In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mas...

in view of the geopolitical statue of caucasus in the region and the world and domestic problems of caucasus region, we face different and sometimes contradictory forces and interests in the region. and political, economic, security, cultural, and… developments are result of interaction between these different and sometimes contradictory forces and interests.

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper we calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submani...

An analysis of the climate parametrization scheme adopted by conventional forest gap models revealed that most models assume a constant climate and are difficult to calibrate consistently. Tree growth showed unrealistically sensitive threshold effects along ecological gradients of temperature and precipitation. A new parametrization was compared with its predecessors in terms of the model's cap...

BACKGROUND Pay for performance (P4P) schemes have become increasingly popular innovations in primary care and have generated questions about their effect on improving quality of care. AIMS To provide a brief outline of the international evidence on the relationship between P4P schemes and quality improvement. METHOD We conducted a literature search using relevant databases and reference lis...

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...