We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward q and periodic boundary conditions. show that Bethe equations of ASEP can be decoupled, at all order in perturbation variable q, by introducing a formal Laurent series mapping roots totally case q=0 (TASEP) to ASEP. The probability height for is then written as single contour integral on Riemann sur...

Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently by Fedorčuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Col...

Persistent trajectories of the Poincaré map T generated by the ndimensional periodic system ẋi = xiNi(t, x1, · · · , xn), xi ≥ 0, are studied under the assumptions that the system is dissipative, competitive and strongly competitive in C = {x : xi > 0}. The main result is that there is a canonically defined countable family of disjoint, totally invariant sets which attract all persistent trajec...

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as...

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set X in a metric space, it is proved the existence of an almost periodic sequence {ψk}k∈Z such that {ψk; k ∈ Z} = X and ψk = ψk+lq(k), l ∈ Z for all...