One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth’s subsurface into prismatic cells. We have developed a new method of solving this problem based on 3D Ca...

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission ...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element.

In this paper we take a refreshing look at a Cauchy–Schwarz type inner product inequalities. We also provide a Cauchy–Schwarz based proof and a refinement of Buzano’s inequality in inner product spaces. Some elementary applications such as trace inequalities for unitary matrices and discrete or integral inequalities are given. 2013 Elsevier Inc. All rights reserved.

The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three about inner product. main goal of this article is to present refinements Cauchy-Schwarz inequalities, a new proof refined version Kre\u{\i}n-type inequality. Applications that include Buzano-type for certain operators, operator norm numerical radius Hilbert space operators will be presented.

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...