Sigma Models and Minimal Surfaces

Correspondence is established between sigma models, minimal surfaces and the Monge–Ampére equation. The Lax pairs of the minimality condition of the minimal surfaces and the Monge–Ampére equations are given. Existence of infinitely many nonlocal conservation laws is shown and some Bäcklund transformations are also given.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

Functionalization of saturated hydrocarbons. High temperature bromination of octahydropentalene. Part 19

The synthesis and thermal bromination of octahydropentalene was studied. The reaction afforded 1a,3a,4b,6b-tetrabromo-1,2,3,4,5,6-hexahydropentalene (14) with remarkable regio- and stereospecificity. The structure of the product was determined by ¹H and ¹³C NMR data and single X-ray structural analysis. The treatment of octahydropentalene with tenfold bromine gave the octabromopentalene derivative. The formation mechanism of the products is discussed.     

Bicyclic allenes : Generation and trapping of 6,7-benzobicyclo [3.2.1] octa-2,3-diene

Treatment of 3-bromo-6,7-benzobicyclo [3.2.1] octa-2,3-diene (9) with potassium tert.-butoxide produces the strained bicyclic allene (10) which is trapped by 1,3-diphenylbenzo[c]furan (DBI) to give five isomeric cycloadducts. In the absence of DBI, allene (10) gave rise to enol ether (18) by addition of tert.-butanol.     

Synthesis and structure of cyclopropano-annelated homosesquinorbornene derivatives containing pyramidalized double bonds: evidence for the sterical effect of a cyclopropyl group on the degree of C=C double-bond pyramidalization

[reaction: see text] endo- and exo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl esters have been synthesized, and their Diels-Alder cycloaddition reactions with maleic anhydride, dimethyl acetylenedicarboxylate and singlet oxygen have been investigated. The X-ray analysis of four adducts indicated the pyramidalization of the central double bond. Density functional theory calculations on the isolated products and model compounds showed excellent agreement between the experimental and theoretical determined butterfly angles. Furthermore, it has been shown that a cyclopropyl group fused to [2.2.2] system decreases significantly the degree of the pyramidalization which is attributed to the steric interactions between the cyclopropyl group and ethano bridge of the norbornene systems. Due to the instability of the bicyclic endoperoxides, their X-ray analysis could not be carried out. DFT calculations on model compounds showed increased bending in the case of the product obtained by the addition of singlet oxygen to endo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl ester.     

On the strong almost convergence of double sequences

In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.     

An auto-coherent variational scheme for Yukawa potential

The variational principle is used to obtain solutions to Schrödinger's equation for a particle in the Yukawa potential. A Laguerre basis set extended by an extra function is employed in the calculations. A special parameter used in the extra function and its relation with the systems energy results in utilizing an auto-coherent scheme. Considerable improvement seems to be achieved especially in the critical region where the screening parameter approaches its threshold value.