where λ > 0 is a parameter. We will be interested in large values of this parameter. Note that, for every function y : R → R the “translates” yt : [−M, 0]→ R are defined by yt(θ) . = y(t + θ), where −M ≤ θ ≤ 0. Equation (Eλ) includes equations with constant delays (e.g. f(φ) = g(φ(−M)), φ ∈ C([−M, 0];R), for some g : R → R) or state dependent delays (e.g. f(φ) = g(φ(−r(φ(0)))), for some r : R →...

A first-order sentence θ of vocabulary σ ∪ {S} is successor-invariant in the finite if for every finite σ-structure M and successor relations S1 and S2 on M, (M, S1) |= θ ⇐⇒ (M, S2) |= θ. In this paper I give an example of a non-first-order definable class of finite structures which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for o...

1 Context Given a finite set of m examples z 1 ,. .. , z m and a strictly convex differen-tiable loss function ℓ(z, θ) defined on a parameter vector θ ∈ R d , we are interested in minimizing the cost function min θ C(θ) = 1 m m i=1 ℓ(z i , θ). One way to perform such a minimization is to use a stochastic gradient algorithm. Starting from some initial value θ[1], iteration t consists in picking ...

The problem of estimating the parameter θ, when it is restricted to an interval of the form [ ,1] m , in a class of discrete distributions, including Binomial ( , ), k θ Negative Binomial ( , ), r θ discrete Weibull ( ) θ and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of , θ with respect to a two points boundary supported prior is minimax unde...

For a proper continuous map f : M → N between smooth manifolds M and N with m = dimM < dimN = m + k, a homology class θ(f) ∈ H m−k(M ; Z2) has been defined and studied by the first and the third authors, where H ∗ denotes the singular homology with closed support. In this paper, we define θ(f) for maps between generalized manifolds. Then, using algebraic topological methods, we show that f̄∗θ(f)...

Godsil showed that if Γ is a distance-regular graph with diameter D > 3 and valency k > 3, and θ is an eigenvalue of Γ with multiplicity m > 2, then k 6 (m+2)(m−1) 2 . In this paper we will give a refined statement of this result. We show that if Γ is a distance-regular graph with diameter D > 3, valency k > 2 and an eigenvalue θ with multiplicity m > 2, such that k is close to (m+2)(m−1) 2 , t...

2.2 Estimation and convexity. In an estimation problem, we are given a family P of laws (probability measures) on a sample space (X, B), we observe a point x of X, where often X is an n-fold product, x = (X 1 ,. .. , X n), and we want to estimate a real-valued function g on P. Usually P = {P θ , θ ∈ Θ} and g is written as a function of the parameter(s), g(P θ) = g(θ). Estimation problems are de...

Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output tracking control problem of MIMO nonlinear systems is studied and gain scheduled reference model system is used for generating desired state trajectories. Usi...

Let m be the least cardinal θ such that MA θ fails. The only known model for " m is singular " was constructed by Kunen [K1]. In Kunen's model cof (m) = ω 1. It is unknown whether " ω 1 < cof (m) < m " is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality. The following...