The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

in this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. tractability and dierentiability index are introduced based on the-smoothing property of a volterra integral operator and index reduction procedure, respectively. using the notion of index, we give sucient conditions for the...

The asymmetric cipher protocol, based on decomposition problem in matrix semiring M over semiring of natural numbers N is presented. The security of presented cipher protocol is based on matrix decomposition problem (MDP), which is linked to the problem of solution of multivariate polynomial system of equations. Compromitation of proposed scheme relies on the solution of system of multivariate ...

POLYNOMIAL systems of equations frequently arise in solid modelling, robotics, computer vision, chemistry, chemical engineering, and mechanical engineering. Locally convergent iterative methods such as quasi-Newton methods may diverge or fail to find all meaningful solutions of a polynomial system. This paper proposes a parallel homotopy algorithm for polynomial systems of equations that is gua...

We propose a new method for registering a cloud of points in 2D onto a planar curve. This method does not require the knowledge of an initial guess for the position of the point cloud and proceeds without having to order, smooth out or otherwise process the points of the query point cloud in any way. The method consists in representing the planar curve by an algebraic curve, and in fitting the ...

A new homotopy method for solving systems of polynomial equations is presented. The homotopy equation is extremely simple: It is linear with respect to the homotopy parameter and only one auxiliary parameter is needed to regularize the problem. Within some limits, an arbitrary starting problem can be chosen, as long as its solution set is known. No restrictions on the polynomial systems are mad...

We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree.

We show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small amplitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded region to be a center.

The analysis and solving of polynomial systems are fundamental problems in computational algebra. In many applications, polynomial systems are highly structured and it is very useful to develop specific methods in order to take into account a particular structure. In this talk, we will focus on systems of n homogeneous polynomials f1, . . . , fn in n variables x1, . . . ,xn that are globally in...