Let (M, θ) be a strictly pseudoconvex pseudo-Hermitian compact hypersurface in C in the sense of Webster [34] with a pseudo-Hermitian real oneform θ on M . Let Rθ be the Webster pseudo scalar curvature for M with respect to θ. By the solution of the CR Yamabe problem given by Jerison and Lee [18], Gamara and Yacoub [10] and Gamara [9] (for n = 1), there is a pseudo-Hermitian real one-form θ so ...

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...

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...

We consider the classes M(p)  (1 < p < ∞) of holomorphic functions on the open unit disk 𝔻 in the complex plane. These classes are in fact generalizations of the class M introduced by Kim (1986). The space M (p) equipped with the topology given by the metric ρ p defined by ρp (f, g) = ||f - g|| p = (∫0(2π) log(p) (1 + M(f - g)(θ))(dθ/2π))(1/p), with f, g ∈ M (p) and Mf(θ) = sup 0 ⩽ r<1 ⁡|f(re(i...

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.