On an additive representation function

Let A be an infinite subset of natural numbers, and X a positive real number. Let r(n) denotes the number of solution of the equation n=a₁+a₂ where a₁?a₂ and a₁, a₂∈A. Also let |A(X)| denotes the number of natural numbers which are less than or equal to X and belong to A. For those A which satisfy the condition that for all sufficiently large natural numbers n we have r(n)≠1, we improve the lower bound of |A(X)| given by Nicolas et. al. [NRS98]. The bound which we obtain is essentially best possible.     

On the existence of solutions of variational inequalities in Banach spaces

In this paper, we study the existence of the solution of the variational inequality 〈Tx−ξ,y−x〉?0 by applying the generalized projection operator , where B is a Banach space with dual space B∗ and by using the well-known FanKKM Theorem.     

A criterion for regular sequences

LetR be a commutative noetherian ring and ƒ₁, …, ƒ_r ∃ R. In this article we give (cf. the Theorem in §2) a criterion for ƒ₁, …, ƒ_r to be regular sequence for a finitely generated module overR which strengthens and generalises a result in [2]. As an immediate consequence we deduce that if V(g ₁, …,g _r ) ⊆ V(ƒ₁, …, ƒ_r) in SpecR and if ƒ₁, …, ƒ_r is a regular sequence inR, theng ₁, …,g _r is also a regular sequence inR.     

Parametric decomposition of powers of ideals versus regularity of sequences

Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .

     

A brief remark on van der Waerden spaces

We demonstrate that Martin's axiom for -centered notions of forcing implies the existence of a van der Waerden space that is not a Hindman space. Our proof is an adaptation of the one given by M. Kojman and S. Shelah that such a space exists if one assumes the continuum hypothesis to be true.

     

Domains of Holomorphy of Generating Functions of Pólya Frequency Sequences of Finite Order*

A domain is the domain of holomorphy of the generating function of a Pólya frequency sequence of order r if and only if it satisfies the following conditions: (A) G contains the point z = 0, (B) G is symmetric with respect to the real axis, (C) T = dist(0,G)G.     

Influences of Heating Condition and Substrate-Surface Roughness on the Characteristics of Sol-Gel-Derived Hydroxyapatite Coatings

A prepared transparent HA solution was coated on Ti6Al4V substrates by a spin-coating technique. The crystallization of the sol-gel-derived HA coated on the metallic substrates could be done at relatively low firing temperatures (as low as 600°C). The characteristics of the HA-coated layer were dependent on the surface roughness of substrates and heating conditions such as firing temperature, holding time, heating rate, and atmosphere. The heat treatment at a slow heating rate (<2°C/min.) and a long heating time (>10 hrs) at 600°C in air produced the uniform surface and improved the crystallinity. The HA layer coated on 20 m grit-blasted substates was more uniform and had fever cracks after firing, compared with that coated on 100 m grit-blasted rougher substrates.     

On the Growth of Entire Functions of Exponential Type near a Straight Line

Let be a sequence of complex numbers such that as . For close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in .     

Production of high quality shocks for equation of state experiments

In this paper we describe the quality requirements that a shock wave must fulfil to make equation of state (EOS) measurements possible: planarity, no-preheating and stationarity of the shock. Experimental measurements have been performed at the Max Planck Institut für Quantenoptik (Garching). We also present simple analytical models that allow to verify shock stationarity and absence of preheating. Received 17 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: batani@mib.infn.it RID="b" ID="b"Present address: Pro-beam, Behrinsta?e 6, 85152 Planegg b. München, Germany. RID="c" ID="c"UMR 7605