Інтегро-диференціальні системи псевдопараболічного типу: апріорні оцінки та імпульсно-точкова керованість

Для вольтеррівського інтегро-диференціального оператора псевдопараболічного типу одержано апріорні оцінки у негативних нормах, теореми існування та єдиності узагальнених розв'язків відповідних крайових задач. Розглянуто питання імпульсно-точкової керованості систем, що описуються інтегро-диференціальними псевдопараболічними рівняннями.Для вольтерровского интегро-дифференциального оператора псевдопараболического типа получены априорные оценки в негативных нормах, теоремы существования и единственности обобщенных решений соответствующих граничных задач. Рассмотрен вопрос импульсно-точечной управляемости систем, описываемых интегро-дифференциальными псевдопараболическими уравнениями.For a pseudoparabolic Volterra integro-differential operator, the a priori estimates in negative norms and the unique generalized solvability theorems for the corresponding boundary value problems are obtained. The question of impulse-point controllability of systems governed by pseudoparabolic integro-differential equations is investigated

Kidney cell electrophoresis in space flight: Rationale, methods, results and flow cytometry applications

Cultures of human embryonic kidney cells consistently contain an electrophoretically separable subpopulation of cells that produce high levels of urokinase and have an electrophoretic mobility about 85 percent as high as that of the most mobile human embryonic kidney cells. This subpopulation is rich in large epithelioid cells that have relatively little internal structure. When resolution and throughput are adequate, free fluid electrophoresis can be used to isolate a broad band of low mobility cells which also produces high levels of plasminogen activators (PAs). In the course of performing this, it was discovered that all electrophoretic subpopulations of cultured human embryonic kidney cells produce some PAs and that separate subpopulations produce high quantities of different types of PA's. This information and the development of sensitive assays for this project have provided new insights into cell secretion mechanisms related to fibrinolysis. These advances would probably not have been made without the NASA program to explore fundamental questions of free fluid electrophoresis in space

The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improve

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

The Geoff Egan Memorial Lecture 2011. Artefacts, art and artifice: reconsidering iconographic sources for archaeological objects in early modern Europe

A first systematic analysis of historic domestic material culture depicted in contemporaneous Western painting and prints, c.1400-1800. Drawing on an extensive data set, the paper proposes to methodologies and hermeneutics for historical analysis and archaeological correspondence

Can be gravitational waves markers for an extra-dimension?

The main issue of the present letter is to fix specific features (which turn out being independent of extradimension size) of gravitational waves generated before a dimensional compactification process. Valuable is the possibility to detect our prediction from gravitational wave experiment without high energy laboratory investigation. In particular we show how gravitational waves can bring information on the number of Universe dimensions. Within the framework of Kaluza-Klein hypotheses, a different morphology arises between waves generated before than the compactification process settled down and ordinary 4-dimensional waves. In the former case the scalar and tensor degrees of freedom can not be resolved. As a consequence if were detected gravitational waves having the feature here predicted (anomalous polarization amplitudes), then they would be reliable markers for the existence of an extra dimension.Comment: 5 pages, two figure, to appear on Int. Journ. Mod. Phys.

Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure

Large-scale magnetic fields from inflation due to Chern-Simons-like effective interaction

We discuss the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current in inflationary cosmology. It is shown that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be generated even for the scale of the effective interaction being the Planck scale.Comment: 13 pages, 2 figures, additional explanations include