Abstract A forward modeling technique is developed for determining the characteristic features of observed MHD modes from line-of-sight data soft x-ray (SXR) diagnostics with 64 vertical lines-of-sight in theTokamak à Configuration Variable tokamak. Using excellent spatial resolution, this shown to evaluate poloidal mode numbers m , radial location and ballooning character modes. In first stage...

The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. This research was inspired by the analysis of Calabi–Yau manifolds that arise as smooth models of double covers of P branched along singular octic surfaces ([4, 3]). It is of considerable interest to determine the Hodge numbers for these manifolds, but t...

Numerical methods are not always convergent especially in higher velocities when shock waves are involved. A comparison analysis is performed to study the supersonic flow over conical bodies of three different cross sections circular, elliptic and squircle (square with rounded corners) shaped using  Perturbation techniques to find flow variables analytically. In order to find lift and drag forc...

Second solution: For any λ > 0, the map (x,y) 7→ (λx,λ−1y) preserves both areas and the hyperbola xy = 1. We may thus rescale the picture so that A,B are symmetric across the line y = x, with A above the line. As P moves from A to B, the area of APB increases until P passes through the point (1,1), then decreases. Consequently, P = (1,1) achieves the maximum area, and the desired equality is ob...

We consider N-soliton solutions of the KP equation, (−4ut + uxxx + 6uux)x + 3uyy = 0 . An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. The N-soliton solutions include all possible resonant interactions among those line solitons. We then classify those N-soliton solutions by defining a pair of N-numbers (n,n)...

Second solution: For any λ > 0, the map (x,y) 7→ (λx,λ−1y) preserves both areas and the hyperbola xy = 1. We may thus rescale the picture so that A,B are symmetric across the line y = x, with A above the line. As P moves from A to B, the area of APB increases until P passes through the point (1,1), then decreases. Consequently, P = (1,1) achieves the maximum area, and the desired equality is ob...

This paper contains a proof of the Manin conjecture for the singular del Pezzo surface X : x0x1 − x2 = x0x4 − x1x2 + x3 = 0, of degree four. In fact, if U ⊂ X is the open subset formed by deleting the unique line from X, and H is the usual height function on P(Q), then the height zeta function P x∈U(Q) H(x) −s is analytically continued to the half-plane 9/10. Mathematics Subject Classif...

ions We begin by listing the class abstractions involved in implementing the behavior of both the static and dynamic environments. Our abstractions (classes) include the following: Point, Line, Polygon, (graph) Node, Binary Search Tree, Priority Queue, and Undirected Graph. Both Binary Search Tree and Priority Queue are used for searching in the line intersection function. For the shortest path...