We determine the mass dependence of the coupling constant for N=2 SYM with Nf = 1, 2, 3 and 4 flavours. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to modular functions which enables us to give explicit formulas for the periods. Using the form of the J–functions we are able to determine in an elegant way...

A rejection algorithm, called “transformed density rejection”, is presented. It uses a new method for constructing simple hat functions for a unimodal density f . It is based on the idea of transforming f with a suitable transformation T such that T (f(x)) is concave. The hat function is then constructed by taking the pointwise minimum of tangents which are transformed back to the original scal...

We consider the linearly constrained separable convex programming whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method (ADM) has been well studied in the literature for the special case m = 2. But the convergence of extending ADM to the general case m ≥ 3 is still open. In this paper, we show that the straightf...

We consider calculation of the dimensions of self-affine fractals and multifractals that are the attractors of iterated function systems specified in terms of upper triangular matrices. Using methods from linear algebra we obtain explicit formulae for the dimensions that are valid in many cases.

In this paper, we explore how to constructively manipulate qubits by rotating Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian controls can be constructed to steer qubits when two tunable Hamiltonian controls are available. It is demonstrated in this research that local-wave function controls such as Bang-Bang, triangle-function and quadratic function controls can ...

Based on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type fo...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, in this paper we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 7→ R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular ...

A newMatlab code for the generation of unstructured (3-node or 6-node) triangular meshes in two dimensions is described. The method is based on the Matlab mesh generator distmesh of Persson and Strang [SIAM Rev. 46:329-345, 2004]. As input, the code takes a signed distance function for the domain geometry. A mesh size function, for the spatial node distribution, is constructed using an approxim...

We present the result and accuracy comparison of generalized positivitypreserving schemes for triangular Bézier patches of 1 C and 2 C scattered data interpolants that have been constructed. We compare three methods of 1 C schemes using cubic triangular Bézier patches and one 2 C scheme using quintic triangular Bézier patches. Our test case consists of four sets of node/test function pairs, wit...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.