Synthesis ofS-(+)-hydroprene

A novel path toS-(+)-hydroprene (1) starting from the technical gradeS-(+)-dihydromyrcene (2, e.e. 50%) is proposed. The latter was selectively transformed intoS-3,7-dimethyloctanal (5) in three steps including hydroalumination. The reactions of5 with allyl- or methallylmagnesium chloride followed, respectively, either by oxygenation in the presence of PdCl₂/CuCl or by ozonolysis, affordS,E-6,10-dimethyl-3-undecen-2-one (7) which was treated with ethoxyethynylmagnesium bromide to give the title juvenile hormone analogue in 23% overall yield.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 110–112, January, 1993.     

Concentrated electrolyte solutions at high temperatures and pressures

A survey is given of recent experimental results obtained from high-temperature, high-pressure investigations with water, aqueous solutions, and ionic fluids. Data on the static dielectric constant of water to 550°C and 5 kbar are given and discussed with respect to their relation to water structure. Infrared and Raman spectra of HDO in pure water have been obtained to 400°C and 4 kbar, which give information on hydrogen bonding. Xe–H₂O and CO₂–H₂O mixtures were investigated in the infrared. Ni(II) and Cu(II) complexes were investigated by absorption spectroscopy in aqueous solutions of high chloride content to 350°C and 2–6 kbar. The gas-liquid critical point of ammonium chloride was found at 880°C and 1635 bars. This fluid appears to be predominantly ionic even in the critical region. The possibility of converting pure polar fluids such as ammonia and water into concentrated ionic solutions by self-ionization at very high pressures is mentioned.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

具有不定位势Kirchhoff型Schrödinger-Bopp-Podolsky系统解的存在性

研究Kirchhoff型Schrödinger-Bopp-Podolsky系统,考虑位势函数V不定的情况。此时Schrödinger算子-Δ+V具有有限维负空间。利用Morse理论,得到Kirchhoff型Schrödinger-Bopp-Podolsky系统非平凡解的存在性。     

An indexed set of density bounds on lattice packings

It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR ⁿ , on the other.We give an indexed set of bounds _L (B) a _j , where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

Production of helium fragments in197Au-emulsion collisions at 10.6 A GeV

We present a systematic analysis on the helium projectile fragments produced from 10.6 A GeV¹⁹⁷Auemulsion interactions in an experiment conducted at the Brookhaven AGS. Total charge changing and partial production cross-sections are measured experimentally on the basis of helium multiplicity. The multiplicity distribution of helium fragments which are produced collectively obey a KNO scaling. The transverse momentum distribution of these particles indicates that they are produced from two different independent sources.We are thankful to the BNL technical staff and specially to Dr. D. Beavis for his help in the exposure of emulsion stacks. Thanks are due to Profs. Y. Takahashi and G. Romano for their help in the preparation and development of the emulsion stacks. We appreciate the discussions with Prof. H. Stocker and J. Aichelin. This work was supported by D.O.E. under Grant No. DE-FGO2-90ER 40566.     

High-resolution laser spectroscopy on H2 at 97–98 nm

A narrowband tunable eXtreme UltraViolet (XUV) laser source is used for a high resolution study of the Lyman (B ¹ _u ⁺ X ¹ _g ⁺ ) band system of molecular hydrogen. Seven rotational transitions of two vibrational bands, (10,0) and (11,0), in the wavelength range from 97.2–98.3 nm have been investigated for the first time under sub-Doppler molecular beam conditions. A calibration procedure using the I₂ standard in the visible yielded an absolute frequency accuracy of 0.02 cm^–1. The obtained H₂ transition frequencies provide a calibration standard in the extreme ultraviolet wavelength region.     

Combinatorial invariance of Stanley-Reisner rings

In this short note we show that Stanley—Reisner rings of simplicial complexes, which have had a dramatic application in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.     

Representation of elements of a sequence by sumsets

In this note the method of [5] and a result from [3] are combined to treat the following classical problem: Given a finite setA and an infinite sequenceS (both inZ), what is the minimal number of elements ofA whose sum lies inS? We obtain an upper bound depending only on the densities ofA andS (but not on their arithmetic nature).     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.