Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

While decomposing graphs in simpler items greatly helps to design more efficient algorithms, some classes of graphs can not be handled using the classical techniques. We show here that a graph having enough symmetries can be factored into simpler blocks through a standard morphism and that the inverse process may be formalized as a pullback rewriting system.

Resumen We first study the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations with delay in the locally Lipschitz case. The asymptotic behaviour of solutions, and the existence of pullback attractor are also analyzed.

If a normal quartic surface admits a singular point that is not a rational double point, then the surface is determined by the triplet (M,D,E) consisting of the minimal desingularization M , the pullback D of a general hyperplane section, and a non-zero effective anti-canonical divisor E of M . Geometric constructions of all the possible triplets (M,D,E) are given.

The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of recurrence are studied. The generalized concircular recurrence, as a new conc...

In this paper we study the asymptotic dynamics for the nonautonomous stochastic strongly damped wave equation driven by additive noise defined on unbounded domains. First we introduce a continuous cocycle for the equation and then investigate the existence and uniqueness of tempered random attractors which pullback attract all tempered random sets.

In this paper, we introduce the notion of “(n, d)-perfect rings” which is in some way a generalization of the notion of “S-rings”. After we give some basic results of this rings and we survey the relationship between “A(n) property” and “(n, d)-perfect property”. Finally, we investigate the “(n, d)-perfect property” in pullback rings.

The form of the Seiberg-Witten differential is derived from the Mtheory approach to N = 2 supersymmetric Yang-Mills theories by directly imposing the BPS condition for twobranes ending on fivebranes. The BPS condition also implies that the pullback of the Kähler form onto the space part of the twobrane world-volume vanishes.

We show the lower semicontinuity of the family of pullback attractors for the singularly nonautonomous plate equation with structural damping utt + a(t, x)ut + (−∆)ut + (−∆)u+ λu = f(u), in the energy space H2 0 (Ω)×L2(Ω) under small perturbations of the damping term a.

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).