continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

As demand for advanced photographic applications on hand-held devices grows, these electronics require the capture of high quality depth. However, under low-light conditions, most devices still suffer from low imaging quality and inaccurate depth acquisition. To address the problem, we present a robust depth estimation method from a short burst shot with varied intensity (i.e., Auto Bracketing)...

The prolongation of a transformation group to jet bundles forms the geometric foundation underlying Lie’s theory of symmetry groups of differential equations, the theory of differential invariants, and the Cartan theory of moving frames. Recent developments in the moving frame theory have necessitated a detailed understanding of the geometry of prolonged transformation groups. This paper begins...

Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation which corresponds to the transition from the Lagrangian formalism to the Hamiltonian formalism is non-trivial in this case. The resulting phase bundle, i.e. th...

At present, HRSI (High-resolution Satellite Imagery) is more and more widely applied for surveying, land, constructing, production and living field, and it becomes increasingly important to acquire orthophotograph by processing geometric rectification of satellite original images. Less or without GCPs (Ground Control Points) in several parts of area is a puzzled problem for remote sensing image...

A high-order spectral difference (SD) method has been further extended to solve the three dimensional compressible Navier–Stokes (N–S) equations on deformable dynamic meshes. In the SD method, the solution is approximated with piece-wise continuous polynomials. The elements are coupled with common Riemann fluxes at element interfaces. The extension to deformable elements necessitates a time-dep...

While we have previously reported on multiscale segmentation of single-figure anatomic objects from medical images by deformable m-rep models, here we report on a method of segmentation of multiple geometrically related single-figure objects from a medical image. Inter-object geometric effects within segmentation of structures in the male pelvis from CT in the planning of radiation therapy of t...

In this paper we provide an explicit construction of any arbitrary unitary transformation on n qubits from one qubit and a single two qubit quantum gate. Building on the previous work demonstrating the universality of two qubit quantum gates, we present here an explicit implementation. The construction is based on the Cartan decomposition of the semi-simple Lie group SU(2) and uses the geometri...

Introduction The biosynthesis process description belongs to the class of non-linear, non-stationary, complex systems. The implementation of optimisation methods as well as Pontryagin’s maximum principle-based method is problematic when a non-linear model is used. A differential geometric technique permits the utilisation of a new non-linear transformation of a biotechnological kinetic model in...

Most watermarking algorithms are either robust watermarking for copyright protection or fragile watermarking for tamper detection. This paper proposes a fragile video watermarking algorithm that has the ability to detect tamper in spatial domains. The original video frame is converted from RGB color space into YCbCr color space, then the chrominance component Cb is partitioned into non-overlapp...