the simple method for height determination is spirit leveling. the leveled height differences are path-dependent. ergo height from spirit leveling is not unique. the problem can be solved by converting the path-dependent leveled height differences into unique path-independent height differences (vanicek and krakiwsky, 1986). the difference between the potentials of two close equipotential surfa...

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the earth’s surface. downward continuation is a...

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

precise geoid determination on islands suffers from the lack of accurate gravity data on the open seas. nowadays, sub-microgal accuracy for the land gravity observations is obtainable. but the sea gravity data which are collected via shipborne techniques, due to the measuring environment at sea area, are usually highly noisy and are contaminated with various systematic errors. on the other hand...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.