On the shape of solution sets of systems of (functional) equations

Solution sets of systems of linear equations over fields are characterized as being affine subspaces. But what can we say about the “shape” of the set of all solutions of other systems of equations? We study solution sets over arbitrary algebraic structures, and we give a necessary condition for a set of n-tuples to be the set of solutions of a system of equations in n unknowns over a given algebra. In the case of Boolean equations we obtain a complete characterization, and we also characterize solution sets of systems of Boolean functional equations.     

Coordination Complexes to Combat Bacterial Infections: Recent Developments,Current Directions and Future Opportunities

Drug discovery aimed at the efficient eradication of life-threatening bacterial infections, especially in light of the emergence of multi-drug resistance of pathogenic bacteria, has remained a challenge for medicinal chemists over the past several decades. As nutrient acquisition and metabolism at the host-pathogen interface become better elucidated, new drug targets continue to emerge. Metal homeostasis is among these processes, and thus provides opportunities for medicinal inorganic chemists to alter or disrupt these processes selectively to impart bacteriostatic or bacteriotoxic effects. In this minireview, we showcase some of the recent work from the field of metal-based antibacterial agents and highlight divergent strategies and mechanisms of action.     

Discrete pseudo-integrals

Integration of simple functions is a corner stone of general integration theory and it covers integration over finite spaces discussed in this paper. Different kinds of decomposition and subdecomposition of simple functions into basic functions sums, as well as different kinds of pseudo-operations exploited for integration and sumation result into several types of integrals, including among others, Lebesgue, Choquet, Sugeno, pseudo-additive, Shilkret, PAN, Benvenuti and concave integrals. Some basic properties of introduced discrete pseudo-concave integrals are discussed, and several examples of new integrals are given.     

A scalable Nenitzescu synthesis of 2‐methyl‐4‐(trifluoromethyl)‐1H‐indole‐5‐carbonitrile

2‐Methyl‐4‐(trifluoromethyl)‐1H‐indole‐5‐carbonitrile is a key intermediate in the synthesis of selective androgen receptor modulators discovered in these laboratories. A practical and convergent synthesis of the title compound starting from 4‐nitro‐3‐(trifluoromethyl)phenol and tert‐butyl acetoacetate was developed, including a telescoped procedure for synthesis (without isolation) and Nenitzescu reaction of 2‐trifluoromethyl‐1,4‐benzoquinone. Conversion of the known Nenitzescu indole product to a novel triflate intermediate followed by palladium‐catalyzed cyanation afforded a penultimate carbonitrile. Removal of the C‐3 tert‐butyl ester group on the indole through a decarboxylative pathway completed the synthesis of the title compound in six steps (27% overall yield) from 4‐nitro‐3‐(trifluoromethyl)phenol (five steps, 37% overall yield from tert‐butyl acetoacetate). J. Heterocyclic Chem., (2011).     

Pion exchange and the H1 forward spectrometer data

We point out that the component of the nucleon wave function is vital to the interpretation of the recent H1 data for leading baryon production. While the n/p ratio is equal to two with the component alone, the inclusion of the component brings this ratio very near to unity, as observed in the experiment. This result demonstrates that pion exchange can not only account for leading neutron but also for a large fraction of the leading proton production. Received: 4 December 1998 / Revised version: 1 February 1999 / Published online: 27 April 1999     

An approximate Dirac-type theorem for k-uniform hypergraphs

A k-uniform hypergraph is hamiltonian if for some cyclic ordering of its vertex set, every k consecutive vertices form an edge. In 1952 Dirac proved that if the minimum degree in an n-vertex graph is at least n/2 then the graph is hamiltonian. We prove an approximate version of an analogous result for uniform hypergraphs: For every K ≥ 3 and γ > 0, and for all n large enough, a sufficient condition for an n-vertex k-uniform hypergraph to be hamiltonian is that each (k − 1)-element set of vertices is contained in at least (1/2 + γ)n edges. Research supported by NSF grant DMS-0300529. Research supported by KBN grant 2P03A 015 23 and N201036 32/2546. Part of research performed at Emory University, Atlanta. Research supported by NSF grant DMS-0100784.