# Elliptic problems on networks with constrictions

## Related Articles

- Exact norms of a Stein-type operator and associated stochastic orderings. Lef�vre, Claude; Utev, Sergey // Probability Theory & Related Fields;2003, Vol. 127 Issue 3, p353
Motivated by asymptotic expansions in the central limit theorem, we find exact norms of a sequence of Stein-type operators. The proof is based on new stochastic comparisons in distribution between the difference of two independent transformed normal variables and the standard normal distribution.

- Multiscale Expansion Method in the Hilbert Problem. Chekmarev, I. B.; Chekmareva, O. M. // Fluid Dynamics;Jul/Aug2003, Vol. 38 Issue 4, p646
The problem of constructing an asymptotic approximation to the solution of the kinetic Boltzmann equation is considered for the hydrodynamic region of low Knudsen numbers. The problem is linearized for one-dimensional perturbations in a gas at rest. The distribution function is sought in the...

- Time Development of Exponentially Small Non-Adiabatic Transitions. Hagedorn, George A.; Joye, Alain // Communications in Mathematical Physics;Sep2004, Vol. 250 Issue 2, p393
Optimal truncations of asymptotic expansions are known to yield approximations to adiabatic quantum evolutions that are accurate up to exponentially small errors. In this paper, we rigorously determine the leading order non-adiabatic corrections to these approximations for a particular family of...

- On the Asymptotic Behavior of the Distributions of First-Passage Times, I. Borovkov, A. A. // Mathematical Notes;Jan/Feb2004, Vol. 75 Issue 1/2, p23
In this paper, the asymptotic behavior of and estimates for the distribution of first-passage times for a random walk are obtained in the cases of fixed and increasing levels. In the first part of the paper, the case of zero level is studied.

- Estimate for the remainder in the Weyl asymptotics of the spectrum of the Maxwell operator in Lipschitz domains. Veniaminov, N. A. // Journal of Mathematical Sciences;Aug2010, Vol. 169 Issue 1, p46
We study the asymptotics of the spectrum of the Maxwell operator M in a bounded Lipschitz domain $ \Omega \subset {\mathbb{R}^3} $ under the condition of the perfect conductivity of the boundary âˆ‚Î©. We obtain the following estimate for the remainder in the Weyl asymptotic expansion of...

- Asymptotic Results for a Class of Fourth Order Quasilinear Difference Equations. Thandapani, Ethiraju; Pandian, Subbiah; Dhanasekaran, Rajamannar // Kyungpook Mathematical Journal;2006, Vol. 46 Issue 4, p477
In this paper, the authors first classify all nonoscillatory solutions of equation (1) Î”Â² Â¦Î”Â² ynÂ¦Î±-1 Î”Â² yn + qnÂ¦yÏƒ(n)Â¦Î²-1 yÏƒ(n) = 0, n âˆˆ N into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and...

- On convergence of gradient-dependent integrands. Martin Kru��k // Applications of Mathematics;Dec2007, Vol. 52 Issue 6, p529
Abstractï¿½ï¿½We study convergence properties of {?(?u k )}k?N if ? ? C(R m?m ), |?(s)| ? C(1+|s| p ), 1 p u k ? u weakly in W 1,p (O; R m ) and for some g ? C(O) it holds that ?O g(x)?(?u k (x))dx ? ?O g(x)Q?(?u(x))dx as k ? 8. In particular, we give necessary and sufficient...

- An Analysis of the Vertical Structure Equation in Sigma Coordinates. Staniforth, A.; B�land, M.; C�t�, J. // Atmosphere -- Ocean (Canadian Meteorological & Oceanographic Soc;Dec1985, Vol. 23 Issue 4, p323
An analysis of the vertical structure equation of sigma coordinate primitive equation models is given that brings together and extends the work of several authors. We derive the vertical structure equation, and obtain its solution for a two-parameter family of vertical structure profiles that...

- SZK Proofs for Black-Box Group Problems. Arvind, V.; Das, Bireswar // Theory of Computing Systems;Aug2008, Vol. 43 Issue 2, p100
In this paper we classify several algorithmic problems in group theory in the complexity classes PZK and SZK (problems with perfect/statistical zero-knowledge proofs respectively). Prior to this, these problems were known to be in $\mbox {\rm AM}\cap \mbox {\rm coAM}$ . As $\mbox {\rm...