The paper is concerned with estimating the number of integers smaller than x whose largest prime divisor is smaller than y, denoted ψ(x, y). Much of the related literature is concerned with approximating ψ(x, y) by Dickman’s function ρ(u), where u = lnx/ ln y. A typical such result is that ψ(x, y) = xρ(u)(1 + o(1)) (1) in a certain domain of the parameters x and y. In this paper a different typ...

Let Ω ⊂ Rd be a bounded domain with smooth boundary and let A ⊂⊂ Ω be a smooth, compactly embedded subdomain. Consider the operator − 1 2 ∆ in Ω − Ā with the Dirichlet boundary condition at ∂A and the Neumann boundary condition at ∂Ω, and let λ0(Ω, A) > 0 denote its principal eigenvalue. We discuss the question of monotonicity of λ0(Ω, A) in its dependence on the domain Ω. The main point of thi...

Several pieces of different musical kinds were studied measuring A(t), the output amplitude of a peak detector driven by the electric signal arriving to the loudspeaker, which was digitized by a PC with a frequency rate of 100 samples/s. Fixed a valuable threshold (Ā = 100mV), we considered N(A), the number of times that A(t) > Ā, each of them we named event and N(t), the number of events whose...

Abstract An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset is used as a constraint in an optimization problem with very few variables corresponding to the 1% of the data kept. The remainder of the data can be thrown away after so...

Wh-phrases in English can appear both raised and in-situ. However, only in-situ wh-phrases can take semantic scope beyond the immediately enclosing clause. I present a denotational semantics of interrogatives that naturally accounts for these two properties. It neither invokes movement or economy, nor posits lexical ambiguity between raised and in-situ occurrences of the same wh-phrase. My anal...

Let F be a free finitely generated group and A ∈ Matn×m(C[F ]). For each quotient G = F/N of F we can define a von Neumann rank function rkG(A) associated to the l 2-operator l2(G)n → l2(G)m induced by right multiplication by A. For example, in the case where G is finite, rkG(A) = rkC(Ā) |G| is the normalized rank of the matrix Ā ∈ Matn×m(C[G]) obtained by reducing the coefficients of A module ...

Abstract The article establishes the inflection of proper names in Luwian and Lycian, which differs from appellative all oblique cases. It is argued that locative, genitive ablative were reshaped after pattern ā-stems, most frequent type names. characteristic dative *-Vi̯o, however, was generalised i-stems, whose had become restricted to names, especially personal PD i-stems been appellatives. o...

K.Sienkiewicz-Małyjurek, Si lesian University of Technology, Faculty of Organization and Management, Zabrze, Poland This paper gives an overview of direct consequences of serious weather events and mitigation actions undertaken in this respect by the Commission of the European Union (EU). The potential ramiĀ cations of climate change have been illustrated based on the example of the iron and st...

Given a cardinal κ, a set A ⊂ ω is κ-universally Baire if there exist trees S, T which project to A and its complement respectively, and which continue to project to complements after the forcing Coll(ω, κ). Todorcevic [3] has shown that under Martin’s Maximum every set of reals of cardinality א1 is א1-universally Baire but not א2-universally Baire. Here we present alternate proofs of these two...

Observations show that the central black hole in galaxies has a mass M only ∼ 10 of the stellar bulge mass. Thus whatever process grows the black hole also promotes star formation with far higher efficiency. We interpret this in terms of the generic tendency of AGN accretion discs to become self–gravitating outside some small radius Rsg ∼ 0.01− 0.1 pc from the black hole. We argue that mergers ...