For a left vector space V over a totally ordered division ring F, let Co(V ) denote the lattice of convex subsets of V . We prove that every lattice L can be embedded into Co(V ) for some left F-vector space V . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form Co(V,Ω) = {X ∩Ω | X ∈ Co(V )}, for some f...

Consider the Liénard equation with a deviating argument x (t)+ f (x(t))x (t)+ g1(x(t))+ g2(x(t − τ(t))) = e(t), where f, g1 and g2 are continuous functions on R = (−∞,+∞), τ (t) ≥ 0 is a bounded continuous function on R, and e(t) is a bounded continuous function on R = [0,+∞). We obtain some new sufficient conditions for all solutions and their derivatives to be bounded, which substantially ext...

In two recent papers, Facchinei 7] and Facchinei and Kanzow 8] have shown that for a continuously diierentiable P 0-function f , the nonlinear complementarity problem NCP(f ") corresponding to the regularization f " (x) := f (x) + "x has a unique solution for every " > 0, that dist (x("); SOL(f)) ! 0 as " ! 0 when the solution set SOL(f) of NCP(f) is nonempty and bounded, and NCP(f) is stable i...

This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x ?2d f (x), where f (x) is bounded and bounded away from zero. A form of log-periodogram regression technique is presented both in the parametric context (i.e. f (x) is a nite order exponential ...

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...

Given a monomial ideal I = 〈m1,m2, · · · ,mk〉 where mi are monomials and a polynomial f as an arithmetic circuit the Ideal Membership Problem is to test if f ∈ I . We study this problem and show the following results. (a) If the ideal I = 〈m1,m2, · · · ,mk〉 for a constant k then there is a randomized polynomial-time membership algorithm to test if f ∈ I . This result holds even for f given by a...

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...

Let G be an infinite geometric graph; in particular, a graph whose vertices are a countable discrete set of points on the plane, with vertices u, v adjacent if their Euclidean distance is less than 1. A “fire” begins at some finite set of vertices and spreads to all neighbors in discrete steps; in the meantime f vertices can be deleted at each time-step. Let f(G) be the least f for which any fi...

The study of typical continuous functions has been one of the most popular topics in classical real analysis. Several people have also investigated typical behaviour in other families of functions, such as those of bounded functions of Baire class 1, of bounded Darboux functions of Baire class 1, and of bounded derivatives, where the topology is given by the supremum norm. Kostyrko and Šalát [2...