and scalar quadratic forms. In models with a low strong-coupling scale this action also incorporates the strongly coupled mode which cannot be ...

We give a formula for the Lipschitz constant in Thompson’s part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This provides an explicit form of a characterization of Nussbaum concerning non order-preserving flows. As an application of this formula, we show that the flow of the generalized Riccati equation arising in stochast...

Saccade curvature is becoming a popular measure for detecting the presence of competing saccadic motor programs. Several different methods of quantifying saccade curvature have been employed. In the present study, we compared these metrics with each other and with novel measures based on curve fitting. Initial deviation metrics were only moderately associated with the more widely used metric of...

In bosonic closed string field theory the " tachyon potential " is a potential for the tachyon, the dilaton, and an infinite set of massive fields. Earlier computations of the potential did not include the dilaton and the critical point formed by the quadratic and cubic interactions was destroyed by the quartic tachyon term. We include the dilaton contributions to the potential and find that a ...

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algo...

In the study of nonlinear physical systems, one encounters apparently random or chaotic behavior, although the systems may be completely deterministic. Applying techniques from symbolic dynamics to maps of the interval, we compute two measures of chaotic behavior commonly employed in dynamical systems theory: the topological and metric entropies. For the quadratic logistic equation, we find tha...

Harmonic maps X:(S,h) --> N from a 2-manifold S with indefinite metric h to a semi-Riemannian manifold N are characterized, assuming that the induced metric I is nondegenerate. Except in one very special case, the characterizations involve a canonically determined holomorphic quadratic differential on a naturally chosen conformal structure. This is surprising because the Euler-Lagrange equation...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Abstract We construct a numerical relativity code based on the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation for gravitational quadratic f(R) Starobinsky model. By removing assumption that determinant of conformal 3-metric is unity, we first generalize BSSN general gravity theories in metric formalism to accommodate arbitrary coordinates time. then describe implementation this paradigma...