Chemoselective Reductive Nucleophilic Addition to Tertiary Amides,Secondary Amides,and N‐Methoxyamides

As the complexity of targeted molecules increases in modern organic synthesis, chemoselectivity is recognized as an important factor in the development of new methodologies. Chemoselective nucleophilic addition to amide carbonyl centers is a challenge because classical methods require harsh reaction conditions to overcome the poor electrophilicity of the amide carbonyl group. We have successfully developed a reductive nucleophilic addition of mild nucleophiles to tertiary amides, secondary amides, and N‐methoxyamides that uses the Schwartz reagent [Cp₂ZrHCl]. The reaction took place in a highly chemoselective fashion in the presence of a variety of sensitive functional groups, such as methyl esters, which conventionally require protection prior to nucleophilic addition. The reaction will be applicable to the concise synthesis of complex natural alkaloids from readily available amide groups.     

Effects of Chitin/Chitosan and Their Oligomers/Monomers on Migrations of Macrophages

The effects of chitin/chitosan and their oligomers/monomers on the migrations of mouse peritoneal macrophage (PEM) and the rat macrophage cell line (rMp) were evaluated in vitro. In direct migratory assay using the blind well chamber method, the migratory activity of PEM was enhanced significantly by chitin and chitosan oligomers (NACOS and COS, respectively), but reduced by chitin, chitosan, and the chitosan monomer (GlcN). The migratory activity of rMp was increased significantly by chitin, chitosan, and the polymers, NACOS and GlcN.     

Synthesis of 4‐Arylisocoumarins (=4‐Aryl‐1H‐2‐benzopyran‐1‐ones) through Acidic Hydrolysis of (Z)‐2‐(1‐Aryl‐2‐methoxyethenyl)benzaldehydes,Followed by Oxidation

4‐Arylisocoumarins (=4‐aryl‐1H‐2‐benzopyran‐1‐ones) 6 were prepared from 2‐(1‐aryl‐2‐methoxyethenyl)‐1‐bromobenzenes 1 . Successive treatment of these bromo styrenes with BuLi and 1‐formylpiperidine gave a mixture of (E)‐ and (Z)‐2‐(1‐aryl‐2‐methoxyethenyl)benzaldehydes 2 . Hydrolysis of (Z)‐isomers with conc. HBr, followed by pyridinium chlorochromate (PCC) oxidation of the resulting 1H‐2‐benzopyran‐1‐ol derivatives 4 (and 5 ), afforded the desired products.     

Synthesis of Deuterium-Labeled Vitamin D Metabolites as Internal Standards for LC-MS Analysis

Blood levels of the vitamin D₃ (D₃) metabolites 25-hydroxyvitamin D₃ (25(OH)D₃), 24R,25-dihydroxyvitamin D₃, and 1α,25-dihydroxyvitamin D₃ (1,25(OH)₂D₃) are recognized indicators for the diagnosis of bone metabolism-related diseases, D₃ deficiency-related diseases, and hypercalcemia, and are generally measured by liquid-chromatography tandem mass spectrometry (LC-MS/MS) using an isotope dilution method. However, other D₃ metabolites, such as 20-hydroxyvitamin D₃ and lactone D₃, also show interesting biological activities and stable isotope-labeled derivatives are required for LC-MS/MS analysis of their concentrations in serum. Here, we describe a versatile synthesis of deuterium-labeled D₃ metabolites using A-ring synthons containing three deuterium atoms. Deuterium-labeled 25(OH)D₃ (2), 25(OH)D₃-23,26-lactone (6), and 1,25(OH)₂D₃-23,26-lactone (7) were synthesized, and successfully applied as internal standards for the measurement of these compounds in pooled human serum. This is the first quantification of 1,25(OH)₂D₃-23,26-lactone (7) in human serum.     

