The temperature distribution in a sphere for heat transfer coefficient h equal 0 is presented. The main point is that the functional form is quite different from that for h not equal zero. This is not in the literature. It is a useful approximation for small h and small times and it makes the solution much clearer intuitively. For example recent research in cryobiology thaws cells at ultra-fast...

introduction: in the present study, potential differences between the effects of l-carnitine (lc) and acetyl-lcarnitine (alc) on ischemia/reperfusion (i/r)-induced myocardial infarction size were investigated. methods: male wistar rats were randomly divided into five groups and then anesthetized by sodium pentobarbital. hearts of the animals were removed and quickly mounted on a langendorff app...

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x(t) + ψ(x(t− r), x′(t− r), x′′(t− r), x′′′(t− r), x(t− r))x(t) +f(x′′(t− r), x′′′(t− r)) + α3x(t) + α4x(t) + α5x(t) = 0 are obtained by using Lyapunov’s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null soluti...

on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a nega...

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete R-tree; (ii) M is hyperconvex and has unique metric segments.

We present a new spatial index belonging to R-tree family. Since our new index comes out from the R-tree and holds the concept of nonoverlapping nodes we call it R-tree. The original R-tree was designed for both point and spatial data. Using R-tree for indexing spatial data is very inefficient. In our research we face the problem of indexing product catalogues data that can be represented as po...

R-tree based access methods for moving objects are hardly applicable in practice, due mainly to excessive space requirements and high management costs. To overcome the limitations of such R-tree based access methods, we propose a new index structure called AIM (Adaptive cell-based Index for Moving objects). The AIM is a cell-based multiversion access structure adopting an overlapping technique....