Recently Published
On the Cardinality of the Set of Solutions to Congruence Equation Associated with Quintic Form Image
Conference paper

On the Cardinality of the Set of Solutions to Congruence Equation Associated with Quintic Form

The exponential sum associated with f is defined aswhere the sum is taken over a complete set of residues modulo q and let x = (x1, x2, ... , xn) be a vector in the space Zn with Z ring of integers and q be a positive integer, f a polynomial in x with coefficients in Z. The value of S(f; q)has been shown to depend on the estimate of the cardinality |jV|, the number of elements contained in the setwhere fx is the partial derivative of f with respect to x = (x1, x2, ..., xn). This paper will give an explicit estimate of |V| for polynomial f(x; y) in Zp[x; y] of degree five. Earlier authors have investigated similar polynomials of lowerdegrees. The polynomial that we consider in this paper is as follows:The approach is by using p-adic Newton Polyhedron technique associated with this polynomial.
Numerical Simulations of Indian Ocean Tsunami by Tuna\u002Dm2 Image
Conference paper

Numerical Simulations of Indian Ocean Tsunami by Tuna-m2

The Sumatra-Andaman earthquake of magnitude 9.3 on the Richter scale occurred on 26 December 2004. It triggered off a series of tsunami waves that caused tremendous damage to the properties and lives along the affected coastal areas. The earthquake was located where the India Plate dives under the Burma Plate, and was extremely large in geographical extent, beginning off the coast of Aceh and proceeding northwesterly over a period of about 100 seconds. An estimated fault length is about 800 km, with a fault width of about 85 km and an initial vertical displacement of 11 m. There were no tsunami warning systems in the Indian Ocean to detect tsunamis, nor to warn the general populace living around the ocean. Thus, there is a need for early warning systems to predict the characteristics of tsunami propagation, including tsunami wave heights and arrival times. There are three phases of tsunami evolution, which are generation, propagation and runup. Tsunami is generated by the disturbance associated with seismic activity, explosive volcanism, and submarine landslide phenomena. Propagation of tsunami waves transports seismic energy away from the earthquake source. During the deep ocean propagation stage, the wave height is small compared to the wavelength and the ocean depth. Therefore, the linear wave theory can be applied. Tsunami runup is the most destructive phase of tsunami evolution. The wave behavior at the shoreline depends on such characteristics as the relationships between wavelength and water depth and between the wavelength of the wave and its height. This paper will present the simulations of these tsunami propagations in the Indian Ocean and discuss wave height characteristics near the coast of Sri Lanka, Bangladesh and India to highlight tsunami hazards and coastal vulnerability. The need for an early warning system in the Indian Ocean would appear urgent. The simulation is performed by means of an in-house tsunami numerical simulation model TUNA-M2 that solves the shallow water equation by the staggered finite difference method.
Most Viewed