Anomalies in homologous relationships: When to suspect extrapolations

Summary The rule that addition of a CH₂ group to a molecule increases the retention index by 100±3 is subject to a greater uncertainty than ±3 when (a) the stationary phase has very strong intermolecular attractions comparable to the nitriles and the analyte has a polar group in the 1-position, (b) the alkyl chain to which the CH₂ is added has 3 or fewer carbons and (c) when a group that is remote from the end of the chain, such as an ester group or a double bond, introduces rigidity in that part of the chain.In cases (a) and (c), it is still true that the retention index increases linearly in a specific homologous series, but it may deviate from 100 units per carbon by as much as 10 or, in the case of nitrile stationary phases, may be as low as 70.     

On infinitesimalh-conformal motions of Finsler metric

The conformai theory of Finsler spaces was initiated by Knebelman in 1929 and lately Kikuchi [7] gave the conditions for a Finsler space to be conformai to a Minkowski space. However under theh-condition, the third author [4] obtained the conditions for a Finsler space to beh-conformal to a Minkowski space. The purpose of the paper is to investigate the infinitesimalh-conformal motions of Finsler metric and its application to anH-recurrent Finsler space. We obtain the following results.

The elastic properties of sodium montmorillonite suspensions

Shear wave rigidity moduliG have been determined using a shear wave propagation technique for sodium montmorillonite suspensions. Measurements were made as a function of time at various values of pH, NaCl concentration (C) and solids concentration and the data used to estimateG _e the value of the modulus att=. The dependency ofG _e on pH,C and solids concentration is interpreted in terms of the mode of interaction between particles and the associated volume filling structure. The results suggest that whether a coagulated or dispersive structure develops in these suspensions depends not only on pH andC but also on the degree of delamination of the clay.     

Riemannian foliations admitting transversal conformal fields

Let be a closed, connected Riemannian manifold with a foliation of codimension q and a bundle-like metric g _M . We study the relationship between several infinitesimal automorphisms. Moreover under the some curvature condition, if M admits a transversal conformal field, then is transversally isometric to the action of a finite subgroup of O(q) acting on the q-sphere of constant curvature.      

Elliptic genera of homogeneous spin manifolds and theta functions identities

By Witten rigidity theorem and the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, the elliptic genus of a homogeneous spin manifold G/H can be expressed as a sum of theta functions quotients over the Weyl group of G. Consequently, we obtain several classes of combinatorial identities of theta functions.     

Rigidity of Minimal Isometric Immersions of Spheres into Spheres

We show two specific uniqueness properties of a certain minimal isometric immersion from S3 into S6. This particular immersion has been extensively studied. We give the first uniqueness results for any such map within the full class of all minimal isometric immersion from S3(1) into S6( ). We also derive an explicit necessary and sufficient condition for linear rigidity of a general minimal isometric immersion from a sphere into a sphere.     

On asymptotics of solutions to semilinear elliptic equations near the first eigenvalue of the nonperturbed problem

We writef=(g) iff(x)cg(x) with some positive constantc for allx from the domain of functionsf andg. We show that at least (n ² /r) entries must be changed in an arbitrary (generalized) Hadamard matrix in order to reduce its rank belowr. This improves the previously known bound (n ²/r ²). If we additionally know that the changes are bounded above in absolute value by some numbern/r, then the number of these entries is bounded below by (n ³/(r ² )), which improves upon the previously known bound (n ² / ² ).Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 535–540, April, 1998.The research of the first author was supported by the Russian Foundation for Basic Research under grants No. 96-01-00094 and No. 96-15-96102 and by the INTAS Foundation under grant No. 93-1376. The research of the second author was supported by the Russian Foundation for Basic Research under grants No. 96-01-01222 and No. 96-15-96090.     

First-order rigidity of rings satisfying polynomial identities

We prove that every finitely generated Noetherian ring which satisfies a polynomial identity is first-order rigid. This generalizes a result of Aschenbrenner, Khélif, Naziazeno and Scanlon on commutative rings.