In this paper, we analyse the existence and uniqueness of a time-periodic solution to chemotaxis-shallow water system in periodic domain. Under assumption some smallness symmetric external force, is established using method parabolic regularization limit process. The proved by energy estimates.

|curlu0| ) is sufficiently small, ‖Du0‖ 2 ≤ χ0. In fact, this smallness condition is such that the enstrophy is always non-increasing. In this paper we provide a numerical procedure that will verify regularity of solutions for any bounded set of initial conditions, ‖Du0‖ 2 ≤ χ1. Under the assumption that the equations are in fact regular we show that this procedure can be guaranteed to terminat...

We report on our experience implementing category theory in Coq 8.5 . The repository of this development can be found at https://bitbucket.org/amintimany/ categories/. This implementation most notably makes use of features primitive projections for records and universe polymorphism that are new to Coq 8.5. The latter provides relative smallness and largeness in the development. This will be ela...

We present an estimate of a chiral-odd contribution to the single transverse spin asymmetry in the large-pT pion production in the nucleon-nucleon collision. In this contribution the transversity distribution and the chiral-odd spin-independent twist-3 distribution appear. Because of the smallness of the corresponding hard cross section, this term turned out to be negligible in all kinematic re...

In this paper, we study on knots and closed incompressible surfaces in the 3-sphere via Morse functions. We show that both of knots and closed incompressible surfaces can be isotoped into a ”related Morse position” simultaneously. As an application, we have following results. • Smallness of Montesinos tangles with length two • Classification of closed incompressible and meridionally incompressi...

We present a method to study the time variation of the orbital parameters of a Post–Keplerian binary system undergoing a generic external perturbation. The method is the relativistic extension of the planetary Lagrangian equations. The theory only assumes the smallness of the external perturbation while relativistic effects are already included in the unperturbed problem. This is the major adva...

We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in R. The class of stable flows contains all two dimensional weak solutions. The only assumption which is required is smallness of the L2norm of initial perturbation or its derivative with respect to the ‘z’-coordinate in the same norm. The magnitude of the res...

We consider the problem of finding target vectors for which the nonzero duality gap exists in the problem of convex optimization. An infinitesimal approach to the duality gap analysis of convex problems is proposed. The approach is based on finding the order of smallness and the proportionality coefficient of perturbation function of the original optimization problem. We show that in case of du...

We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of [7], we replace the smallness condition obtained by energy methods in [6]...

We study the theory of scattering for the Wave-Schrödinger system with Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the wave data in the framework of a direct method which requires smallness of the Schrödinger data, and we determine the asymptotic behaviour in time of solutions in the range...