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.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

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.     

Conversion of Allylic Alcohols into Allylic Nitromethyl Compounds via a Palladium-Catalyzed Solvolysis: An Enantioselective Synthesis of an Advanced Carbocyclic Nucleoside Precursor(1)

A two-step reaction sequence to homoallylic nitro compounds from allylic alcohols is presented. Ethoxy carbonylation of the alcohols with ethyl chloroformate provides the corresponding allylic ethyl carbonates in high yields. Exposure of these substrates to catalytic palladium(0) in CH(3)NO(2) initiates a reaction sequence, ionization-decarboxylation-nitromethylation, that culminates with the formation of nitroalkenes. The regio- and stereochemical outcomes of the nitromethyl allylation reaction can be explained by the behavior of the transient pi-allylpalladium complexes. This methodology serves as a centerpiece for the synthesis of an important carbocyclic nucleoside intermediate.     

99mTc-labelled human serum albumin: Chemical and electrochemical labelling methods

The labelling of human serum albumin /HSA/ with^99mTc has been investigated using a chemical method /stannous citrate/ and electrolytically generated tin/II/ ions. A comparative study of various chemical parameters and current intensities has been carried out in order to find the optimal conditions for labelling. The labelling yield was over 95%, for the chemical and electrolytical methods.     

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.