Dirac–Kratzer problem with spin and pseudo-spin symmetries in curved space–time

In this work, the Dirac–Kratzer problem with spin and pseudo-spin symmetries in a deformed nucleus is analyzed. Thus, the Dirac equation in curved space–time was considered, with a line element given by [Formula: see text], where [Formula: see text] is a scalar potential, coupled to vector [Formula: see text] and tensor [Formula: see text] potentials. Defining the vector and scalar potentials of the Kratzer type and the tensor potential given by a term centrifugal-type term plus a term cubic singular at the origin, we obtain the Dirac spinor in a quasi-exact way and the eigenenergies numerically for the spin and pseudo-spin symmetries, so that these symmetries are removed due to the coupling of an Coulomb-type effective tensor potential coming from the curvature of space, however, when such potential is null the symmetries return. The probability densities were analyzed using graphs to compare the behavior of the system with and without spin and pseudo-spin symmetries.

The ground states and the first radially excited states of D-wave vector ρ and ϕ mesons

In this paper, we first derive two QCD sum rules QCDSR I and QCDSR II which are, respectively, used to extract observable quantities of the ground states and the first radially excited states of the D-wave vector [Formula: see text] and [Formula: see text] mesons. In our calculations, we consider the contributions of vacuum condensates up to dimension-7 in the operator product expansion. The predicted masses for [Formula: see text] [Formula: see text] meson and [Formula: see text] [Formula: see text] meson are consistent well with the experimental data of [Formula: see text]([Formula: see text]) and [Formula: see text]([Formula: see text]), respectively. Besides, our analysis indicates that it is reliable to assign the recent reported [Formula: see text]([Formula: see text]) state as the [Formula: see text] [Formula: see text] meson. Finally, we obtain the decay constants of these states with QCDSR I and QCDSR II. These predictions are helpful not only to reveal the structure of the newly observed [Formula: see text]([Formula: see text]) state, but also to establish [Formula: see text] meson and [Formula: see text] meson families.

The pseudo-null geometric phase along optical fiber

In this study, a pseudo-null space curve in Minkowski 3-space is used to describe an optical fiber that is injected into monochromatic linear polarized light. The direction of the electric field vector with respect to the Frenet frame of a pseudo-null curve determines the state polarization of a monochromatic linearly polarized light wave traveling along an optical fiber. For the Frenet frame of a pseudo-null curve in Minkowski 3-space, the polarization vector [Formula: see text] is assumed to be perpendicular to the tangent vector [Formula: see text] with respect to anholonomic coordinates. Anholonomic coordinates for the Frenet frame of a pseudo-null curve are used to describe pseudo-null electromagnetic curves in the normal and binormal directions along an optical fiber. For the Frenet frame of the pseudo-null curve, Lorentz force equations in the normal and binormal directions along the optical fiber are presented. Pseudo-normal and binormal Rytov parallel transport laws for electric fields in the normal and binormal directions along with the optical fiber for the Frenet frame of the pseudo-null curve via anholonomic coordinates are presented. For anholonomic coordinates in Minkowski 3-space, rotations of the polarization planes of a light wave traveling in the normal and binormal directions along with the optical fiber with respect to the Frenet frame of the pseudo-null curve are obtained. Finally, a pseudo-null curve’s Maxwellian evolution is determined.

What Graphs are 2-Dot Product Graphs?

Let [Formula: see text] be an integer. From a set of [Formula: see text]-dimensional vectors, we obtain a [Formula: see text]-dot by letting each vector [Formula: see text] correspond to a vertex [Formula: see text] and by adding an edge between two vertices [Formula: see text] and [Formula: see text] if and only if their dot product [Formula: see text], for some fixed, positive threshold [Formula: see text]. Dot product graphs can be used to model social networks. Recognizing a [Formula: see text]-dot product graph is known to be NP -hard for all fixed [Formula: see text]. To understand the position of [Formula: see text]-dot product graphs in the landscape of graph classes, we consider the case [Formula: see text], and investigate how [Formula: see text]-dot product graphs relate to a number of other known graph classes including a number of well-known classes of intersection graphs.

