On modular inequalities in variable L p spaces

We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L^p spaces if and only if the variable exponent p(x) ∼ const. Received: 15 September 2004     

Galactic model of element formation

A cosmological model is presented that produces He, C, O, D, Li, Be, and B in their observed abundances without a Big Bang. The elements are produced during the 1.5-Gy formation period of a galaxy, with C, O, and other heavy elements produced by stars of M>12 M₃ , He by stars of 6 M_s<M<12 M_s, and D, Li, Be, and B by cosmic-ray reactions in a nearly pure H plasma halo. Thus, the model shows that the major elements used in astrophysical studies can be produced during galactic formation by exactly the same processes known to function today at much lower rates     

Kristallstruktur des Zinkamids Zn[N(SiMe3)2]2

Crystal Structure of the Zinc Amide Zn[N(SiMe₃)₂]₂ X‐ray quality crystals of Zn[N(SiMe₃)₂]₂ (monoclinic, P2₁/c) are obtained by sublimation of the zinc amide Zn[N(SiMe₃)₂]₂ at —30 °C in vacuo (300 torr). According to the result of the X‐ray structural analysis, Zn[N(SiMe₃)₂]₂ contains an almost linear N‐Zn‐N unit with two short N‐Zn bonds.     

A new polymorph of tetraphenyldiboroxane

A new polymorph of tetraphenyldiboroxane [or oxybis(diphenylborane)], C₂₄H₂₀B₂O, (Ia), has been found. It is monoclinic, like the already known form, (Ib), and can be refined in the same space group, namely P2₁/c, or in the equivalent setting P2₁/n. The molecular conformations of the two polymorphs differ in the rotations of two of the phenyl rings about the B—C bonds, leading to markedly different packing patterns and cell dimensions.     

A novel type of phosphide: synthesis and X-ray crystal structure analysis of (tBu3Si)3P4Li3

The tetraphosphides (tBu3Si)3P4M3 (M = Li, Na) and (tBu2PhSi)3P4Na3 have been synthesized in high yield from the reaction of 3 equivalents of the silanides tBu3SiM (M = Li, Na) and tBu2PhSiNa with P4 in benzene. (tBu3Si)3P4M3 (M = Li, Na) are transformed into the unsaturated triphosphides (tBu3Si)2P3M (M = Li, Na) and tBu3SiPM2 in tetrahydrofuran at ambient temperature.     

Isothermal degradation of poly-2,2′-(m-phenylene)-5,5′-bibenzimidazole

The isothermal degradation of poly-2,2′-(m-phenylene)-5,5′-bibenzimidazole in vacuo has been studied. Measurement of the increase in pressure with time, coupled with infrared analysis, was used to determine the distribution of the degradation products. Processes A and B with different second-order rate laws were determined to be significant in the temperature range of 550–700°C. Process A leads to the formation of equimolar quantities of hydrogen and ammonia and has an activation energy of 68 kcal/mole. Process B leads to the production of HCN, NH₃, and H₂ in the ratio of 1:1:2.5 and has an activation energy of 77 kcal/mole. The activation energies and the rate laws are consistent with a mechanism in which the initial degradation step is the bimolecular reaction of two aromatic rings.     

Determination of the alkaline earths in glass

The alkaline-earth group was isolated, after removal of silica, by precipitation as sulfates from an alcoholic solution. Those sulfates were reduced and dissolved by treatment with hydriodic acid. The alkaline earths were separated from each other by ion-exchange chromatography. The results are in good agreement with the values reported by the National Bureau of Standards.