PHANTOM MAPS AND SPACES OF THE SAME n-TYPE FOR ALL n

1.IntroductionLetXbeaconnectedCWcomplexandX.denoteitsn-skeleton.Amapf:X-YiscalledaphantommapifitsrestrictiontoeachskeletonXuisnullhomotopic.ItiseasytoknowthateveryphantommapfromafiniteCWcomplexortoaspacewithonlyfinitenootrivialhomotopygroupsisnecessarilytrivialuptohomotopy.HenceessentialphantommapcanoccuronlywhenthedomainXisaninfinitedimensionalspaceorthetargetisaspacewithinfinitenontrivialhomotopygroups.Suchmapsappeartobenullhomotopicfromanumberofdifferentpoilltsofview;e.g.,theyinducethe…     

A facile synthesis of 2,3-disubstituted furo[2,3-b]pyridines

In a three-step sequence starting from readily available starting materials, 2,3-carbon disubstituted furo[2,3-b]pyridines can be accessed in good yields and purity. Furo[2,3-b]pyridines bearing ester, amide and ketone groups at the 2-position can be prepared with a variety of aryl and alkyl groups at the 3-position.     

Using the Pummerer cyclization-deprotonation-cycloaddition cascade of imidosulfoxides for alkaloid synthesis

The Pummerer reaction of imidosulfoxides bearing tethered alkenyl groups has been employed for the synthesis of several alkaloids. The required imidosulfoxides necessary for the cascade sequence were easily obtained by heating the appropriate amide with (ethylsulfeny)acetyl chloride followed by sodium periodate oxidation. The initially formed thionium ion, obtained by treating the imidosulfoxide with acetic anhydride and p-toluenesulfonic acid, reacts with the neighboring imido group, and the resulting oxonium ion undergoes subsequent deprotonation to produce an isomünchnone dipole. This mesoionic betaine intermediate undergoes ready intramolecular dipolar cycloaddition across the neighboring pi-bond. Exposure of the resulting cycloadducts to additional acetic anhydride leads to ring opening and formation of a 5-acetoxy-substituted 2(1H)-pyridone. This six-ring heterocyclic system constitutes a valuable building block for the synthesis of a variety of pyridine, quinolizidine, and clavine alkaloids. The cyclization-deprotonation-cycloaddition cascade has been successfully applied to the synthesis of the naturally occurring alkaloids onychnine, dielsiquinone, (+/-)-lupinine, (+/-)-anagyrine, (+/-)-pumiliotoxin C, and (+/-)-costaclavine.     

Tandem Pummerer/Mannich cyclization cascade of alpha-sulfinylamides as a method to prepare aza-heterocycles

A series of alpha-sulfinylenamides was conveniently prepared by the condensation of a primary amine with a ketone, followed by reaction of the resulting imine with ethylsulfenylacetyl chloride and subsequent oxidation with sodium periodate. When treated with p-TsOH, cyclization occurred to produce fused isoquinoline lactams by a mechanism that involves an initial Pummerer reaction followed by a subsequent cyclization of the resulting N-acyliminium ion onto the tethered aromatic ring. The isolation of a single diastereomer was rationalized in terms of a Nazarov-type 4pi-electrocyclic reaction followed by pi-cyclization onto the least hindered side of the N-acyliminium ion. Another method that was used to generate the alpha-acylthionium ion intermediate involved the reaction of bis(ethylsulfenylacetyl)acetamides with dimethyl(methyl)thiosulfonium tetrafluoroborate (DMTSF). Treatment of several bis-ethylsulfenylenamides with DMTSF delivered novel spiro-heterocycles as single diastereomers in good yield by a related process. The convergency and stereochemical control associated with this cascade sequence make it particularly suited for the assembly of natural product scaffolds. Some preliminary studies were directed toward both mesembrine and deethylibophyllidine. When the model Z-enamido sulfoxide 33 was heated with p-TsOH, a 80% yield of tosylate 34 was obtained as a single diastereomer. In this case, the carbocation intermediate derived from cyclization onto the terminal pi-bond was trapped with p-TsOH from the least hindered face, opposite the angular carbomethoxy and methyl groups. Related cyclization cascades were also found to occur with systems containing tethered indole rings.     

