L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Growth and characteristics of amorphous Sb2Se3 thin films of various thicknesses for memory switching applications

Thin films of different thicknesses in the range of 200-720 nm have been deposited on glass substrates at room temperature using thermal evaporation technique. The structural investigations revealed that the as-deposited films are amorphous in nature. The surface roughness of the films shows an increasing trend at higher thickness of the films. The surface roughness of the films shows an increasing trend at higher thickness of the films. Interference fringes in the transmission spectra of these films suggest that the films are fairly smooth and uniform. The optical absorption in Sb2Se3 film is described using indirect transition and the variation in band gaps is explained on the basis of defects and disorders in the chalcogenide systems. Raman spectrum confirms the increase of orderliness with film thickness. From the I-V characteristics, a memory type switching is observed whose threshold voltage increases with film thickness. (C) 2015 Elsevier B.V. All rights reserved.

Smooth Path Planning for Passages with Heading and Curvature Discontinuities

The problem of continuous curvature path planning for passages is considered. This problem arises when an autonomous vehicle traverses between prescribed boundaries such as corridors, tunnels, channels, etc. Passage boundaries with curvature and heading discontinuities pose challenges for generating smooth paths passing through them. Continuous curvature half-S shaped paths derived from the Four Parameter Logistic Curve family are proposed as a prospective path planning solution. Analytic conditions are derived for generating continuous curvature paths confined within the passage boundaries. Zero end curvature highlights the scalability of the proposed solution and its compatibility with other path planners in terms of larger path planning domains. Various scenarios with curvature and heading discontinuities are considered presenting viability of the proposed solution.