Non-vanishing Parameters Research Articles

Constrained [formula omitted]CDM dark energy models in higher derivative [formula omitted]-gravity theory

In the present paper, we have investigated dark energy scenarios in higher derivative f(R,Lm) gravity theory in a flat spacetime universe by constraining cosmographic series of Hubble function with Hubble constant H(z) datasets. We have considered an arbitrary function f(R,Lm)=γR2+λLmn, where R is the Ricci-scalar, Lm is matter Lagrangian, γ, λ and n are non-vanishing parameters. We have obtained contour plots of model parameters for the best fit values of (H0,q0,j0,s0,γ,λ,n,Ωm0) with 1−σ and 2−σ errors with H(z) datasets, and using these best fit model parameters, we have tried to explore the effective dark energy properties of the universe by defining the terms ρeff, peff and ωeff. We have found the values of effective equation of state parameter ωeff≈−0.96 at present and tends to cosmological constant value at late-time. We have found that the dark energy density term ρΛ∼Λ and it behaves just like time-dependent cosmological constant Λ-term. We have found a constrained ΛCDM transit phase expanding and currently accelerating dark energy model. Also, we have estimated the present age of the universe as t0=14.28 Gyrs.

Post-Newtonian limit of generalized scalar-torsion theories of gravity

In this article we derive the post-Newtonian limit of a class of teleparallel theories of gravity, where the action is a free function $L(T,X,Y,\phi)$ of the Torsion scalar $T$ and scalar quantities $X$ and $Y$ built from the dynamical scalar field $\phi$. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only non-vanishing parameters are $\gamma$ and $\beta$. For a particular choice of the function $L(T,X,Y,\phi)$ the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.

On the existence of a natural common gauge-origin for the calculation of magnetic properties of atoms and molecules via gaugeless basis sets

It is proven that, within the conventional approach using a common origin and gaugeless basis sets for the calculation of atomic magnetizability and Larmor current density induced by an external magnetic field, the natural gauge origin coincides with the nucleus. Recipes for defining an optimal gauge origin for the calculation of magnetizability and magnetic shielding at the nuclei of a molecule are given. Within the common origin approach, the paramagnetic contributions to the components of magnetic tensors of a molecule are represented by a minimum number of non-vanishing parameters if the gauge origin is chosen at a point characterized by the total molecular symmetry, e.g., the center of electronic charge for magnetizabilities. It is shown that total values of diagonal components of the magnetic shielding tensor σ(I) at a nucleus I in a molecule, as well as separate diamagnetic σ(dI) and paramagnetic σ(pI) contributions, calculated via the common origin method, are origin independent for a number of local point group symmetries. The diagonal components (and the average value) of σ(I) depend on the gauge origin only for nuclear site symmetries C(1), C(s), C(n), C(nv), n = 2, 3.... Group-theoretical methods show interesting features, e.g., for S(4) local symmetry, in a coordinate transformation, the paramagnetic contribution to the zz component and to the trace of the shielding tensor is origin independent, whereas the xx and yy components mix into one another, in such a way that their sum remains constant.

Surface operators in abelian gauge theory

We consider arbitrary embeddings of surface operators in a pure, non-supersymmetric abelian gauge theory on spin (non-spin) four-manifolds. For any surface operator with a priori simultaneously non-vanishing parameters, we explicitly show that the parameters transform naturally under an SL(2, Z) (or a congruence subgroup thereof) duality of the theory. However, for non-trivially-embedded surface operators, exact S-duality holds only if the quantum parameter effectively vanishes, while the overall SL(2, Z) (or a congruence subgroup thereof) duality holds up to a c-number at most, regardless. Via the formalism of duality walls, we furnish an alternative derivation of the transformation of parameters - found also to be consistent with a switch from Wilson to 't Hooft loop operators under S-duality. With any background embedding of surface operators, the partition function and the correlation functions of non-singular, gauge-invariant local operators on any curved four-manifold, are found to transform like modular forms under the respective duality groups.

Granger causality and path diagrams for multivariate time series

In this paper, we introduce path diagrams for multivariate time series which visualize the dynamic relationships among the variables. In these path diagrams, the vertices represent the components of the time series and are connected by arrows or lines according to the nonvanishing parameters in the autoregressive representation of the time series. We show that these path diagrams provide a framework for the analysis of the dependence structure of the time series. In particular, we give sufficient graphical conditions for Granger-noncausality and Granger-noncausality up to a certain horizon.

Symmetry properties of the effective hamiltonians of some nonrigid molecules

Group-theoretical methods are used to identify the nonvanishing parameters τ and establish relations between them in the effective Hamiltonians which describe rotation and motion with large amplitude. The cases considered are 1) bending vibration in molecules of the type XY2 and XYZ and 2) inversion vibration in pyramidal molecules of the type XY3. For the latter type of molecule, the symmetry properties of the parameters τ in the effective centrifugal Hamiltonian for quasidegenerate inversion states are investigated. The general form of this Hamiltonian and its symmetry properties are established and studied in an arbitrary order in the small parameter.

Deuteron Spin Alignment as a Test for Double-Scattering Contributions in the Glauber Theory

It is shown that in the single-scattering approximation to the Glauber theory of high-energy deuteron scattering there exists a relation between the two nonvanishing parameters describing the deuteron spin alignment. The failure of this relation can be used as a test for the expected importance of double-scattering terms at larger angles in elastic $\ensuremath{\pi}\ensuremath{-}d$ or $p\ensuremath{-}d$ scattering.