Wyniki wyszukiwania - BazTech

1

On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions

Khelifi Abdessatar, Jaouabi Ahlem

Journal of Applied Analysis

|

2022

|

Vol. 28, nr 1

149--164

EN

In this paper, we provide a rigorous derivation of an asymptotic formula for the perturbation of eigenvalues associated to the Stokes eigenvalue problem with Dirichlet conditions and in the presence of small deformable inclusions. Taking advantage of the small sizes of the inclusions immersed in an incompressible Newtonian fluid having kinematic viscosity different from the background one, we show that our asymptotic formula can be expressed in terms of the eigenvalue in the absence of the inclusions and in terms of the viscous moment tensor (VMT).

2

A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber

Louchard G.

Mathematica Applicanda

|

2017

|

Vol. 45, No. 2

95--118

EN

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1, X2,…,Xn be a sequence of independent and identically distributed random variables which can take three values: {+1,−1, 0}. The goal is to maximize the probability of stopping on a value +1 or −1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.

PL

Klasyczny problem sekretarki został uogólniony na przestrzeni lat w kilku kierunkach. W niniejszym artykule ograniczamy nasze zainteresowanie do tych uogólnień, które mają związek z bardziej ogólnym problemem zatrzymania na ostatniej obserwacji określonego rodzaju. Problemy Brussa-Webera, które rozważamy, koncentrują się wokół następującego modelu: Obserwowany jest ciąg niezależnych zmiennych losowych o tym samym rozkładzie przyjmujących trzy wartosci: +1; −1; 0. Celem jest maksymalizacja prawdopodobieństwa zatrzymania na wartości +1 lub −1 pojawiającej się po raz ostatni w sekwencji. Badamy pokrewne problemy zarówno z czasem dyskretnym, jak i ciągłym, ze znaną lub nieznaną liczbą obserwacji oraz znanym i nieznanym rozkładem. W szczególności bierze się pod uwagę tak zwaną strategię z niepełną informacją. Nowością w niniejszej pracy jest udoskonalona analiza kilku problemów w tej klasie oraz badanie asymptotycznego zachowania się rozwiązań. Prezentujemy również symulacje odpowiednich kompletnych algorytmów wyboru.

3

Topological sensitivity analysis for a coupled nonlinear problem with an obstacle

Abdelbari M., Nachi K., Sokolowski J.

Control and Cybernetics

|

2017

|

Vol. 46, no. 1

5--25

EN

The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-diﬀerential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.

4

On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity

Parusnikova A. V.

Opuscula Mathematica

|

2014

|

Vol. 34, no. 3

591--599

EN

The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevé equations near infinity.We consider the fifth Painlevé equation in two cases: when αβγδ ≠ 0 and when αβγ ≠ 0, δ =0 and the third Painlevé equation when all the parameters of the equation are not equal to zero. In the paper we prove Gevrey summability of the formal solutions to the fifth Painlevé equation and to the third Painlevé equation, respectively.