A new branch of inflationary speed limits

We present a new mechanism for inflation which exhibits a speed limit on scalar motion, generating accelerated expansion even on a steep potential. This arises from explicitly integrating out the short modes of additional fields coupled to the inflaton ϕ via a dimension six operator, yielding an expression for the effective action which includes a nontrivial (logarithmic) function of (∂ϕ)2. The speed limit appears at the branch cut of this logarithm arising in a large flavor expansion, similarly to the square root branch cut in DBI inflation arising in a large color expansion. Finally, we describe observational constraints on the parameters of this model.

Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind

We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second kind by using a limit representation. For the 18 hypergeometric arguments which correspond to these representations, we give geometrical descriptions of the corresponding convergence regions in the complex plane. In addition, we consider a corresponding single sum Fourier expansion for the Ferrers function of the second kind. In four of the eighteen cases, the determination of the Ferrers function of the second kind requires the evaluation of the hypergeometric function separately above and below the branch cut at [1,infty). In order to complete these derivations, we use well-known results to derive expressions for the hypergeometric function above and below its branch cut. Finally we give a detailed review of the 1888 paper by Richard Olbricht who was the first to study hypergeometric representations of Legendre functions.

Hybrid Technique of the Branch-Cut and the Quality-Guided for Insar Phase Unwrapping

Phase unwrapping is a key step for interferometric synthetic aperture radar imaging. It is widely used for earth mapping and surface change detection. Several residue-immune phase unwrapping algorithms have been proposed; among them, we find branch-cut and quality-guided in the path-following category. Branch-cut methods are usually faster than the quality-guided techniques; however, the accuracy of their unwrapped phase images is lower. In this paper, a hybrid model which combines both algorithms is proposed in order to establish a satisfactory compromise between processing time and accuracy. In order to verify the usefulness of the proposed hybridization, it is tested on simulated and real inSAR data. The obtained results are compared with the two methods under several relevant metrics.