Stability estimate for a partial data inverse problem for the convection-diffusion equation

<p style='text-indent:20px;'>In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension <inline-formula><tex-math id="M1">\begin{document}$ n\ge 2 $\end{document}</tex-math></inline-formula>, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.</p>

Dirac Field as a Source of the Inflation in2+1Dimensional Teleparallel Gravity

In this paper, we study early-time inflation and late-time acceleration of the universe by nonminimally coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with that of the3+1dimensional teleparallel gravity under Noether symmetry approach. And we see that the study explains early-time inflation and late-time acceleration of the universe.

Classification of static plane symmetric spacetime via Noether gauge symmetries

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions [Formula: see text], [Formula: see text] and [Formula: see text]. Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between [Formula: see text], [Formula: see text] and [Formula: see text]. For all cases, different forms of unknown functions of radial factor [Formula: see text] are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.

Noether gauge symmetry approach in Gauss–Bonnet dilatonic theory of gravity

The approach of Noether symmetries with gauge term in the Gauss–Bonnet dilatonic theory of gravity is used for different values of the state parameter, ω, of the background matter. It is found that for ω = –1 (dark energy Universe), ω = 0 (matter-dominated Universe), and ω = 1 (the case of stiff matter), for the existence of Noether gauge symmetries, the potential V([Formula: see text]) and the coupling of the Gauss–Bonnet term with gravity Λ([Formula: see text]) are obtained as exponential functions of the scalar field [Formula: see text]. For the case of arbitrary ω the coupling parameter Λ([Formula: see text]) is found as a linear function of the scalar field [Formula: see text] and the potential is a constant, for the existence of Noether gauge symmetries. Here it is observed that both the potential and coupling parameter depend on the evolutionary history of the Universe.

THE sp(3) BRST HAMILTONIAN FORMALISM FOR THE YANG–MILLS FIELDS

The paper presents in all its nontrivial details the sp(3) BRST Hamiltonian formalism. It is based on structuring the extended phase space on many levels. In this picture, the standard BRST symmetry appears as being only the first approximation of a generalized symmetry, acting as a horizontal (same level) operator. The gauge-fixing problem is completely solved by formulating a theorem and a general rule which allow the choice of a simple gauge term. As an example, the Hamiltonian sp(3) quantization of the Yang–Mills model is exhaustively presented.

THE MOST GENERAL AND RENORMALIZABLE MAXIMAL ABELIAN GAUGE

We construct the most general gauge fixing and the associated Faddeev–Popov ghost term for the SU(2) Yang–Mills theory, which leaves the global U(1) gauge symmetry intact (i.e. the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD.

Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher-Dimensional Space

We explain in a context different from that of Maraner the formalism for describing the motion of a particle, under the influence of a confining potential, in a neighborhood of an n-dimensional curved manifold Mn embedded in a p-dimensional Euclidean space Rp with p ≥ n + 2. The effective Hamiltonian on Mn has a (generally non-Abelian) gauge structure determined by the geometry of Mn. Such a gauge term is defined in terms of the vectors normal to Mn, and its connection is called the N connection. This connection is nothing but the connection induced from the normal connection of the submanifold Mn of Rp. In order to see the global effect of this type of connections, the case of M1 embedded in R3 is examined, where the relation of an integral of the gauge potential of the N connection (i.e. the torsion) along a path in M1 to the Berry phase is given through Gauss mapping of the vector tangent to M1. Through the same mapping in the case of M1 embedded in Rp, where the normal and the tangent quantities are exchanged, the relation of the N connection to the induced gauge potential (the canonical connection of the second kind) on the (p - 1)-dimensional sphere Sp - 1 (p ≥ 3) found by Ohnuki and Kitakado is concretely established; the former is the pullback of the latter by the Gauss mapping. Further, this latter which has the monopole-like structure is also proved to be gauge-equivalent to the spin connection of Sp - 1. Thus the N connection is also shown to coincide with the pullback of the spin connection of Sp - 1. Finally, by extending formally the fundamental equations for Mn to the infinite-dimensional case, the present formalism is applied to the field theory that admits a soliton solution. The resultant expression is in some respects different from that of Gervais and Jevicki.