1,367 research outputs found
Physical applications of second-order linear differential equations that admit polynomial solutions
Conditions are given for the second-order linear differential equation P3 y"
+ P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of
degree n. Several application of these results to Schroedinger's equation are
discussed. Conditions under which the confluent, biconfluent, and the general
Heun equation yield polynomial solutions are explicitly given. Some new classes
of exactly solvable differential equation are also discussed. The results of
this work are expressed in such way as to allow direct use, without preliminary
analysis.Comment: 13 pages, no figure
A hierarchy of models related to nanoflows and surface diffusion
In last years a great interest was brought to molecular transport problems at
nanoscales, such as surface diffusion or molecular flows in nano or
sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V.
Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to
analyze the mechanisms that determine mobility of molecules in nanoscale
channels. This approach proved to be remarkably useful to give new insight on
these issues, such as density dependence of the diffusion coefficient. In this
paper we revisit these works to derive the kinetic and diffusion models
introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M.
Beenakker by using classical tools of kinetic theory such as scaling and
systematic asymptotic analysis. Some results are extended to less restrictive
hypothesis
Transplantable Subcutaneous Hepatoma 22a Affects Functional Activity of Resident Tissue Macrophages in Periphery
Tumors spontaneously develop central necroses due to inadequate blood supply. Recent data indicate that dead cells and their products are immunogenic to the host. We hypothesized that macrophage tumor-dependent reactions can be mediated differentially by factors released from live or dead tumor cells. In this study, functional activity of resident peritoneal macrophages was investigated in parallel with tumor morphology during the growth of syngeneic nonimmunogenic hepatoma 22a. Morphometrical analysis of tumor necroses, mitoses and leukocyte infiltration was performed in histological sections. We found that inflammatory potential of peritoneal macrophages in tumor-bearing mice significantly varied depending on the stage of tumor growth and exhibited two peaks of activation as assessed by nitroxide and superoxide anion production, 5′-nucleotidase activity and pinocytosis. Increased inflammatory reactions were not followed by the enhancement of angiogenic potential as assessed by Vascular Endothelial Growth Factor mRNA expression. Phases of macrophage activity corresponded to the stages of tumor growth characterized by high proliferative potential. The appearance and further development of necrotic tissue inside the tumor did not coincide with changes in macrophage behavior and therefore indirectly indicated that activation of macrophages was a reaction mostly to the signals produced by live tumor cells
A stochastic-Lagrangian particle system for the Navier-Stokes equations
This paper is based on a formulation of the Navier-Stokes equations developed
by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to
appear), where the velocity field of a viscous incompressible fluid is written
as the expected value of a stochastic process. In this paper, we take
copies of the above process (each based on independent Wiener processes), and
replace the expected value with times the sum over these
copies. (We remark that our formulation requires one to keep track of
stochastic flows of diffeomorphisms, and not just the motion of particles.)
We prove that in two dimensions, this system of interacting diffeomorphisms
has (time) global solutions with initial data in the space
\holderspace{1}{\alpha} which consists of differentiable functions whose
first derivative is H\"older continuous (see Section \ref{sGexist} for
the precise definition). Further, we show that as the system
converges to the solution of Navier-Stokes equations on any finite interval
. However for fixed , we prove that this system retains roughly
times its original energy as . Hence the limit
and do not commute. For general flows, we only
provide a lower bound to this effect. In the special case of shear flows, we
compute the behaviour as explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
Two problems related to prescribed curvature measures
Existence of convex body with prescribed generalized curvature measures is
discussed, this result is obtained by making use of Guan-Li-Li's innovative
techniques. In surprise, that methods has also brought us to promote
Ivochkina's estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo
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