On the error of compound quadrature formulas forr-convex functions

LetC _m be a compound quadrature formula, i.e.C _m is obtained by dividing the interval of integration [a, b] intom subintervals of equal length, and applying the same quadrature formulaQ _n to every subinterval. LetR _m be the corresponding error functional. Iff ^(r) > 0 impliesR _m [f] > 0 (orR _m [f] < 0),=" then=" we=" say=">C _m is positive definite (or negative definite, respectively) of orderr. This is the case for most of the well-known quadrature formulas. The assumption thatf ^(r) > 0 may be weakened to the requirement that all divided differences of orderr off are non-negative. Thenf is calledr-convex. Now letC _m be positive definite or negative definite of orderr, and letf be continuous andr-convex. We prove the following direct and inverse theorems for the errorR _m [f], where , denotes the modulus of continuity of orderr:

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

On the existence of equilibrium states in local quantum field theory

It is shown that any local quantum field theory admits thermodynamical equilibrium states (KMS-states) for all positive temperatures provided it satisfies a nuclearity condition, proposed by Wichmann and one of the authors, which restricts the admissible number of local degrees of freedom.Dedicated to E. H. Wichmann on the occasion of his 60th birthday     

On digital smoothing filters: A brief review of closed form solutions and two new filter approaches

The concept of smoothing noisy data using appropriate polynomials turns out to be equivalent to the application of suitable nonrecursive digital filters having the following properties: They process the data in such a way that the moments are conserved up to a desired order while the energy of their impulse response is minimum. Flatness constraints of their frequency response at =0 are equivalent to the moment condition. By using orthogonal polynomials, an explicit solution is known from the literature. A second approach which uses a special decomposition also yields closed form solutions. The realization is simplified, especially in the case where a large number of moments is supposed to be conserved.     

1,3,6,9,12,14,17,20-octaethynyltetrabenz[a,b,f,j,k,o]-4,5,10,11,15,16,21,22- octadehydro[18]annulene: a carbon-rich hydrocarbon

Dodecaynes 1a-d have been prepared via a convergent strategy that employs Sonogashira couplings as the carbon-carbon bond-forming tool. Due to the steric bulk of the DMTS groups, 1c adopts a nonplanar conformation, the dynamics of which have been probed by VT-NMR. The cobalt-catalyzed isomerization of 1a,b produced the new conjugated phenylenes 2a,b and 3a,b, respectively. [structure: see text]     

2-Phosphinophenolate complexes: formation and crystal structure of a novel trinuclear mu-O nickel(II)-tris(P(intersection)O-chelate)

A novel linear trinuclear mu-O-bridging 2-phosphinophenolate nickel(II) complex with fac-tris(P(intersection)O- chelates) in the terminal positions and the three oxygen atoms each facing the central nickel(II) cation was synthesized and structurally characterized by X-ray crystallography. To the best of our knowledge, this is the first example of an octahedral Ni(II) tris(P(intersection)O- chelate).     

Detection of processed genetically modified food using CIM monolithic columns for DNA isolation

The availability of sufficient quantities of DNA of adequate quality is crucial in polymerase chain reaction (PCR)-based methods for genetically modified food detection. In this work, the suitability of anion-exchange CIM (Convective Interaction Media; BIA Separations, Ljubljana, Slovenia) monolithic columns for isolation of DNA from food was studied. Maize and its derivates corn meal and thermally pretreated corn meal were chosen as model food. Two commercially available CIM disk columns were tested: DEAE (diethylaminoethyl) and QA (quaternary amine). Preliminary separations were performed with standard solution of salmon DNA at different pH values and different NaCl concentrations in mobile phase. DEAE groups and pH 8 were chosen for further isolations of DNA from a complex matrix-food extract. The quality and quantity of isolated DNA were tested on agarose gel electrophoresis, with UV-scanning spectrophotometry, and by amplification with real-time PCR. DNA isolated in this way was of suitable quality for further PCR analyses. The described method is also applicable for DNA isolation from processed foods with decreased DNA content. Furthermore, it is more effective and less time-consuming in comparison with the existing proposed methods for isolation of DNA from plant-derived foods.