The classical theorem of general projection for surfaces says that a general projection in P of a smooth complex projective surface S of P is a surface F with ordinary singularities i.e. its singular locus is either empty or is a curve γ such that (i) γ is either non singular or has at most a finite number of ordinary triple points; (ii) every smooth point of γ is either a nodal point or a pinc...

There are two basic theorems. Let G be a strong parapolar space with these three properties: (1) For each point x and symplecton S, x is collinear to some point of S. (2) The set of points at distance at most two from a point forms a geometric hyperplane. (3) If every symplecton has rank at least three, every maximal singular subspace has finite projective rank. Then G is either D6; 6;A5; 3 or ...

In this paper, He's highly prolic variational iteration method is applied ef-fectively for showing the existence, uniqueness and solving a class of singularsecond order two point boundary value problems. The process of nding solu-tion involves generation of a sequence of appropriate and approximate iterativesolution function equally likely to converge to the exact solution of the givenproblem w...

We propose an effective method to design a modified particle swarm optimization MPSO singularity control method for a fully parallel robot manipulator. By adopting MPSO to obtain simple and effective estimated damping values, the result automatically adjusts the damping value around a singular point and greatly improves the accuracy of system responses. This method works by damping acceleration...

We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurca...

This paper proposes a proximal iteratively reweighted algorithm to recover a low-rank matrix based on the weighted fixed point method. The weighted singular value thresholding problem gains a closed form solution because of the special properties of nonconvex surrogate functions. Besides, this study also has shown that the proximal iteratively reweighted algorithm lessens the objective function...

Adaptive dynamics in two-dimensional phenotype space is investigated by computer simulation. The model assumes Lotka-Voltera-type competition and a stochastic mutation process. The carrying capacity has a single maximum in the origin of the strategy space and the competition coefficient decreases with strategy difference. Evolutionary branching, an asexual analog of adaptive speciation, is obse...

Let L ⊆ C be a lattice and consider the compact complex torus XL = C/L. Let Γ 6 Aut(L) ∩ SL2m C be a (finite) group of automorphisms of L whose action on C is semifree (i.e., free away from 0). X L consists of finitely many isolated fixed points, so the orbifold XL/Γ has finitely many isolated singularities. We can resolve these singularities by ‘blowing up’ each of the singular points. In fact...

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...

A number of facts about quadratic load ow problems y = f(x) = 0, x 2 R n x , y 2 R n y is proved. The main results are the following 1]. If any point x belongs to a straight line connecting a pair of distinct solutions in the state space R n x , the Newton-Raphson iterative process goes along this line. If a loading process y() reaches a singular point of the problem, the corresponding trajecto...