Twin semigroups and delay equations

In the standard theory of delay equations, the fundamental solution does not 'live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, in turn, has as a consequence that the Riemann integral no longer suffices for giving meaning to the variation-of-constants formula. To compensate, we develop the Stieltjes-Pettis integral in the setting of a norming dual pair of spaces. Part I provides general theory, Part II deals with "retarded" equations, and in Part III we show how the Stieltjes integral enables incorporation of unbounded perturbations corresponding to neutral delay equations

Маркерные иммунофенотипические признаки бластов при т-клеточном остром лимфобластном лейкозе у детей

Острые лимфобластные лейкозы (ОЛЛ) Т-клеточного происхождения у детей составляют около 12% среди всех ОЛЛ. Они отличаются чрезвычайно тяжелым клиническим течением и неблагоприятным прогнозом. По морфоцитохимическим признакам невозможно разграничить Т-клеточные ОЛЛ от В-клеточных, поэтому важным является определение иммунофенотипа бластных клеток. У 168 детей с ОЛЛ в возрасте от 1 года до 14 лет проведено иммунофенотипирование бластных клеток; Т-ОЛЛ выявлен у 23 больных. Выявлены особенности фенотипа бластных клеток при T-I, T-II и T-III подвариантах ОЛЛ у детей.T-lineage acute lymphoblastic leukaemias (ALL) represent approximately 12% of all ALL in children. They feature unfavorable prognosis and extraordinarily hard clinical course. T-cell ALL cannot be differentiated from B-cell ALL by morphocytochemical features; therefore, it is crucial to define the immunophenotype of blast cells. Immunophenotyping of blast cells in 168 children with ALL aged from 1 to 14 was carried out. In 23 patients T-ALL was revealed. Peculiarities of the immunophenotype of blast cells in T-I, T-II, and T-III subgroups of ALL were established in children

Control by time delayed feedback near a Hopf bifurcation point

In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying the Floquet multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.Comment: 20 page

Asymptotic behavior and stability of second order neutral delay differential equations

Abstract We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed point method is introduced as a third approach to study the asymptotic behavior. We conclude the paper with an application to a mechanical model of turning processes