The dependence of the variances of the parameters in non-linear regression analysis on the number of data points

In designing an experimentin which non-linear regression analysis is used to evaluate the physicochemical parameters that chracterize the behavior of the system being studied, it would be useful to be able to predict how the number of data points affects th reliabilities of the values obtained. The relation between these depends on hos the points are distributed as well as on the nature of the equation to which thd data are fitted. Weighted non-linear regression analysis has been applied to six common equations involving a total of fourteen parameters, using a number of n of points that was varied from 4 to     

Inter-annual variability in atmospheric input and partitioning of heavy metals in the Lagoon of Venice

Atmospheric bulk deposition of major and trace elements was measured at Venice from November 1995 to October 1997. Collection was carried out using polyethylene bulk passive samplers, samples being collected bi-weekly. In order to highlight the contribution of the atmosphere to water chemistry and particle budgets in the Lagoon of Venice, the geochemical composition (Si, Al, Ca, Mg, K, Na, Mn, Cr, Zn, Pb, Cd, Cu, As) of dissolved and insoluble bulk fractions was determined by AAS + ICP mass spectrometry. Great sample variability was found, with almost two orders of magnitude between maximum and minimum values for several metals. All fluxes in 1995/96 were 30% lower than in 1996/97, ranging from -3% (Ca) to -57% (Li), except for Zn, Cd and As. On the contrary, the solubility of all elements decreased during 1996/97. Partitioning between soluble and insoluble phases shows that Al, Cr, Fe and Si are mainly in the insoluble form, whereas for As, Ca, Cu, Mg, Na, Ni, K, Pb and Zn the dissolved fraction represents 50-90% of total input. The amount of particle load affects partitioning between dissolved and particulate, especially for Al and Pb. Seasonal variability was evident. The lowest pH values (approximately 5.2) were recorded in winter, causing an increase of solubility for all metals except for As, which showed the highest solubility in summer.     

Assembling heterocycle-tethered C-glycosyl and alpha-amino acid residues via 1,3-dipolar cycloaddition reactions

The 1,3-dipolar cycloadditions of C-glycosyl nitrile oxides and acetylenes to an alkyne and an azide, respectively, bearing a masked glycinyl moiety furnished disubstituted isoxazoles and triazoles. Unveiling the glycinyl group in these cycloadducts afforded C-glycosyl alpha-amino acids in which the two bioactive entities were tethered through rigid five-membered heterocycles. Optimized entries to the same compounds involved the use of unmasked but protected alkyne- and azide-containing amino acids as the partners of 1,3-dipolar cycloadditions.     

Unusual and unexpected reactivity of t-butyl dicarbonate (Boc2O) with alcohols in the presence of magnesium perchlorate. A new and general route to t-butyl ethers

[reaction: see text] A new mild method for protecting alcohols as t-butyl ethers is reported. The reaction proceeds with Mg(ClO4)2 and Boc2O and shows general applicability. The deprotection of t-butyl ethers has also been revisited. Preliminary results indicate the CeCl3 x 7H2O/NaI system is a very suitable catalyst for their removal.     

Synthesis of α-Oxo and α-hydroxy-1-benzyl-1,4-dihydro-3(2H)-isoquinolinones

The reaction of some primary amines with the methyl 2-[(α-oxobenzyl)-(α-bromo)methyl]phenylacetate ( 5 ) afforded the isoquinolinones 7a-d , which in turn were hydrogenated to 10a-d . The synthesis of these compounds was designed on the basis of a potential depressant and antiinflammatory activity found in other structurally related compounds.     

Computations of instanton invariants using Donaldson-Floer Theory

Summary We compute the Donaldson SU(2)-invariants of the double cover of ² branched over a smooth algebraic curve of degree eight. From this we deduce a formula for the relative invariants of the blow-up of the Gompf nucleusN ₂, and we show how this gives a blow-up formula for a class of 4-manifolds which includes essentially all the simply connected 4-manifolds known to have big diffeomorphism group. We apply the result on the nucleus also to prove a formula for the invariants of minimal simply connected elliptic surfaces which reduces the computation to the case of geometric genus one. In particular, we compute all the Donaldson invariants of minimal simply connected elliptic surfaces without multiple fibers. Our main tool is Donaldson-Floer theory.Oblatum IX-1993 & 26-IV-1994     

An exact algorithm for the capacitated shortest spanning arborescence

We are given a complete and loop-free digraphG=(V, A), whereV={1,...,n} is the vertex set,A={(i, j) :i, j V} the arc set, andr V is a distinguishedroot vertex. For each arc (i, j) A, letc _ij be the associatedcost, and for each vertexi, letq _i 0 be the associateddemand (withq _r =0). Moreover, a nonnegativebranch capacity, Q, is defined.A Capacitated Shortest Spanning Arborescence rooted at r (CSSA _r ) is a minimum cost partial digraph such that: (i) each vertexj r has exactly one entering arc; (ii) for each vertexj r, a path fromr toj exists; (iii) for each branch leaving vertexr, the total demand of the vertices does not exceed the branch capacity,Q. A variant of theCSSA _r problem (calledD-CSSA _r ) arises when the out-degree of the root vertex is constrained to be equal to a given valueD. These problems are strongly NP-hard, and find practical applications in routing and network design. We describe a new Lagrangian lower bound forCSSA _r andD-CSSA _r problems, strengthened in a cutting plane fashion by iteratively adding violated constraints to the Lagrangian problem. We also present a new lower bound based on projection leading to the solution of min-cost flow problems. The two lower bounds are then combined so as to obtain an overall additive lower bounding procedure. The additive procedure is then imbedded in a branch-and-bound algorithm whose performance is enhanced by means of reduction procedures, dominance criteria, feasibility checks and upper bounding. Computational tests on asymmetric and symmetric instances from the literature, involving up to 200 vertices, are given, showing the effectiveness of the proposed approach.     

On the capacity of boolean graph formulæ

In a recent paper we have solved several well-known combinatorial problems treating them as special cases of our generalization of Shannon's notion of graph capacity. We present a new simple formalism to deal with all such problems in a unified manner, considering graphs or families of graphs as special formulæ the variables of which are pairs of vertices of their common vertex sets. In all of these problems, the maximum size of a set ofn-length sequences from a fixed alphabet is to be determined under various restrictions on the element pairs present in the same coordinate of any two sequences from the set. For sufficiently homogeneous formulæ capacity becomes computable.New applications include generalizations of our result on the maximum number of pairwise qualitatively independentk-partitions of ann-set from independence to various forms of qualitative dependence.Work partially supported by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative.     

Sobolev spaces associated to a polyhedron and Fourier integral operations inR n

The theory of the Sobolev spacesH _m ^p (R ⁿ ) (mR,p polyhedron in R ²ⁿ )of [BG]is revisited here in the frame of new classes of pseudodifferential operators related to the same polyhedron p.These operators generalize to corresponding classes of Fourier integral operators, for which we present the main lines of a symbolic calculus and results of continuity on the H _m ^p (R ⁿ ) spaces.