A Dutch book coherence condition for conditional completely alternating Choquet expectations

Stemming from de Finetti’s coherence for finitely additive (conditional) probabilities, the paradigm of coherence has been extended to other uncertainty calculi. We study the notion of coherence for conditional completely alternating Choquet expectations, providing an avoiding Dutch book like condition.

Tertiary Amines Paired with Trialkyl Boranes: A Simple Organocatalyst for Fully Alternating Copolymerization of Carbon Dioxide and Propylene Oxide

Metal-free synthesis of fully alternating polycarbonates from carbon dioxide (CO2) and epoxides is highly desired but a huge challenge. Here, we disclose the combination of tertiary amines with trialkyl boranes for completely alternating copolymerization of CO2 with epoxides. Triethylamine (TEA) pairing with triethyl borane (TEB), the simplest catalyst for the copolymerization of CO2 and propylene oxide (PO), afforded fully alternating poly(propylene carbonate) (PPC) with a turnover frequency (TOF) of 54 h-1 at 60 oC. Remarkably, diamine such as, N,N,N',N'-tetraethylethylenediamine (TEED) and triamine such as N,N,N',N'',N''-pentamethyldiethylene triamine (PMDETA) pairing with TEB exhibited improved the copolymer selectivity of up to 99%. Supplementally, the effect of trialkylborane structure on the copolymerization were also investigated. Moreover, PPCs prepared from these tertiary amines/ trialkyl boranes Lewis pairs showed the head-to-tail diad content of around 80%. The number-average molecular weight of PPC was up to 56.0 kg/mol with narrow distribution (Đ =1.16) and could be easily adjusted by simply varying the feeding ratios. The 1H NMR spectra and MALDI-TOF-MS spectra suggest that both tertiary amine-activating CO2 and TEB-masked end anions cooperatively promote the fully alternating CO2/epoxide copolymerization. This work provides an organocatalytic platform for well-defined CO2/epoxide copolymers using simple small molecules with high atomic utilization.<br>

Tertiary Amines Paired with Trialkyl Boranes: A Simple Organocatalyst for Fully Alternating Copolymerization of Carbon Dioxide and Propylene Oxide

Metal-free synthesis of fully alternating polycarbonates from carbon dioxide (CO2) and epoxides is highly desired but a huge challenge. Here, we disclose the combination of tertiary amines with trialkyl boranes for completely alternating copolymerization of CO2 with epoxides. Triethylamine (TEA) pairing with triethyl borane (TEB), the simplest catalyst for the copolymerization of CO2 and propylene oxide (PO), afforded fully alternating poly(propylene carbonate) (PPC) with a turnover frequency (TOF) of 54 h-1 at 60 oC. Remarkably, diamine such as, N,N,N',N'-tetraethylethylenediamine (TEED) and triamine such as N,N,N',N'',N''-pentamethyldiethylene triamine (PMDETA) pairing with TEB exhibited improved the copolymer selectivity of up to 99%. Supplementally, the effect of trialkylborane structure on the copolymerization were also investigated. Moreover, PPCs prepared from these tertiary amines/ trialkyl boranes Lewis pairs showed the head-to-tail diad content of around 80%. The number-average molecular weight of PPC was up to 56.0 kg/mol with narrow distribution (Đ =1.16) and could be easily adjusted by simply varying the feeding ratios. The 1H NMR spectra and MALDI-TOF-MS spectra suggest that both tertiary amine-activating CO2 and TEB-masked end anions cooperatively promote the fully alternating CO2/epoxide copolymerization. This work provides an organocatalytic platform for well-defined CO2/epoxide copolymers using simple small molecules with high atomic utilization.<br>

Tertiary Amines Paired with Trialkyl Boranes: A Simple Organocatalyst for Fully Alternating Copolymerization of Carbon Dioxide and Propylene Oxide

Metal-free synthesis of fully alternating polycarbonates from carbon dioxide (CO2) and epoxides is highly desired but a huge challenge. Here, we disclose the combination of tertiary amines with trialkyl boranes for completely alternating copolymerization of CO2 with epoxides. Triethylamine (TEA) pairing with triethyl borane (TEB), the simplest catalyst for the copolymerization of CO2 and propylene oxide (PO), afforded fully alternating poly(propylene carbonate) (PPC) with a turnover frequency (TOF) of 54 h-1 at 60 oC. Remarkably, diamine such as, N,N,N',N'-tetraethylethylenediamine (TEED) and triamine such as N,N,N',N'',N''-pentamethyldiethylene triamine (PMDETA) pairing with TEB exhibited improved the copolymer selectivity of up to 99%. Supplementally, the effect of trialkylborane structure on the copolymerization were also investigated. Moreover, PPCs prepared from these tertiary amines/ trialkyl boranes Lewis pairs showed the head-to-tail diad content of around 80%. The number-average molecular weight of PPC was up to 56.0 kg/mol with narrow distribution (Đ =1.16) and could be easily adjusted by simply varying the feeding ratios. The 1H NMR spectra and MALDI-TOF-MS spectra suggest that both tertiary amine-activating CO2 and TEB-masked end anions cooperatively promote the fully alternating CO2/epoxide copolymerization. This work provides an organocatalytic platform for well-defined CO2/epoxide copolymers using simple small molecules with high atomic utilization.<br>

Synthesis of perfectly alternating copolymers for polymers of intrinsic microporosity

A two-pot synthetic strategy was developed to accomplish sequence control in a completely alternating fashion for co-polymers of intrinsic microporosity.

Positive Definite and Related Functions on Hypergroups

In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive definite and negative definite functions on hypergroups.