Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Thermal neutron activation: Sample preparation utilizing graphite as a diluent

A sample preparation method has been developed which produces both standard and unknown samples of the same size, shape, composition and density (a necessary condition for minimum error). A solution of standard or unknown material was pipetted onto graphite wetted with acetone, the material was dried and mixed with additional graphite to give a homogeneous mixture containing≥99% graphite. Portions of the mixture were pressed into uniform cylindrical pellets. Application of the method to the activation analysis of several copper compounds gave results which generally agreed with analysis by thiosulfate titration of liberated iodine to within less than 1%. This work was supported by the United States Atomic Energy Commission.     

Direct probing of zwitterion formation in unsolvated peptides

Molecular beam electric deflection measurements have been used to determine electric susceptibilities for small unsolvated alanine-based peptides. The electric susceptibility provides information about the charge distribution within the peptide and can be used to distinguish between zwitterionic and canonical forms. Measured electric susceptibilities for WAn peptides (n = 1-5) are similar to those for capped Ac-WAn-NH2 peptides (which cannot form zwitterions). Susceptibilities calculated using a simulated tempering-based approach are substantially larger for the zwitterionic form than for the canonical form. The measured susceptibilities are in good agreement with those calculated for the canonical form. For the larger peptides, the lowest potential energy structure found in the simulations is hairpin-like, while the lowest free energy structure found at room temperature is extended. The zwitterionic form is constrained by intramolecular interactions which make it entropically unfavorable.     

Relaxometric study of copper [15]metallacrown-5 gadolinium complexes derived from alpha-aminohydroxamic acids

Proton nuclear magnetic relaxation dispersion (NMRD) profiles were recorded between 0.24 mT and 1.4 T for lanthanum(III)- and gadolinium(III)-containing [15]metallacrown-5 complexes derived from alpha-aminohydroxamic acids and with copper(II) as the ring metal. The influence of the different R-groups on the proton relaxivity was investigated, and a linear relationship between the relaxivity and the molecular mass of the metallacrown complex was found. The selectivity of the metallacrown complexes was tested by transmetalation experiments with zinc(II) ions. The crystal structure of the copper [15]metallacrown-5 gadolinium complex with glycine hydroximate ligands is reported.     

ETUDE DE LA FRAGMENTATION DE N-ARYL ET DE N-ALKYL AMINOCETONES EN SPECTROMETRIE DE MASSE

A Comparison of the chemical ionisation and elctron-impact mass spectra of alkyl and aryl aminoketones has bee carried out. This has revealed the particular stabilization of the N-aryl grops in all cases.     

Detection of banned meat and bone meal in feedstuffs by near-infrared microscopic analysis of the dense sediment fraction

In this paper we present an alternative method for detection of meat and bone meal (MBM) in feedstuffs by near-infrared microscopic (NIRM) analysis of the particles in the sediment fraction (dense fraction (d >1.62) from dichloroethylene) of compound feeds. To apply this method the particles of the sediment fraction are spread on a sample holder and presented to the NIR microscope. By using the pointer of the microscope the infrared beam is focussed on each particle and the NIR spectrum (1112–2500 nm) is collected. This method can be used to detect the presence of MBM at concentrations as low as 0.05% mass fraction. When results from the NIRM method were compared with the classical microscopic method, a coefficient of determination (R²) of 0.87 was obtained. The results of this study demonstrated that this method could be proposed as a complementary tool for the detection of banned MBM in feedstuffs by reinforcement of the monitoring of feeds.     

Interactions électriques dans les phases mésomorphes des systèmes amphiphile-eau: Rôle de la teneur en eau,de la longueur de la chaîne paraffinique,de la nature du cation,et de la température

Summary Using X-ray diffraction techniques, we have determined the specific surface of polar groups in the two structures observed for binary soap-water systems in the mesomorphic state: the cylindrical structure and the lamellar one.This parameter depends upon the temperature, the nature of the polar group, the type of structure of the system and the quantity of water present in the mixture. It is, on the contrary, independent of the length of the paraffin chain of the soap. This result suggests that the role of the electrical state of the aqueous regions is by far the most important.

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Zusammenfassung Mit Hilfe der Röntgenstrahlen-Diffraktion wurde die spezifische Fläche polarer Gruppen der zwei wichtigsten Strukturen der binären Seifen/Wasser-Systeme im mesomorphen Zustand bestimmt: die zylindrische und die lamellare Struktur.Diese Größe ist von der Temperatur, der Natur der polaren Gruppen, der Struktur des Systems und des Wassergehaltes der Mischung abhängig. Die spezifische Fläche ist jedoch von der Länge der Seifen-Paraffin-Kette unabhängig. Der elektrische Zustand des wässerigen Teiles scheint also sehr wichtig zu sein.

     

Efficient nickel-mediated intramolecular amination of aryl chlorides

The use of an in situ generated Ni(0) catalyst associated with 2,2'-bipyridine or N,N'-bis(2,6-diisopropylphenyl)dihydroimidazol-2-ylidene (SIPr) as a ligand and NaO-t-Bu as the base for the intramolecular coupling of aryl chlorides with amines is described. The procedure has been applied to the formation of five-, six-, and seven-membered rings. [reaction: see text]     

Structural and magnetic properties of the solid solution () YMn1−x(Cu3/4Mo1/4)xO3

Recently, the ferroelectromagnet YMnO₃ has been the focus of interest because it exhibits both antiferromagnetism (Néel temperature 80 K) and ferroelectricity (Curie temperature 914 K). There have been no reports of complete YMn_1−xM_xO₃ solid solutions in which substitution of the foreign M cation preserves the hexagonal P6₃cm structure. In contrast there exist several homeotypic phases with the general formula, Ln_1+nCu_nMO_3+3n (n=1 (M=Ti), 2 (M=V) and 3 (M=Mo); Ln: lanthanide). Several YMn_1−x(Cu_3/4Mo_1/4)_xO₃ compounds have been synthesized. The solid solution, from YMnO₃ (x=0) to YCu_3/4Mo_1/4O₃ (x=1) has been characterized by X-ray diffraction and transmission electron microscopy study. For 0<x<0.9, the compounds are found to crystallize in the non-centrosymmetric structure, space group P6₃cm, of YMnO₃. The Mn-free end member, x=1, crystallizes in a complex multiple cell, the superstructure being associated to Cu³⁺/Mo⁶⁺ cationic ordering. Dilution of the Mn³⁺ magnetic array by the paramagnetic (Cu²⁺) and diamagnetic (Mo⁶⁺) cations is found to decrease the antiferromagnetic ordering temperature and it becomes undetectable for x0.5 compositions.