We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give examples of groups with and without this property. For our example of a group Γ without AGA the group K(BΓ) cannot be covered by asymptotic representations of Γ...

We consider the problem of proving circuit lower bounds against the polynomialtime hierarchy. We give both positive and negative results. For the positive side, for any fixed integer k > 0, we give an explicit Σp2 language, acceptable by a Σ p 2-machine with running time O(nk 2 log n), that requires circuit size > nk. This provides a constructive version of an existence theorem of Kannan [Kan82...

The problem of robust stabilization is considered for a class of systems with the delayed state perturbations, uncertainties, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with σ– modification is first introduced to estimate these unknown bounds. Then, by making...

Proof. It is clear that {Sn 6 t} is completely determined by the history Ft = σ(X(u), u 6 t) until time t. Lemma 1.2. For a homogeneous CTMC, each sojourn time Tn is a continuous memoryless random variable, and the sequence of sojourn times (Tj : j > n) is independent of the past FSn−1 conditioned on Xn−1. Proof. We observe that the sojourn time Tn equals the excess time Y (Sn−1) in state X(Sn−...

0. Introduction 1 1. Background on infinitary logic 2 1.1. Expressive power of Lω1ω 2 1.2. The back-and-forth construction 3 1.3. The Scott isomorphism theorem 4 1.4. ω-logic 7 1.5. Familiar theorems 8 1.6. Failure of compactness 9 2. Background on admissible sets 10 2.1. ∆0 formulas and Σ-formulas in set theory 10 2.2. Axioms of KP 11 2.3. Examples of admissible sets 12 2.4. The admissible set...

We give a new, combinatorial proof for the necklace splitting problem for two thieves using only Tucker's lemma (a combinatorial version of the Borsuk-Ulam theorem). We show how this method can be applied to obtain a related recent result of Simonyi and even generalize it. 1 Necklace Splitting This paper was inspired by the combinatorial proof of Matou2ek [7] of the Lovász-Kneser theorem [6]. H...

Proof. It is clear that {Sn 6 t} is completely determined by the history Ft = σ(X(u), u 6 t) until time t. Lemma 1.2. For a homogeneous CTMC, each sojourn time Tn is a continuous memoryless random variable, and the sequence of sojourn times (Tj : j > n) is independent of the past FSn−1 conditioned on Xn−1. Proof. We observe that the sojourn time Tn equals the excess time Y (Sn−1) in state X(Sn−...

This section provides theoretical support for the strategy outlined in §2.2. For convenience, to ease the presentation of the case in which auctioneer a’s reservation price is not met, we imagine there arema+1 “reservation” dedicated bidders installed in auction a at the market’s outset, where each such bidder’s valuation equals auctioneer a’s reservation price. Thus in this section of the appe...

Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...