Around splitting and reaping for partitions of ω

We investigate splitting number and reaping number for the structure (ω) ^ω of infinite partitions of ω. We prove that \mathfrakr_d ￡ non(M),non(N),\mathfrakd{\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}} and \mathfraks_d 3 \mathfrakb{\mathfrak{s}_{d}\geq\mathfrak{b}} . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})} . To prove the consistency \mathfrakr_d < add(M){\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and \mathfraks_d < cof(M){\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})} we introduce new cardinal invariants \mathfrakr_pair{\mathfrak{r}_{pair}} and \mathfraks_pair{\mathfrak{s}_{pair}} . We also study the relation between \mathfrakr_pair, \mathfraks_pair{\mathfrak{r}_{pair}, \mathfrak{s}_{pair}} and other cardinal invariants. We show that cov(M),cov(N) ￡ \mathfrakr_pair ￡ \mathfraks_d,\mathfrakr{\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}} and \mathfraks ￡ \mathfraks_pair ￡ non(M),non(N){\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})} .     

Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space

The nondifferentiable optimization theory with equality and inequality constraints is extended to a multiobjective program on a Banach space. We derive generalized conditions of the Fritz-John type given by Clarke's generalized gradient formula, which are necessary for weak Pareto-optimal solutions.     

Hecke algebras and cohomotopical Mackey functors

In this paper, we define the concept of the cohomotopical Mackey functor, which is more general than the usual cohomological Mackey functor, and show that Hecke algebra techniques are applicable to cohomotopical Mackey functors. Our theory is valid for any (possibly infinite) discrete group. Some applications to topology are also given.

     

Construction of α-phosphonolactams via rhodium (II)-catalyzed intramolecular C?H insertion reactions

The Rh(II)-catalyzed intramolecular C H insertion reactions of N,N-dialkyl-α-diazo-α-(diethylphosphono)acetamides 2a , f–j in CHCl₃ or ClCH₂CH₂Cl were found to give monocyclic and bicyclic α-phosphono-β-lactams, 3a and 3f–j , in 43–67% yields via regiospecific α-C H insertion of the N-alkyl groups. Similar treatment of N-benzyl-N-isopropyl-α-diazo-α-(diethylphosphono)acetamide ( 2b ) and the corresponding N-isobutyl-N-methylacetamide 2d in ClCH₂CH₂Cl afforded mixtures of β-lactams 3b (35%) and and 3b ′ (16%), β-lactam 3d (47%), and γ-lactam 4d (10%), respectively, each of which is formed by the competitive C H insertion reaction between benzylic and isopropyl α-C H bonds and between methyl α-C H and methine β-C H bonds, respectively. For the formation of β-lactams, the selectivity in the rhodium-mediated C H insertion in ClCH₂CH₂Cl follows the order methyl > methine > benzylic α-C H bond on N-substituents. The N,N-dibutyl-α-diazo homologue 2c and Nα[α-diazo-α-(diethylphosphono)acetyl]-2-methylindoline ( 2k ) exclusively produced γ-lactams 4c (67%) and 4k (81%) via insertion into the methylene β-C H and methyl β-C H bonds. tert-Butyl N-[α-diazo-α-(dibenzylphosphono)acetyl]-piperidine-2-carboxylate ( 2m ) on similar treatment, followed by deprotection of the benzyl ester afforded the 7-phosphono carbacepham 6 in 32% overall yield. Similar Rh(II)-catalyzed cyclization of N-methyl-N[4-benzyloxy-α-(diethylphosphono)-phenyl(diethyl-phosphono)methyl]-α-diazo-acetamide ( 2n ) led to 1-[4′-benzylphenyl(diethylphosphono)methyl] -3-(diethyl-phosphono)azetidin-2-one ( 3n ) in 78% yicld. The phosphono group at C-7 of 3f was converted into the acetylamino group via a four-step reaction. Application of chiral rhodium(II) carboxylates 12a–c to the insertion reactions of 2b , c produced α-phosphono-β-and γ-lactams, 3b and 4c , in 6–24% ee and 25–29% ee, respectively.