We consider the class of polynomial differential equations ẋ = Pn(x, y)+Pn+1(x, y) +Pn+2(x, y), ẏ = Qn(x, y)+Qn+1(x, y)+Qn+2(x, y), for n ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. These systems have a linearly zero singular point at the origin if n ≥ 2. Inside this class we identify a new subclass of Darboux integrable systems, and some of them having a degenerate center,...

A submodule [Formula: see text] of is summand absorbing, if implies for any text]. Such submodules often appear in modules over (additively) idempotent semirings, particularly tropical algebra. This paper studies amalgamation and extensions these submodules, more generally upper bound modules.

According to theorems of C. Gordon, J. Luecke, and W. Parry, if a knot exterior X has two distinct planar boundary slopes r1, r2, then at least one of the manifolds X(r1), X(r2) has a connected summand M with nontrivial torsion in first homology. The 3-manifolds M obtained in this way, which we call t-manifolds, have special Heegaard splittings, or t-manifold structures. In this paper we study ...

Forming limit diagrams (FLDs) are calculated based on both the Marciniak and Kuczynski (M-K)  model and the analysis proposed by Jones and Gillis (J-G). J-G analysis consisted of plastic deformation approximation by three deformation phases. These phases consisted of homogeneous deformation up to the maximum load (Phase I), deformation localization under constant load (phase II) and local necki...

We analyse the fast reaction limit in reaction-diffusion system with nonmonotone function and one nondiffusing component. As speed of tends to infinity, concentration component exhibits oscillations. identify precisely its Young measure which, as a by-product, proves strong convergence diffusing component, result that is not obvious from priori estimates. Our work based on an analysis regulariz...