Low temperature organocopper-mediated two-component cross coupling/cycloisomerization approach toward N-fused heterocycles

Organocopper reagents smoothly react with heterocyclic propargyl mesylates at low temperature to produce N-fused heterocycles. The copper reagent plays a "double duty" in this novel cascade transformation, which proceeds via an SN2' substitution followed by a subsequent cycloisomerization step.     

Numerical radius and zero pattern of matrices

Let A be an n×n complex matrix and r be the maximum size of its principal submatrices with no off-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting ‖A‖ be the Frobenius norm of A, we show that

|〈Ax,x〉^|2?(1−1/2r−1/2n)‖A^‖2.     

Graphs with many r-cliques have large complete r-partite subgraphs

Let r2 and c>0. Every graph on n vertices with at least cn^rcliques on r vertices contains a complete r-partite subgraphwith r–1 parts of size c^rlog n and one part of size greaterthan n^1–cr–1. This result implies a quantitativeform of the Erdös–Stone theorem.     

A spectral condition for odd cycles in graphs

Let G be a graph of sufficiently large order n, and let the largest eigenvalue μ(G) of its adjacency matrix satisfies . Then G contains a cycle of length t for every t?n/320This condition is sharp: the complete bipartite graph T₂(n) with parts of size ⌊n/2⌋ and ⌈n/2⌉ contains no odd cycles and its largest eigenvalue is equal to .This condition is stable: if μ(G) is close to and G fails to contain a cycle of length t for some t?n/321, then G resembles T₂(n).     

Spectralizable Operators

We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral operators and give some examples where spectralizable operators occur naturally. Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1.     

Cyclic oxonium derivatives of polyhedral boron hydrides and their synthetic applications

Cyclic oxonium derivatives of polyhedral boron hydrides are a relatively new class of boron compounds. They have great potential for the modification of various types of organic and bioorganic molecules and the synthesis of compounds that could be used in different fields from the treatment of nuclear wastes to the treatment of cancer. In the present Perspective we would like to present an overview of the results of the preparation and synthetic application of these compounds.     

Optimization of enzymatic biochemical logic for noise reduction and scalability: how many biocomputing gates can be interconnected in a circuit?

We report an experimental evaluation of the "input-output surface" for a biochemical AND gate. The obtained data are modeled within the rate-equation approach, with the aim to map out the gate function and cast it in the language of logic variables appropriate for analysis of Boolean logic for scalability. In order to minimize "analog" noise, we consider a theoretical approach for determining an optimal set for the process parameters to minimize "analog" noise amplification for gate concatenation. We establish that under optimized conditions, presently studied biochemical gates can be concatenated for up to order 10 processing steps. Beyond that, new paradigms for avoiding noise buildup will have to be developed. We offer a general discussion of the ideas and possible future challenges for both experimental and theoretical research for advancing scalable biochemical computing.     

Reactive organoallyl species generated from aryl halides and allene: allylation of α,β-unsaturated aldehydes and cyclic ketones employing Pd/In transmetallation processes

Allylation of α,β-unsaturated aldehydes and cyclic ketones promoted by Pd/In transmetallation processes has been studied. The unsaturated aldehydes underwent regioselective 1,2-addition to afford secondary homoally alcohols. The reactions have been performed using Pd(OAc)₂/PPh₃ as catalytic system and metallic indium affording the products in good yields. The same transformation with unsaturated ketones proved to be less efficient, while saturated cyclic ketones delivered generally excellent yields in the presence of CuI. In these latter processes the presence of a distal heteroatom influences the reaction rate.     

Stereochemistry of the products of reductive amination of 2,6-bis[(2-oxocyclohexyl)methyl]cyclohexanone, an alicyclic 1,5,9-triketone

The reductive amination of alicyclic 1,5,9-triketone—2,6-bis[(2-oxocyclohexyl)methyl]cyclohexanone—has been studied under Leuckart reaction conditions and in the presence of NaBH₃CN. A mixture of diastereomers of quinolizidine structure (2,3,5,6-bistetramethylenehexahydrojulolidine) is obtained. The stereochemistry of seven isomers is determined by the study of their NMR spectra using 2D NMR experiments (¹H-¹H COSY, HSQC, and HMBC).