Using airborne vector magnetic data to calculate the projection of magnetic anomaly vector onto normal geomagnetic field

The total-field magnetic anomaly [Formula: see text] is an approximation of the projection [Formula: see text] of the magnetic anomaly vector [Formula: see text] onto the normal geomagnetic field [Formula: see text]. However, for highly magnetic sources, the approximation error of [Formula: see text] cannot be ignored. To reduce the error, we have developed a method for calculating [Formula: see text] by using airborne vector magnetic data based on the vector relationship of geomagnetic field [Formula: see text]. The calculation uses the magnitude of the vectors [Formula: see text], [Formula: see text], and [Formula: see text] through a simple approach. To ensure that each magnitude has the same level, we normalize the magnitude of [Formula: see text] using the total-field magnetic data measured by the scalar magnetic sensor. The method is applied to the measured airborne vector magnetic data at the Qixin area of the East Tianshan Mountains in China. The results indicate that the calculated [Formula: see text] has high precision and can distinguish the approximation error less than 3.5 nT. We also analyze the characteristics of the approximation error that are caused by the effects of different total magnetization inclinations. These error characteristics are used to predict the total magnetization inclination of a 2D magnetic source based on the measured airborne vector magnetic data.

CPT-violating z = 3 Horava–Lifshitz QED and generation of the Carroll–Field–Jackiw term

We study the new extension of the [Formula: see text] Horava–Lifshitz QED involving a CPT-breaking term, characterized by the axial vector [Formula: see text], and calculate the Carroll–Field–Jackiw (CFJ) term in the one-loop approximation. Explicitly, we use two regularization schemes and demonstrate that in our case, the CFJ term is finite but ambiguous, so that its exact coefficient depends on the used regularization.

A new sufficient condition for sparse vector recovery via ℓ1 − ℓ2 local minimization

In this paper, we provide a necessary condition and a sufficient condition such that any [Formula: see text]-sparse vector [Formula: see text] can be recovered from [Formula: see text] via [Formula: see text] local minimization. Moreover, we further verify that the sufficient condition is naturally valid when the restricted isometry constant of the measurement matrix [Formula: see text] satisfies [Formula: see text]. Compared with the existing [Formula: see text] local recoverability condition [Formula: see text], this result shows that [Formula: see text] local recoverability contains more measurement matrices.

A lower bound for the Hausdorff dimension of the set of weighted simultaneously approximable points over manifolds

Given a weight vector [Formula: see text] with each [Formula: see text] bounded by certain constraints, we obtain a lower bound for the Hausdorff dimension of the set [Formula: see text], where [Formula: see text] is a twice continuously differentiable manifold. From this we produce a lower bound for [Formula: see text] where [Formula: see text] is a general approximation function with certain limits. The proof is based on a technique developed by Beresnevich et al. in 2017, but we use an alternative mass transference style theorem proven by Wang, Wu and Xu (2015) to obtain our lower bound.

A note on discrete wave packet frames in ℂN

We show that for every nonzero vector [Formula: see text] in [Formula: see text], the discrete wave packet system [Formula: see text] constitutes a frame for the unitary space [Formula: see text]. An application of this result is given, where frame conditions cannot be derived from discrete wavelet systems in [Formula: see text]. The canonical dual of discrete wave packet frame is also discussed.

A New Solving Procedure for the Kelvin–Kirchhoff Equations in Case of a Falling Rotating Torus

We present a new solving procedure in this paper for Kelvin–Kirchhoff equations, considering the dynamics of a falling rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation for the rotating body, [Formula: see text]. The fundamental law of angular momentum conservation is used for the aforementioned solving procedure. The system of Euler equations for the dynamics of torus rotation is explored for an analytic way of presentation of the approximated solution (where we consider the case of laminar flow at slow regime of torus rotation). The second finding is that the Stokes boundary layer phenomenon on the boundaries of the torus also assumed additionally at the formulation of basic Kelvin–Kirchhoff equations (for which the analytical expressions for the components of fluid’s torque vector [Formula: see text] were obtained earlier). The results for calculating the components of angular velocity [Formula: see text] should then be used for full solving the momentum equation of Kelvin–Kirchhoff system. The trajectories of motion can be divided into, preferably, three classes: zigzagging, helical spiral motion, and the chaotic regime of oscillations.