On the continuity of the feasible set in extremally linear problems

The purpose of this paper is to investigate continuity properties of the feasible set in extremally linear problems. Feasible sets of such problems are subsets of Fⁿ (the n-fold cartesian product of a fully ordered group (F,º)) and are described by a finite or an infinite number of inequalities or equalities, which are linear with respect to the operations ? and º. Thereby, the operation ? is induced by the fully-order in F by setting x?y = y iff x ≤ y for x, y in F. In particular, we derive conditions for the upper- and lower-semi-continuity of the feasible-set-mapping Z and investigate the structure of certain parameter sets. Especially, we show that the compactness of the feasible set, resp. the condition that the closure of the set of the strict feasible points is the feasible set, is sufficient for the upper-semi-continuity (u.s.c), resp. the lower-semi-continuity (l.s.c.) of Z, but - unlike to semi-infinite linear optimization - is not necessary for the u.s.c, resp. l.s.c. If we restrict Z on a certain subset of the parameter set, these conditions are also necessary. This paper is a continuation of the author's work in [6] and [7].     

Palladium‐Catalyzed Domino CH/NH Functionalization: An Efficient Approach to Nitrogen‐Bridged Heteroacenes

Palladium‐catalyzed domino C?H/N?H functionalization for the synthesis of novel nitrogen‐bridged thienoacenes and 10H‐benzo[4,5]thieno[3,2‐b]indole derivatives from dihaloarene is reported. This domino sequence consists of initial C?H functionalization of the benzo[b]thiophene moiety, followed by Buchwald–Hartwig coupling. This transformation is also useful for the synthesis of highly π‐extended compounds.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Metal-Free Twofold Electrochemical C−H Amination of Activated Arenes: Application to Medicinally Relevant Precursor Synthesis

The efficient production of many medicinally or synthetically important starting materials suffers from wasteful or toxic precursors for the synthesis. In particular, the aromatic non-protected primary amine function represents a versatile synthetic precursor, but its synthesis typically requires toxic oxidizing agents and transition metal catalysts. The twofold electrochemical amination of activated benzene derivatives via Zincke intermediates provides an alternative sustainable strategy for the formation of new C−N bonds of high synthetic value. As a proof of concept, we use our approach to generate a benzoxazinone scaffold that gained attention as a starting structure against castrate-resistant prostate cancer. Further improvement of the structure led to significantly increased cancer cell line toxicity. Thus, exploiting environmentally benign electrooxidation, we present a new versatile and powerful method based on direct C−H activation that is applicable for example the production of medicinally relevant compounds.     

Active Molybdenum‐Based Anode for Dehydrogenative Coupling Reactions

A new and powerful active anode system that can be operated in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) has been discovered. In HFIP the molybdenum anode forms a compact, conductive, and electroactive layer of higher‐valent molybdenum species. This system can replace powerful but stoichiometrically required Mo^V reagents for the dehydrogenative coupling of aryls. This electrolytic reaction is more sustainable and allows the conversion of a broad scope of activated arenes.     

Electrifying Organic Synthesis

The direct synthetic organic use of electricity is currently experiencing a renaissance. More synthetically oriented laboratories working in this area are exploiting both novel and more traditional concepts, paving the way to broader applications of this niche technology. As only electrons serve as reagents, the generation of reagent waste is efficiently avoided. Moreover, stoichiometric reagents can be regenerated and allow a transformation to be conducted in an electrocatalytic fashion. However, the application of electroorganic transformations is more than minimizing the waste footprint, it rather gives rise to inherently safe processes, reduces the number of steps of many syntheses, allows for milder reaction conditions, provides alternative means to access desired structural entities, and creates intellectual property (IP) space. When the electricity originates from renewable resources, this surplus might be directly employed as a terminal oxidizing or reducing agent, providing an ultra‐sustainable and therefore highly attractive technique. This Review surveys recent developments in electrochemical synthesis that will influence the future of this area.