Let N(5, D5, X) be the number of quintic number fields whose Galois closure has Galois group D5 and whose discriminant is bounded by X. By a conjecture of Malle, we expect that N(5, D5, X) ∼ C · X 1 2 for some constant C. The best known upper bound is N(5, D5, X) X 3 4, and we show this could be improved by counting points on a certain variety defined by a norm equation; computer calculations g...

A polynomial curve of degree 5, α, is a helix if and only if both ||α′|| and ||α′ ∧ α′′|| are polynomial functions.

A new noise generation algorithm called amortized noise generates smooth noise using dynamic programming techniques to amortize the cost of floating point multiplications over neighboring points. The amortized 2D noise algorithm uses a factor of 17/3 ≈ 5.67 fewer floating point multiplications than the 2D Perlin noise algorithm, resulting in a speedup by a factor of 3 in practice on current des...

In many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. Since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, GIS-based modeling approach was utilized to zoning PM2.5 dispersion over Tehran, du...

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...

In this paper a numerical method is proposed to approximate the solution of the nonlinear general Rosenau-RLW Equation. The method is based on collocation of quintic B-splines over finite elements so that we have continuity of the dependent variable and its first four derivatives throughout the solution range. We apply quintic B-splines for spatial variable and derivatives which produce a syste...

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

In this paper, a new method for gray-scale image and color zooming algorithm based on their local information is offered. In the proposed method, the unknown values of the new pixels on the image are computed by Moving Least Square (MLS) approximation based on both the quadratic spline and Gaussian-type weight functions. The numerical results showed that this method is more preferable to biline...