Likelihood ratio tests for symmetry against one-sided alternatives

A random variableX is said to have a symmetric distribution (about 0) if and only ifX and –X are, identically distributed. By considering various types of partial orderings between the distributions ofX and –X, one obtains various notions of skewness or one-sided bias. In this paper we study likelihood ratio tests for testing the symmetry of a discrete distribution about zero against the alternatives, (i)X is stochastically greater than –X; and (ii) pr(X=j)pr(X=–j) for allj>0. In the process, we obtain maximum likelihood estimators of the distribution function under the above alternatives. The asymptotic null distributions of the test statistics have been obtained and are of the chi-bar square type. A simulation study was performed to compare the powers of these tests with other tests.     

Synthesis and rearrangements of 2,3,4,5-tetrahydro-3-benzazocin-6(1H)ones

The preparation of 3-benzenesulfonyl- and 3-benzoyl-2,3,4,5-tetrahydro-3-benzazoein-6(1H)-ones by intramolecular acylation is described. Acid catalyzed rearrangements of these 3-benzazocin-6-ones occurs by 3,4-bond cleavage, which is followed by intramolecular or intermolecular alkylation, to produce indanones (i.e. XIV) or a 3,4-dihydroisoquinoline (II), respectively. In addition to spectral support for these structures, an independent synthesis of II is described from a known 3,4-dihydroisoquinoline. Two rearrangements of 3-benzazocin-6-ones under alkaline conditions are also described, and the products are again evidence for 3,4-bond cleavage to vinylphenones. These beuzazocine rearrangements have been observed only with the 6-keto compounds.     

The strong,linear hydrogen bond in Al2H−7

Self-consistent field calculations have been used to determine the equilibrium structure of Al₂H^?₇. The unique AlHAl bond is confirmed to be linear and symmetric. Breaking the hydrogen bond to form AlH₃ and AlH₄ requires a hefty 37 kcal. Electron correlation plays a small role in the relative energetics, and so the nature of this strong hydrogen bond can be understood within a molecular orbital picture. The bridging proton acts as a bond stretcher to minimize electrostatic repulsion between the two halves of the ion.     

Multinomial estimation procedures for two stochastically ordered distributions

Standard estimation procedures in a multinomial setting are the methods of maximum likelihood, minimum chi-square, Neyman modified minimum chi-square, minimum discrimination information, and the Freeman-Tukey criteria. In this paper it is shown that if the parameter region of interest is restricted to be that of stochastic ordering between two multinomial parameters, then all these procedures can also be related as in Dykstra and Lee (1991) and the corresponding estimates can be expressed in terms of a simple weighted least square projection.     

Porcine dentin sialoprotein glycosylation and glycosaminoglycan attachments

Background  

Dentin sialophosphoprotein (Dspp) is a multidomain, secreted protein that is critical for the formation of tooth dentin. Mutations in DSPP cause inherited dentin defects categorized as dentin dysplasia type II and dentinogenesis imperfecta type II and type III. Dentin sialoprotein (Dsp), the N-terminal domain of dentin sialophosphoprotein (Dspp), is a highly glycosylated proteoglycan, but little is known about the number, character, and attachment sites of its carbohydrate moieties.