‎Artificial neural networks have the advantages such as learning, ‎adaptation‎, ‎fault-tolerance‎, ‎parallelism and generalization‎. ‎This ‎paper is a scrutiny on the application of diverse learning methods‎ ‎in speed of convergence in neural networks‎. ‎For this aim‎, ‎first we ‎introduce a perceptron method based on artificial neural networks‎ ‎which has been applied for solving a non-singula...

This article is concerned with the defect indices of singular symmetric linear difference equations of order 2n with complex coefficients and one singular endpoint. We first show that the positive and negative defect indices d+ and dof a class of singular symmetric linear difference equations of order 2n with complex coefficients satisfy the inequalities n ≤ d+ = d≤ 2n and all values of this ra...

This paper proposes a cross-associative neural network (CANN) for singular value decomposition (SVD) of a non-squared data matrix in signal processing, in order to improve the convergence speed and avoid the potential instability of the deterministic networks associated with the cross-correlation neural-network models. We study the global asymptotic stability of the network for tracking all the...

Dynamic Bayesian Networks (DBNs) have been proposed [16] as an efficient abstraction formalism of biochemical models. They have been shown to approximate well the dynamics of biochemical models, while offering improved efficiency for their analysis [17,18]. In this paper, we compare different representations and simulation schemes on these DBNs, testing their efficiency and accuracy as abstract...

Let X be a Kähler manifold of complex dimension n with smooth Kähler metric ω, and Z ⊂ X a smooth complex hypersurface. Let L→ X be a holomorphic line bundle with a possibly singular Hermitian metric e−φ whose singular locus does not lie in Z, i.e., such that e|Z is a metric for L|Z . Assume also that the line bundle EZ → X associated to the divisor Z has a holomorphic section fZ such that Z = ...

1. Preview 2 Complex multiplication on elliptic curves over C 2 Traces of singular moduli 3 Class field theory 3 The Kronecker limit formula and Kronecker’s solution of Pell’s equation 4 Application to Diophantine equations (Villegas) 4 L-series and CM modular forms 5 Other topics 6 2. Complex Multiplication on Elliptic Curves over C 6 Elliptic Curves over C 6 Elliptic functions 7 Complex multi...

This paper presents numerical computations of complex singular solutions to the 3D incompressible Euler equations. The Euler solutions found here consist of a complex valued velocity field u+ that contains all positive wavenumbers; u+ satisfies the usual Euler equations but with complex initial data. The real valued velocity u = u++u− (where u− = u+) is an approximate singular solution to the E...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...