Photoredox-Catalyzed Giese Reactions: Decarboxylative Additions to Cyclic Vinylogous Amides and Esters

An effective strategy has been developed for the photoredox-catalyzed decarboxylative addition of cyclic amino acids to both vinylogous amides and esters leading to uniquely substituted heterocycles. The additions take place exclusively trans to the substituent present on the dihydropyridone ring affording stereochemical control about the new carbon-carbon bond. These reactions are operationally simplistic and afford the desired products in good to excellent isolated yields.     

PHANTOM MAPS AND SPACES OF THE SAME {\tf n}-TYPE FOR ALL {\tf n}

After reviewing the theory of phantom maps and SNT, the author gives several general results which relate the theory of phantom maps and SNT and which extend that of Harper and Roitberg.     

THE CRITICAL STATE OF THE TWO-DIMEMSIONAL ALTERKATIVE BINARY SYSTEM

The equation of state and the isothermal line for the two-dimensional alternative binary system are discussed in this paper. We found the regularity of variance of the critical state with the composition of binary system, and obtained the linear relationship between the critical pressure and the critical temperature. We showed that the value of the critical coefficient is independent of the composition and coincides with the experimental data for the three-dimensional substances in quantitative 1eve1 .     

Imaging Cracks in Marble with Magnetic Resonance Imaging of Inert Fluorinated Gases

Inspired by the challenge of determining the nature of the cracks in the ankles of Michelangelo's statue David, we undertook a laboratory study to image sulfurhexafluoride gas in cracks with magnetic resonance. We made cracks of known thickness between plates of polycarbonate and also cracked samples of marble. SF₆ at 20 °C and 1 atm (101.29 kPa) was imaged in the cracks by projection imaging with the free induction decays of ¹⁹F. Because a crack appears as a series of bright pixels in a dark background, it is not necessary to make a high-resolution image to see small cracks. It is only necessary for pixels that contain cracks to appear brighter than the surrounding image noise. The threshold for crack detection is the voxel dimension divided by the signal-to-noise ratio of the image. At the field strength of our imager, 1.89 T, and with a data collection time of 4 h for 1 mm isotropic resolution images, our crack detection threshold was 4.6 μm in a 44 mm diameter marble sample. Images showed that cracks which stop inside the sample are associated with expanded pore structure. We calculate the feasibility of imaging the cracks in David's left ankle. Authors' address: Dean O. Kuethe, New Mexico Resonance, Building C-1, 2301 Yale Boulevard SE, Albuquerque, NM 87106, USA     

Synthesis of 5-substituted-1H-indol-2-yl-1H-quinolin-2-ones: a novel class of KDR kinase inhibitors

[reaction: see text] A number of approaches for the synthesis of the 1H-indol-2-yl-1H-quinolin-2-one ring system found in the potent and selective KDR kinase inhibitor 1 are described. The preparation and reaction of trimethylsilylnitrobenzene 26 with 2-methoxy-3-quinolinecarboxaldehyde 28 afforded alcohol 30, which was the key intermediate for the preparation of the target compounds. Conversion of alcohol 30 to either nitroketone 36 or nitrostyrene 45 set the stage for reductive cyclization and the formation of indole 25. The quinolin-2-one functionality was unmasked in the last step to provide compound 1 in 56-60% overall yield from readily available starting materials.     

Reactive resin facilitated preparation of an enantiopure fluorobicycloketone

A facile preparation of enantiopure ethyl (1S,5S,6S)-6-fluoro-2-oxobicyclo[3.1.0]hexane-6-carboxylate is described. The key feature of the synthesis involves copper-catalyzed enantioselective intramolecular cyclopropanation of a diazoketone to form endo-fluorocyclopropane in a single operation. Removal of a problematic chloroketone impurity using a reactive resin treatment enabled a high throughput enantiopurity upgrade by chiral HPLC. The development of a scalable synthesis of is presented, including details of the selection of catalyst and ligand optimization, incorporation of a reactive resin treatment and selection of chiral HPLC media and conditions.